Final Program

The Symposium on Simplicity in Algorithms (SOSA19) will take place on January 8 and 9.

SODA is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory, and the SIAM Activity Group on Discrete Mathematics

The SIAM Activity Group on Discrete Mathematics focuses on combinatorics, graph theory, cryptography, discrete optimization, mathematical programming, coding theory, information theory, game theory, and theoretical computer science, including algorithms, complexity, circuit design, robotics, and parallel processing. We provide an opportunity to unify pure discrete mathematics and areas of applied research such as computer science, operations research, combinatorics, and the social sciences.

3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference Web: siam.org/meetings Membership and Customer Service: (800) 447-7426 (USA & Canada) or +1-215-382-9800 (worldwide) https://www.siam.org/conferences/CM/Main/soda19 https://www.siam.org/conferences/CM/Main/alenex19 https://www.siam.org/conferences/CM/Main/analco19 https://simplicityinalgorithms.com/ 2 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Table of Contents Thore Husfeldt Shang-Hua Teng Lund University, Sweden and IT University University of Southern California, U.S. Program-at-a-Glance… of Copenhagen, Denmark ...... See separate handout Klaus Jansen ALENEX COMMITTEES General Information...... 2 Christian-Albrechts-Universität zu Kiel, Get-togethers...... 5 Germany Program Committee Best Paper and Best Student Paper ...... T.S. Jayram Co-Chairs Awards...... 10 IBM Almaden Research, U.S. Stephen Kobourov Invited Plenary Presentations...... 11 Daniel Kane University of Arizona, U.S. Program Schedule...... 12 University of California, San Diego, U.S. Henning Meyerhenke Speaker Index...... 32 Jonathan Kelner Humboldt-Universität zu Berlin, Germany Hotel Meeting Room Map...Back Cover Massachusetts Institute of Technology, U.S. Tsvi Kopelowitz Bar Ilan University, Israel Program Committee SODA COMMITTEES Pravesh K. Kothari Aaron Archer Program Committee Chair and the Institute for Google, U.S. Advanced Study, U.S. Timothy M. Chan Maike Buchin Fabian Kuhn University of Illinois at Urbana-Champaign, Ruhr Universität Bochum, Germany University of Freiburg, Germany U.S. Aydin Buluc Daniel Lokshtanov Lawrence Berkeley National Laboratory, University of Bergen, Norway U.S. Program Committee Brendan Lucier Markus Chimani Peyman Afshani Microsoft Research, U.S. Osnabrück University, Germany Aarhus University, Denmark Bojan Mohar Pierluigi Crescenzi Shipra Agrawal Simon Fraser University, Canada Università degli Studi di Firenze, Italy Columbia University, U.S. Viswanath Nagarajan Yifan Hu Aditya Bhaskara University of Michigan, U.S. Yahoo!, U.S. University of Utah, U.S. Alantha Newman Yoichi Iwata Yang Cai CNRS, Grenoble, France National Institute of Informatics, Japan McGill University, Canada Ilan Newman Juha Kärkkäinen Amit Chakrabarti University of Haifa, Israel University of Helsinki, Finland Dartmouth College, U.S. Vijaya Ramachandran Ken-Ichi Kawarabayashi Deeparnab Chakrabarty University of Texas at Austin, U.S. National Institute of Informatics, Japan Dartmouth College, U.S. Ilya Razenshteyn Stefan Kratsch Erin Wolf Chambers Microsoft Research, U.S. Humboldt-Universität zu Berlin, Germany Saint Louis University, U.S. Liam Roditty Fredrik Manne Siu On Chan Bar Ilan University, Israel University of Bergen, Norway Chinese University of Hong Kong, Hong Kong Atri Rudra Nicole Megow Daniel Dadush University at Buffalo, SUNY, U.S. Universität Bremen, Germany CWI, Netherlands Laura Sanità Ulrich Meyer Holger Dell University of Waterloo, Canada Goethe University Frankfurt, Germany Saarland University, Germany László A. Végh Matthias Müller-Hannemann Zdenek Dvorak London School of Economics, United Martin-Luther-University Halle-Wittenberg, Charles University, Czech Republic Kingdom Germany Friedrich Eisenbrand Oren Weimann Matthias Petri EPFL, Switzerland University of Haifa, Israel The University of Melbourne, Australia Michael Elkin Udi Wieder Sergey Pupyrev Ben-Gurion University of the Negev, Israel VMware Research, U.S. Facebook, U.S. Jane Gao Barna Saha Monash University, Australia Steering Committee University of Massachusetts, Amherst, U.S. Sariel Har-Peled Renato Werneck University of Illinois at Urbana-Champaign, Pavol Hell Amazon, U.S. U.S. Simon Fraser University, Canada Hamed Hatami Daniel Král McGill University, Canada University of Warwick, United Kingdom Steering Committee Thomas Hayes Dana Randall Andrew V. Goldberg University of New Mexico, U.S. Georgia Institute of Technology, U.S. Amazon.com, U.S. (Chair) Martin Hoefer Cliff Stein Michael Goodrich Goethe University Frankfurt, Germany Columbia University, U.S. (chair) University of California, Irvine, U.S. Conference Program SODA, ALENEX, ANALCO and SOSA 2019 3

Giuseppe F. Italiano SODA Themes Hotel Address University of Rome “Tor Vergata”, Italy The Westin San Diego Rasmus Pagh Aspects of combinatorics and discrete IT University of Copenhagen, Denmark mathematics, such as: 400 West Broadway Vijaya Ramachandran Combinatorial structures San Diego, CA, 92101, U.S. University of Texas, Austin, U.S. Discrete optimization Cliff Stein Discrete probability Hotel Telephone Number Columbia University, U.S. Finite metric spaces Dorothea Wagner Graph theory To reach an attendee or leave a message, Karlsruhe Institute of Technology, Germany Mathematical programming call +1-619-239-4500. If the attendee Random structures is a hotel guest, the hotel operator can ANALCO COMMITTEES Topological problems connect you with the attendee’s room. Program Committee Core topics in discrete algorithms, Co-Chairs such as: Hotel Check-in and Marni Mishna Algorithm analysis Check-out Times Simon Fraser University, Canada Data structures Check-in time is 3:00 p.m. J. Ian Munro Experimental algorithmics Check-out time is 12:00 p.m. University of Waterloo, Canada Algorithmic aspects of other areas of computer science, such as: Child Care Program Committee Combinatorial scientific computing California DMC recommends Martin Dietzfelbinger Communication networks and the Destinations Sitters (https://www. Technische Universität Ilmenau, Germany Internet destinationsitters.com/) for attendees Cecilia Holmgren Computational geometry and topology interested in child care services. Uppsala University, Sweden Computer graphics and computer vision Attendees are responsible for making Mihyun Kang Computer systems their own child care arrangements. Technische Universität Graz, Austria Cryptography and security Yusuke Kobayashi Databases and information retrieval Kyoto University, Japan Data compression Corporate/Institutional Jérémie Lumbroso Data privacy Members Princeton University, U.S. Distributed and parallel computing Hosam Mahmoud SIAM corporate members provide George Washington University, U.S. Game theory and mechanism design their employees with knowledge about, Daniel Panario Machine learning access to, and contacts in the applied Carleton University, Canada Quantum computing mathematics and computational sciences Dominique Poulalhon community through their membership Université Paris Diderot, France SIAM Registration Desk benefits. Corporate membership is more Sebastian Wild than just a bundle of tangible products University of Waterloo, Canada The registration desk is on the 2nd Floor. It is open during the following hours: and services; it is an expression of support for SIAM and its programs. Steering Committee Saturday, January 5 SIAM is pleased to acknowledge its 5:00 p.m. – 8:00 p.m. corporate members and sponsors. In Michael Drmota Technische Universität Wien, Austria recognition of their support, non-member Sunday, January 6 James Allen Fill (Jim Fill) attendees who are employed by the Johns Hopkins University, U.S. 8:00 a.m. – 5:00 p.m. following organizations are entitled to the H.K. Hwang SIAM member registration rate. Institute of Statistical Science, Academia Monday, January 7 Sinica, Taiwan 8:00 a.m. – 5:00 p.m. Conrado Martínez Corporate/Institutional Universitat Politècnica de Catalunya, Spain Tuesday, January 8 Members Markus Nebel 8:00 a.m. – 5:00 p.m. Universität Bielefeld, Germany The Aerospace Corporation Robert Sedgewick Wednesday, January 9 Air Force Office of Scientific Research Princeton University, U.S. 8:00 a.m. – 5:00 p.m. Wojciech Szpankowski Amazon Purdue University, U.S. Argonne National Laboratory Mark Daniel Ward Purdue University, U.S. Bechtel Marine Propulsion Laboratory 4 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

The Boeing Company subscriptions to SIAM Review, SIAM connections. Presenters requiring an CEA/DAM News and SIAM Unwrapped, and enjoy alternate connection must provide their substantial discounts on SIAM books, own adaptor. Cirrus Logic journal subscriptions, and conference Department of National Defence (DND/ registrations. CSEC) Internet Access If you are not a SIAM member and did Attendees booked within the SIAM room DSTO- Defence Science and not join SIAM before you registered, you block will receive complimentary wireless Technology Organisation, Edinburgh can apply the difference of $140 between internet access in their guest rooms and the Exxon Mobil what you paid as a non-member, and public areas of the hotel. All conference what a member paid towards a SIAM IDA Center for Communications attendees will have complimentary wireless membership. Contact SIAM Customer Research, La Jolla internet access in the meeting space of the Service for details or join at the hotel. IDA Institute for Defense Analyses, conference registration desk. Princeton SIAM will provide a limited number If you are a SIAM member, it only costs of email stations for attendees during IDA Institute for Defense Analyses, $15 to join the SIAM Activity Group on registration hours. Bowie, Maryland Discrete Mathematics. Lawrence Berkeley National Laboratory Students who paid the Student Non Registration Fee Includes Lawrence Livermore National Labs Member Rate will be automatically enrolled as SIAM Student Members. • Admission to all technical sessions Lockheed Martin Maritime Systems & Please go to my.siam.org to update (SODA19, ALENEX19, ANALCO19, Sensors your education and contact information SOSA19) Los Alamos National Laboratory in your profile. If you attend a SIAM • ANALCO/ALENEX and SOSA Business meetings Max-Planck-Institute Academic Member Institution or are part of a SIAM Student Chapter you will be • Coffee breaks daily Mentor Graphics able to renew next year for free. • Continental Breakfast daily National Institute of Standards and Join onsite at the registration desk, go • Luncheon on Sunday, January 6 Technology (NIST) to https://www.siam.org/Membership/ • Proceedings (SODA, ALENEX, and National Security Agency Join-SIAM to join online or download ANALCO posted online) an application form, or contact SIAM Oak Ridge National Laboratory • Room set-ups and audio/visual Customer Service: equipment Sandia National Laboratories Telephone: +1-215-382-9800 (worldwide); • SODA Business Meeting Schlumberger or 800-447-7426 (U.S. and Canada only) Fax: +1-215-386-7999 • Welcome Reception Email: [email protected] United States Department of Energy Postal mail: Society for Industrial and Job Postings Applied Mathematics, 3600 Market U.S. Army Corps of Engineers, Please check with the SIAM registration Engineer Research and Development Street, 6th floor, Philadelphia, PA 19104-2688 U.S. desk regarding the availability of job Center postings or visit https://jobs.siam.org/. List current November 2018. Standard Audio-Visual Set-Up in Meeting Rooms Table Top Display Join SIAM and save! SIAM does not provide computers for Cambridge University Press Leading the applied any speaker. When giving an electronic mathematics community . . . presentation, speakers must provide their own computers. SIAM is not responsible SIAM members save up to $140 for the safety and security of speakers’ on full registration for SODA and computers. its associated meetings. Join your peers in supporting the premier A data (LCD) projector and screen will professional society for applied be provided in all technical session mathematicians and computational meeting rooms. The data projectors scientists. SIAM members receive support both VGA and HDMI Conference Program SODA, ALENEX, ANALCO and SOSA 2019 5

Conference Sponsors Statement on Inclusiveness Recording of Presentations As a professional society, SIAM is Audio and video recording of presenta- committed to providing an inclusive tions at SIAM meetings is prohibited climate that encourages the open without the written permission of the expression and exchange of ideas, that presenter and SIAM. is free from all forms of discrimination, 2019 Conference Bag Sponsor harassment, and retaliation, and that Social Media is welcoming and comfortable to all SIAM is promoting the use of members and to those who participate social media, such as Facebook and in its activities. In pursuit of that Twitter, in order to enhance scientific commitment, SIAM is dedicated to the discussion at its meetings and enable philosophy of equality of opportunity and attendees to connect with each other Name Badges treatment for all participants regardless prior to, during and after conferences. A space for emergency contact of gender, gender identity or expression, If you are tweeting about a conference, information is provided on the back of sexual orientation, race, color, national please use the designated hashtag your name badge. Help us help you in the or ethnic origin, religion or religious to enable other attendees to keep event of an emergency! belief, age, marital status, disabilities, up with the Twitter conversation veteran status, field of expertise, or any and to allow better archiving of our other reason not related to scientific merit. Comments? conference discussions. The hashtags This philosophy extends from SIAM for these meetings are #SIAMDA19, Comments about SIAM meetings are conferences, to its publications, and #ANALCO19 and #ALENEX19. encouraged! Please send to: to its governing structures and bodies. Cynthia Phillips, SIAM Vice President for We expect all members of SIAM and SIAM’s Twitter handle is Programs ([email protected]). participants in SIAM activities to work @TheSIAMNews. towards this commitment.is welcoming Get-togethers and comfortable to all members and to those who participate in its activities. Changes to the Printed Welcome Reception In pursuit of that commitment, SIAM is Program Saturday, January 5 dedicated to the philosophy of equality The printed program was current at 6:00 p.m. – 8:00 p.m. of opportunity and treatment for all the time of printing, however, please Poolside and Ivory - 3rd Floor participants regardless of gender, gender review the online program schedule ALENEX and ANALCO Business identity or expression, sexual orientation, (http://meetings.siam.org/program. Meeting race, color, national or ethnic origin, cfm?CONFCODE=da19) for up-to- Sunday, January 6 religion or religious belief, age, marital date information. 6:45 p.m. – 7:45 p.m. status, disabilities, veteran status, field Diamond 2 - 2nd Floor of expertise, or any other reason not related to scientific merit. This philosophy SODA Business Meeting and Awards extends from SIAM conferences, to Presentation its publications, and to its governing Monday, January 7 structures and bodies. We expect all 6:45 p.m. – 7:45 p.m. members of SIAM and participants in Emerald Ballroom - 2nd Floor SIAM activities to work towards this Complimentary beer and wine will be commitment. served. SOSA Business Meeting Tuesday, January 8 Please Note 6:45 p.m. – 7:45 p.m. SIAM is not responsible for the safety and Diamond 2 - 2nd Floor security of attendees’ computers. Do not leave your laptop computers unattended. Please remember to turn off your cell phones, pagers, etc. during sessions. 6 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program Conference Program SODA, ALENEX, ANALCO and SOSA 2019 7 8 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program Conference Program SODA, ALENEX, ANALCO and SOSA 2019 9 10 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Best Paper and Best Student Paper Awards

Best Paper Award Sublinear Algorithms for (∆ + 1) Vertex Coloring Sepehr Assadi, Yu Chen, and Sanjeev Khanna, University of Pennsylvania, U.S. This paper will be presented on Monday, January 7, in session CP14 SODA Session 4A. See page 18 for session details.

Best Student Paper Award

Optimal Las Vegas Approximate Near Neighbors in ℓp Alexander Wei, Harvard University, U.S. This paper will be presented on Tuesday, January 8, in session CP30 SODA Session 8A. See page 25 for session details. Conference Program SODA, ALENEX, ANALCO and SOSA 2019 11

Invited Plenary Speakers All Invited Plenary Presentations will take place in Emerald Ballroom - 2nd Floor

Sunday, January 6 11:30 a.m. - 12:30 p.m IP1 Towards Analysis of Information Content in Dynamic Networks Wojciech Szpankowski, Purdue University, U.S.

Monday, January 7 11:30 a.m. - 12:30 p.m. IP2 Recent Advances on the Complexity of Parameterized Counting Problems Dániel Marx, Hungarian Academy of Sciences, Hungary

Tuesday, January 8 11:30 a.m. - 12:30 p.m. IP3 Inherent Trade-Offs in Algorithmic Fairness Jon M. Kleinberg, Cornell University, U.S.

Wednesday, January 9 11:30 a.m. - 12:30 p.m. IP4 (Hardness of) Approximation and Expansion Irit Dinur, Weizmann Institute of Science, Israel 12 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Program Schedule

Symposium on Simplicity in Algorithms (SOSA19) Conference Program SODA, ALENEX, ANALCO and SOSA 2019 13

Sunday, January 6 Saturday, January 5 Sunday, January 6 CP1 ANALCO Session 1 Registration Registration 9:00 AM-11:05 AM 5:00 PM-8:00 PM 8:00 AM-5:00 PM Room: Diamond 2 - 2nd Floor Room: Registration Desk - 2rd Floor Room: Registration Desk - 2rd Floor Chair: Sebastian Wild, University of Waterloo, Canada 9:00-9:20 Combinatorics of Welcome Reception Continental Breakfast Nondeterministic Walks of the Dyck and Motzkin Type 6:00 PM-8:00 PM 8:30 AM-9:00 AM Elie de Panafieu, Nokia Bell Labs France, Room: Poolside and Ivory - 3rd Floor Room: Ballroom Foyer - 2nd Floor France; Mohamed Lamine Lamali and Michael Wallner, LaBRI - Université de Bordeaux, France 9:25-9:45 Ranked Schröder Trees Antoine Genitrini, Sorbonne Universités, France; Olivier Bodini, Université Paris 13, France; Mehdi Naima, Universite Paris- Nord, France 9:50-10:10 Esthetic Numbers and Lifting Restrictions on the Analysis of Summatory Functions of Regular Sequences Clemens Heuberger and Daniel Krenn, Alpen-Adria-Universität Klagenfurt, Austria 10:15-10:35 Reducing Simply Generated Trees by Iterative Leaf Cutting Benjamin Hackl and Clemens Heuberger, Alpen-Adria-Universität Klagenfurt, Austria; Stephan Wagner, Stellenbosch University, South Africa 10:40-11:00 Protection Number of Recursive Trees Zbigniew Golebiewski and Mateusz Klimczak, Wroclaw University of Science and Technology, Poland 14 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Sunday, January 6 Sunday, January 6 Sunday, January 6 CP2 CP3 CP4 SODA Session 1A SODA Session 1B SODA Session 1C 9:00 AM-11:05 AM 9:00 AM-11:05 AM 9:00 AM-11:05 AM Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 9:00-9:20 Fine-grained Complexity 9:00-9:20 Metrical Task Systems on 9:00-9:20 Dynamic Double Auctions: Meets IP = PSPACE Trees Via Mirror Descent and Unfair Towards First Best Lijie Chen and Shafi Goldwasser, Gluing Santiago Balseiro, Columbia University, Massachusetts Institute of Technology, Sebastien Bubeck, Microsoft Research, U.S.; Vahab Mirrokni, Google, Inc., U.S.; U.S.; Kaifeng Lyu, Tsinghua University, U.S.; Michael B. Cohen, Massachusetts Renato Paes Leme and Song Zuo, Google China; Guy Rothblum, Microsoft Research, Institute of Technology, U.S.; James Research, U.S. U.S.; Aviad Rubinstein, Harvard University, R. Lee and Yin Tat Lee, University of 9:25-9:45 Multi-unit Supply-monotone Washington, U.S. U.S. Auctions with Bayesian Valuations 9:25-9:45 An Equivalence Class for 9:25-9:45 K-Servers with a Smile: Yuan Deng and Debmalya Panigrahi, Duke Orthogonal Vectors Online Algorithms via Projections University, U.S. Lijie Chen and Ryan Williams, Massachusetts Marco Molinaro, Pontifical Catholic 9:50-10:10 Correlation-robust Analysis University of Rio de Janeiro, Brazil; Institute of Technology, U.S. of Single Item Auction Niv Buchbinder, Tel Aviv University, 9:50-10:10 Seth-Based Lower Bounds Xiaohui Bei, Nanyang Technological Israel; Anupam Gupta, Carnegie Mellon for Subset Sum and Bicriteria Path University, Singapore; Nick Gravin and University, U.S.; Joseph Naor, Technion Amir Abboud, IBM Almaden Research Pinyan Lu, Shanghai University of Finance Israel Institute of Technology, Israel Center, U.S.; Karl Bringmann, Max Planck and Economics, China; Zhihao Gavin Tang, Institute for Informatics, Germany; Danny 9:50-10:10 A Nearly-Linear Bound for University of Hong Kong, Hong Kong Chasing Nested Convex Bodies Hermelin and Dvir Shabtay, Ben-Gurion 10:15-10:35 Tight Revenue Gaps C.J. Argue, Carnegie Mellon University, University, Israel among Simple Mechanisms U.S.; Sebastien Bubeck, Microsoft Yaonan Jin, Hong Kong University of Science 10:15-10:35 Fast Modular Subset Sum Research, U.S.; Michael B. Cohen, and Technology, Hong Kong; Pinyan Using Linear Sketching Massachusetts Institute of Technology, Lu, Shanghai University of Finance and Kyriakos Axiotis, Massachusetts Institute U.S.; Anupam Gupta, Carnegie Mellon Economics, China; Zhihao Gavin Tang, of Technology, U.S.; Arturs Backurs, University, U.S.; Yin Tat Lee, University University of Hong Kong, Hong Kong; Tao Toyota Technological Institute at Chicago, of Washington, U.S. Xiao, Shanghai Jiao Tong University, China U.S.; Ce Jin, Tsinghua University, China; 10:15-10:35 A Ø-Competitive Christos Tzamos, University of Wisconsin, Algorithm for Scheduling Packets 10:40-11:00 Assignment Mechanisms Madison, U.S.; Hongxun Wu, Tsinghua with Deadlines under Distributional Constraints University, China Pavel Vesely, University of Warwick, United Itai Ashlagi, Amin Saberi, and Ali Shameli, 10:40-11:00 A Subquadratic Kingdom; Marek Chrobak, University of Stanford University, U.S. Approximation Scheme for Partition California, Riverside, U.S.; Lukasz Jez, Marcin Mucha, Karol Wegrzycki, and Michal Tel Aviv University, Israel and University Wlodarczyk, University of Warsaw, Poland of Wroclaw, Poland; Jiri Sgall, Charles Coffee Break University, Czech Republic 11:05 AM-11:30 AM 10:40-11:00 Elastic Caching Debmalya Panigrahi, Duke University, Room: Ballroom Foyer - 2nd Floor U.S.; Anupam Gupta, Carnegie Mellon University, U.S.; Ravishankar Krishnaswamy, Microsoft Research, India; Amit Kumar, Indian Institute of Technology, Delhi, India Conference Program SODA, ALENEX, ANALCO and SOSA 2019 15

Sunday, January 6 Sunday, January 6 Sunday, January 6 IP1 CP5 CP6 Towards Analysis of ANALCO Session 2 SODA Session 2A Information Content in 2:00 PM-3:40 PM 2:00 PM-4:05 PM Dynamic Networks Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor 11:30 AM-12:30 PM Chair: Hosam Mahmoud, George Washington Chair: To Be Determined Room: Emerald Ballroom - 2nd Floor University, U.S. 2:00-2:20 Deterministic (1/2 + Chair: To Be Determined 2:00-2:20 Sesquickselect: One and ε)-Approximation for Submodular a Half Pivots for Cache-Efficient Maximization over a Matroid Shannon information theory has Selection Niv Buchbinder, Tel Aviv University, Israel; served as a bedrock for advances in Sebastian Wild, University of Waterloo, Moran Feldman and Mohit Garg, Open communication and storage systems Canada; Conrado Martínez, Universidad University of Israel, Israel over the past six decades. However, Politecnica de Catalunya, Spain; Markus 2:25-2:45 Submodular Maximization this theory does not handle well Nebel, Universität Bielefeld, Germany with Nearly Optimal Approximation, higher order structures (e.g., graphs, 2:25-2:45 Moments of Select Sets Adaptivity and Query Complexity geometric structures), temporal aspects Simon H. Langowski and Mark Daniel Ward, Matthew Fahrbach, Georgia Institute of (e.g., real-time considerations), or Purdue University, U.S. Technology, U.S.; Vahab Mirrokni and semantics, which are essential aspects Morteza Zadimoghaddam, Google, Inc., 2:50-3:10 Median-of-K Jumplists and of data and information that underlie U.S. Dangling-Min BSTs a broad class of current and emerging Sebastian Wild, University of Waterloo, 2:25-2:45 Submodular Maximization data science applications. In this talk, Canada; Markus Nebel, Universität with Nearly-optimal Approximation we present some recent results on Bielefeld, Germany; Elisabeth Neumann, and Adaptivity in Nearly-linear Time structural and temporal information in Technische Universität Braunschweig, Alina Ene, Boston University, U.S.; Huy dynamic networks/graphs, in which Germany Nguyen, Northeastern University, U.S. nodes and edges are added and removed 3:15-3:35 QuickSort: Improved Right- 2:25-2:45 An Exponential Speedup in over time. We focus on two related Tail Asymptotics for the Limiting Parallel Running Time for Submodular problems: (i) compression of structures Distribution, and Large Deviations Maximization Without Loss in -- for a given graph model, we exhibit James Allen Fill and Wei-Chun Hung, Johns Approximation an efficient algorithm for invertibly Hopkins University, U.S. Eric Balkanski, Aviad Rubinstein, and Yaron mapping network structures (i.e., graph Singer, Harvard University, U.S. isomorphism types) to bit strings of 2:50-3:10 Submodular Function minimum expected length, and (ii) node Maximization in Parallel via the arrival order inference -- for a dynamic Multilinear Extension graph model, we determine the extent Chandra Chekuri and Kent Quanrud, to which the order of node arrivals can University of Illinois at Urbana- be inferred from a snapshot of the graph Champaign, U.S. structure. For both problems, we apply 3:15-3:35 Stochastic Submodular analytic combinatorics, probabilistic, and Cover with Limited Adaptivity information-theoretic methods to find Arpit Agarwal, Sepehr Assadi, and Sanjeev statistical limits and efficient algorithms Khanna, University of Pennsylvania, U.S. for achieving those limits. 3:40-4:00 Stochastic ℓp Load Balancing and Moment Problems via Wojciech Szpankowski the L-Function Method Purdue University, U.S. Marco Molinaro, Pontifical Catholic University of Rio de Janeiro, Brazil Luncheon **Ticketed Event** 12:30 PM-2:00 PM Room:Crystal Ballroom - 2nd Floor

Please visit the SIAM Registration Desk if you did not receive a luncheon ticket. 16 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Sunday, January 6 Sunday, January 6 Sunday, January 6 CP7 CP8 CP9 SODA Session 2B SODA Session 2C ANALCO Session 3 2:00 PM-4:05 PM 2:00 PM-4:05 PM 4:30 PM-6:35 PM Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Room: Diamond 2 - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: Markus Nebel, Universität Bielefeld, 2:00-2:20 Approximate Nearest 2:00-2:20 An Algorithmic Blend of LPs Germany Neighbor Searching with Non- and Ring Equations for Promise CSPs 4:30-4:50 When Does Hillclimbing Fail euclidean and Weighted Distances Joshua Brakensiek, Stanford University, U.S.; on Monotone Functions? Ahmed Abdelkader, University of Maryland, Venkatesan Guruswami, Carnegie Mellon Anders Martinsson, ETH Zürich, Switzerland U.S.; Sunil Arya, Hong Kong University University, U.S. 4:55-5:15 Degree Distributions of of Science and Technology, Hong Kong; 2:25-2:45 The Complexity of the Ideal Generalized Hooking Networks Guilherme D. da Fonseca, Université Membership Problem for Constrained Colin Desmarais and Cecilia Holmgren, Clermont Auvergne, France; David M. Problems Over the Boolean Domain Uppsala University, Sweden Mount, University of Maryland, U.S. Monaldo Mastrolilli, IDSIA, Switzerland 5:20-5:40 Subcritical Random 2:25-2:45 Colored Range Closest- 2:50-3:10 Perfect Matchings, Rank Hypergraphs, High-Order Pair Problem under General Distance of Connection Tensors and Graph Components, and Hypertrees Functions Homomorphisms Wenjie Fang, Oliver Cooley, Nicola Del Jie Xue, University of Minnesota, Twin Cities, Jin-Yi Cai and Artsiom Hovarau, University Giudice, and Mihyun Kang, Technische U.S. of Wisconsin, Madison, U.S. Universität, Graz, Austria 2:50-3:10 Optimal Algorithm for 3:15-3:35 Probabilistic Tensors 5:45-6:05 Random Walks on Graphs: Geodesic Nearest-point Voronoi and Opportunistic Boolean Matrix New Bounds on Hitting, Meeting, Diagrams in Simple Polygons Multiplication Coalescing and Returning Eunjin Oh, Max Planck Institute for Petteri Kaski and Matti Karppa, Aalto Roberto Oliveira, IMPA, Rio de Janeiro, Informatics, Germany University, Finland Brazil; Yuval Peres, Microsoft Research, 3:15-3:35 New Lower Bounds for the 3:40-4:00 Fast Greedy for Linear U.S. Number of Pseudoline Arrangements Matroids Adrian Dumitrescu and Ritankar Mandal, 6:10-6:30 Arithmetic Progression Huy L. Nguyen, Northeastern University, U.S. University of Wisconsin, Milwaukee, U.S. Hypergraphs: Examining the Second Moment Method 3:40-4:00 Extremal and Probabilistic Michael Mitzenmacher, Harvard University, Results for Order Types Coffee Break U.S. Jie Han, University of Rhode Island, U.S.; Yoshiharu Kohayakawa, Universidade 4:05 PM-4:30 PM de Sao Paulo, Brazil; Marcelo Sales, Room:Ballroom Foyer - 2nd Floor Emory University, U.S.; Henrique Stagni, Universidade of São Paulo, Brazil Conference Program SODA, ALENEX, ANALCO and SOSA 2019 17

Sunday, January 6 Sunday, January 6 Sunday, January 6 CP10 CP11 CP12 SODA Session 3A SODA Session 3B SODA Session 3C 4:30 PM-6:35 PM 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 4:30-4:50 Flow-Cut Gaps and Face 4:30-4:50 Reproducibility and Pseudo- 4:30-4:50 Anaconda: A Non-adaptive Covers in Planar Graphs determinism in Log-space Conditional Sampling Algorithm for Havana Rika and Robert Krauthgamer, Yang Liu, Stanford University, U.S.; Ofer Distribution Testing Weizmann Institute of Science, Israel; Grossman, University of California, Gautam Kamath, Simons Institute for the James R. Lee, University of Washington, Berkeley, U.S. Theory of Computing, U.S.; Christos U.S. 4:55-5:15 Pseudorandomness for Tzamos, University of Wisconsin, Madison, 4:55-5:15 On Constant Multi- Read-k DNF Formulas U.S. Commodity Flow-Cut Gaps for Rocco A. Servedio, Columbia University, 4:55-5:15 Testing Halfspaces over Families of Directed Minor-Free U.S.; Li-Yang Tan, Stanford University, Rotation-invariant Distributions Graphs U.S. Nathaniel Harms, University of Waterloo, Ario Salmasi, Ohio State University, U.S.; 5:20-5:40 Near-optimal Bootstrapping Canada Anastasios Sidiropoulos, University of of Hitting Sets for Algebraic Circuits 5:20-5:40 Every Testable (Infinite) Illinois at Chicago, U.S.; Vijay Sridhar, Mrinal Kumar, Simons Institute for the Property of Bounded-degree Graphs MathWorks, U.S. Theory of Computing, U.S.; Ramprasad Contains An Infinite Hyperfinite 5:20-5:40 Maximum Integer Flows in Saptharishi and Anamay Tengse, Tata Subproperty Directed Planar Graphs with Vertex Institute of Fundamental Research, India Hendrik Fichtenberger, Technische Capacities and Multiple Sources and 5:45-6:05 A Deterministic PTAS for the Universität Dortmund, Germany; Pan Peng, Sinks Algebraic Rank of Bounded Degree University of Sheffield, United Kingdom; Yipu Wang, University of Illinois at Urbana- Polynomials Christian Sohler, Technische Universität Champaign, U.S. Vishwas Bhargava, Rutgers University, Dortmund, Germany 5:45-6:05 A Faster Algorithm for U.S.; Markus Bläser, Saarland University, 5:45-6:05 Testing Matrix Rank, Minimum-Cost Bipartite Matching in Germany; Gorav Jindal, Aalto University, Optimally Minor-Free Graphs Finland; Anurag Pandey, Max Planck Maria-Florina Balcan, Carnegie Mellon Nathaniel Lahn and Sharath Raghvendra, Institute for Informatics, Germany University, U.S.; Yi Li, Nanyang Virginia Tech, U.S. 6:10-6:30 Quantum Algorithms and Technological University, Singapore; David Woodruff and Hongyang Zhang, 6:10-6:30 Finding Maximal Sets of Approximating Polynomials for Laminar 3-Separators in Planar Graphs Composed Functions with Shared Carnegie Mellon University, U.S. Inputs in Linear Time 6:10-6:30 A Ptas for ℓp-Low Rank David Eppstein, University of California, Mark Bun, Simons Institute for the Theory of Approximation Irvine, U.S. Computing, U.S.; Robin Kothari, Microsoft Frank Ban, University of California, Research, U.S.; Justin Thaler, Georgetown Berkeley, U.S.; Vijay Bhattiprolu, Carnegie University, U.S. Mellon University, U.S.; Karl Bringmann and Pavel Kolev, Max Planck Institute for Informatics, Germany; Euiwoong Lee, , U.S.; David Woodruff, Carnegie Mellon University, U.S.

Intermission 6:35 PM-6:45 PM

ALENEX/ANALCO Business Meeting 6:45 PM-7:45 PM Room: Diamond 2 - 2nd Floor 18 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Monday, January 7 Monday, January 7 Monday, January 7 CP13 CP14 ALENEX Session 1 SODA Session 4A Registration 9:00 AM-10:40 AM 9:00 AM-11:05 AM 8:00 AM-5:00 PM Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Room: Registration Desk - 2rd Floor Chair: Henning Meyerhenke, Humboldt- Chair: To Be Determined Universität zu Berlin, Germany 9:00-9:20 Sublinear Algorithms for (∆ + 1) 9:00-9:20 Worst-case Efficient Sorting Vertex Coloring Continental Breakfast with QuickMergesort Sepehr Assadi, Yu Chen, and Sanjeev Khanna, 8:30 AM-9:00 AM Armin Weiß, Universität Stuttgart, Germany; University of Pennsylvania, U.S. Stefan Edelkamp, King’s College London, Room:Ballroom Foyer - 2nd Floor 9:25-9:45 Optimal Distributed Coloring United Kingdom Algorithms for Planar Graphs in the 9:25-9:45 Simple and Fast Local Model BlockQuicksort using Lomuto’s Shiri Chechik and Doron Mukhtar, Tel Aviv Partitioning Scheme University, Israel Martin Aumüller and Nikolaj Hass, IT 9:50-10:10 Distributed Maximal University of Copenhagen, Denmark Independent Set Using Small 9:50-10:10 Lightweight Distributed Messagesu Suffix Array Construction Mohsen Ghaffari, ETH Zürich, Switzerland Florian Kurpicz and Johannes Fischer, 10:15-10:35 Distributed Triangle Technische Universität Dortmund, Detection via Expander Germany Decomposition 10:15-10:35 Approximation of Trees by Yi-Jun Chang and Seth Pettie, University of Self-nested Trees Michigan, U.S.; Hengjie Zhang, Tsinghua Romain Azais, Inria, France; Jean-Baptiste University, China Durand, Université Grenoble Alpes, 10:40-11:00 Oblivious Resampling France; Christophe Godin, Inria, France Oracles and Parallel Algorithms for the Lopsided Lovász Local Lemma David G. Harris, University of Maryland, U.S. Conference Program SODA, ALENEX, ANALCO and SOSA 2019 19

Monday, January 7 Monday, January 7 Monday, January 7 CP15 CP16 IP2 SODA Session 4B SODA Session 4C Recent Advances on the 9:00 AM-11:05 AM 9:00 AM-11:05 AM Complexity of Parameterized Counting Problems Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined 11:30 AM-12:30 PM 9:00-9:20 On the Number of Circuits in 9:00-9:20 On the Rank of a Random Room: Emerald Ballroom - 2nd Floor Regular Matroids (with Connections to Sparse Binary Matrix Chair: To Be Determined Lattices and Codes) Alan Frieze, Carnegie Mellon University, Rohit Gurjar, Indian Institute of Technology U.S.; Colin Cooper, King’s College Research in the past few decades revealed Bombay, India; Nisheeth K. Vishnoi, École London, United Kingdom; Wesley Pegden, that a many of the basic algorithmic Polytechnique Fédérale de Lausanne, Carnegie Mellon University, U.S. problems are fixed-parameter tractable Switzerland with various parameterizations: they 9:25-9:45 On Coalescence Time in can be solved in time f(k)n^c, where k 9:25-9:45 Minimum Cut and Minimum Graphs-When Is Coalescing as Fast k-Cut in Hypergraphs via Branching as Meeting? is some parameter of the input instance. Contractions Varun Kanade, University of Oxford, United There have been significant progress Kyle Fox, University of Texas, Dallas, U.S.; Kingdom; Frederik Mallmann-Trenn, both in the design of parameterized Debmalya Panigrahi, Duke University, Massachusetts Institute of Technology, algorithms and in understanding the U.S.; Fred Zhang, Harvard University, U.S. U.S.; Thomas Sauerwald, University of limitations of these techniques. However, 9:50-10:10 Improving the Smoothed Cambridge, United Kingdom up until recent years, there were relatively Complexity of Flip for Max-cut 9:50-10:10 Rapid Mixing of the Switch few algorithmic and complexity results Problems Markov Chain for Strongly Stable on parameterized counting problems. Ali Bibak, University of Illinois at Chicago, Degree Sequences and 2-Class Joint Similarly to what one experiences in the U.S.; Charles A. Carlson, University of Degree Matrices area of polynomial-time computations, Colorado Boulder, U.S.; Karthekeyan Georgios Amanatidis and Pieter Kleer, there are natural parameterized problems Chandrasekaran, University of Illinois at Centrum voor Wiskunde en Informatica where finding a single solution is fixed- Urbana-Champaign, U.S. (CWI), Netherlands parameter tractable, but counting the 10:15-10:35 Computing all Wardrop 10:15-10:35 Xor Codes and Learning number of solutions is hard. In this talk, I Equilibria Parametrized by the Flow Sparse Parities with Noise will give a survey of recent developments, Demand Andrej Bogdanov, Chinese University of including new results that give a clean Philipp Warode and Max Klimm, Humboldt Hong Kong, Hong Kong; Manuel Sabin and unified explanation for the complexity and Prashant Nalini Vasudevan, University University at Berlin, Germany of #k-Path, #k-Matching, and many other of California, Berkeley, U.S. 10:40-11:00 Nash Flows over Time with parameterized counting problems. Spillback 10:40-11:00 Seeded Graph Matching Leon Sering, Technische Universität Berlin, via Large Neighborhood Statistics Dániel Marx Germany; Laura Vargas Koch, RWTH , Massachusetts Institute Hungarian Academy of Sciences, Hungary Aachen University, Germany of Technology, U.S.; Jiaming Xu, Duke University, U.S. Lunch Break Coffee Break 12:30 PM-2:00 PM 11:05 AM-11:30 AM Attendees on their own Room: Ballroom Foyer - 2nd Floor 20 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Monday, January 7 Monday, January 7 Monday, January 7 CP17 CP18 CP19 ALENEX Session 2 SODA Session 5A SODA Session 5B 2:00 PM-3:40 PM 2:00 PM-4:05 PM 2:00 PM-4:05 PM Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Chair: Andrew Goldberg, Amazon.com, U.S. Chair: To Be Determined Chair: To Be Determined 2:00-2:20 Fast and Exact Public Transit 2:00-2:20 Nearly ETH-tight Algorithms 2:00-2:20 The Streaming k-Mismatch Routing with Restricted Pareto Sets for Planar Steiner Tree with Terminals Problem Daniel Delling, Julian Dibbelt, and Thomas on Few Faces Raphael Clifford, University of Bristol, Pajor, Apple, Inc., U.S. Sándor Kisfaludi-Bak and Jesper Nederlof, United Kingdom; Tomasz Kociumaka, Eindhoven University of Technology, 2:25-2:45 Alternative Multicriteria University of Warsaw, Poland; Ely Porat, Netherlands; Erik Jan van Leeuwen, Routes Bar-Ilan University, Israel Utrecht University, The Netherlands Florian Barth and Stefan Funke, Universität 2:25-2:45 Few Matches or Almost Stuttgart, Germany; Sabine Storandt, 2:25-2:45 Contraction Decomposition Periodicity: Faster Pattern Matching Universität Konstanz, Germany in Unit Disk Graphs and Algorithmic with Mismatches in Compressed Texts Applications in Parameterized Karl Bringmann, Marvin Künnemann, and 2:50-3:10 Concatenated k-Path Complexity Philip Wellnitz, Max Planck Institute for Covers Meirav Zehavi, Ben-Gurion University, Informatics, Germany Moritz Beck, Universität Konstanz, Germany; Israel; Fahad Panolan, University of Kam-Yiu Lam, City University of Hong 2:50-3:10 Lower Bounds for Text Bergen, Norway; Saket Saurabh, Institute Kong, Hong Kong; Joseph Kee Yin Ng, Indexing with Mismatches and of Mathematical Sciences, India and Hong Kong Baptist University, Hong Differences University of Bergen, Norway Kong; Sabine Storandt, Universität Tatiana Starikovskaya, École Normale Konstanz, Germany; Chun Jiang Zhu, 2:50-3:10 Polynomial-time Supérieure Paris, France; Vincent Cohen- University of Connecticut, U.S. Approximation Scheme for Minimum Addad, Sorbonne Universités and CNRS, k-Cut in Planar and Minor-free France; Laurent Feuilloley, Universite 3:15-3:35 Batch-Parallel Euler Tour Graphs Paris Diderot, France Trees Alireza Farhadi, University of Maryland, Thomas Tseng, Laxman Dhulipala, and Guy 3:15-3:35 Efficiently Approximating U.S.; MohammadHossein Bateni, Google Blelloch, Carnegie Mellon University, U.S. Edit Distance Between Research, U.S.; MohammadTaghi Pseudorandom Strings Hajiaghayi, University of Maryland, William Kuszmaul, Massachusetts Institute College Park, U.S. of Technology, U.S. 3:15-3:35 Embedding Planar 3:40-4:00 Approximating Lcs in Linear Graphs into Low-treewidth Graphs Time: Beating the √n Barrier with Applications to Efficient Saeed Seddighin and MohammadTaghi Approximation Schemes for Metric Hajiaghayi, University of Maryland, Problems Eli Fox-Epstein, Tufts University, U.S.; College Park, U.S.; Masoud Seddighin, Philip Klein, Brown University, U.S.; Sharif University of Technology, Iran; Aaron Schild, University of California, Xiaorui Sun, University of Illinois at Berkeley, U.S. Chicago, U.S. 3:40-4:00 A PTAS for Euclidean TSP with Hyperplane Neighborhoods Antonios Antoniadis and Krzysztof Fleszar, Max Planck Institute for Informatics, Germany; Ruben Hoeksma, Universität Bremen, Germany; Kevin Schewior, Technische Universität München, Germany and École Normale Supérieure, France Conference Program SODA, ALENEX, ANALCO and SOSA 2019 21

Monday, January 7 Monday, January 7 Monday, January 7 CP20 CP21 CP22 SODA Session 5C ALENEX Session 3 SODA Session 6A 2:00 PM-4:05 PM 4:30 PM-6:10 PM 4:30 PM-6:35 PM Room: Diamond 1 - 2nd Floor Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Chair: To Be Determined Chair: Cliff Stein, Columbia University, U.S. Chair: To Be Determined 2:00-2:20 The Maximum Number of 4:30-4:50 A New Integer Linear 4:30-4:50 Strategies for Stable Merge Minimal Dominating Sets in a Tree Program for the Steiner Tree Problem Sorting Günter Rote, Freie Universität Berlin, with Revenues, Budget and Hop Samuel Buss and Alexander Knop, University Germany Constraints of California, San Diego, U.S. Adalat Jabrayilov and Petra Mutzel, 2:25-2:45 How to Guess an -Digit 4:55-5:15 A Sort of an Adversary n Technische Universität Dortmund, Number Or Zamir, Haim Kaplan, and Uri Zwick, Tel Germany Zilin Jiang, Massachusetts Institute of Aviv University, Israel 4:55-5:15 SAT-Encodings for Treecut Technology, U.S.; Nikita Polyanskii, 5:20-5:40 A New Path from Splay to Width and Treedepth Skolkovo Institute of Science and Dynamic Optimality Technology, Russia Robert Ganian and Neha Lodha, Technische Caleb Levy, Princeton University, U.S.; Universität Wien, Austria; Sebastian 2:50-3:10 Vector Clique , Princeton University and Ordyniak, University of Sheffield, United Decompositions Intertrust Technologies, U.S. Kingdom; Stefan Szeider, Technische Raphael Yuster, University of Haifa, Israel Universität Wien, Austria 5:45-6:05 A Faster External Memory 3:15-3:35 Four-Coloring P -Free Priority Queue with DecreaseKeys 6 5:20-5:40 Efficiently Enumerating Graphs Shunhua Jiang, Tsinghua University, China; Hitting Sets of Hypergraphs Arising in Maria Chudnovsky and Sophie Spirkl, Data Profiling Kasper G. Larsen, Aarhus University, Princeton University, U.S.; Mingxian Thomas Bläsius, Tobias Friedrich, and Denmark Zhong, Lehman College, CUNY, U.S. Julius Lischeid, Universität Potsdam, 6:10-6:30 Optimal Construction of 3:40-4:00 Polynomial-time Algorithm Germany; Kitty Meeks, University of Compressed Indexes for Highly for Maximum Weight Independent Set Glasgow, Scotland, United Kingdom; Repetitive Texts on P6-Free Graphs Martin Schirneck, Universität Potsdam, Dominik Kempa, University of Warwick, Michal Pilipczuk, University of Warsaw, Germany United Kingdom Poland; Andrzej Grzesik, Jagiellonian 5:45-6:05 Exactly Solving the University, Poland; Tereza Klimošová, Maximum Weight Independent Set Charles University, Czech Republic; Marcin Problem on Large Real-world Graphs Pilipczuk, University of Warsaw, Poland Darren Strash, Colgate University, U.S.; Sebastian Lamm, Karlsruhe Institute of Technology, Germany; Christian Schulz, University of Vienna, Austria Coffee Break and Karlsruhe Institute of Technology, 4:05 PM-4:30 PM Germany; Robert Williger, Karlsruhe Institute of Technology, Germany; Room:Ballroom Foyer - 2nd Floor Huashuo Zhang, Colgate University, U.S. 22 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Monday, January 7 Monday, January 7 Tuesday, January 8 CP23 CP24 SODA Session 6B SODA Session 6C Registration 4:30 PM-6:35 PM 4:30 PM-6:35 PM 8:00 AM-5:00 PM Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Room: Registration Desk - 2rd Floor Chair: To Be Determined Chair: To Be Determined 4:30-4:50 Approximability of P -> Q 4:30-4:50 Towards Tight(er) Bounds for Matrix Norms: Generalized Krivine the Excluded Grid Theorem Rounding and Hypercontractive Julia Chuzhoy, Toyota Technological Continental Breakfast Hardness Institute at Chicago, U.S.; Zihan Tan, 8:30 AM-9:00 AM Vijay Bhattiprolu, Carnegie Mellon , U.S. Room: Ballroom Foyer - 2nd Floor University, U.S.; Mrinalkanti Ghosh, 4:55-5:15 Polynomial Planar Directed Toyota Technological Institute at Chicago, Grid Theorem U.S.; Venkatesan Guruswami, Carnegie Meike Hatzel, Technische Universität Berlin, Mellon University, U.S.; Euiwoong Lee, Germany; Ken-ichi Kawarabayashi, New York University, U.S.; Madhur National Institute of Informatics, Japan; Tulsiani, Toyota Technological Institute at Stephan Kreutzer, Technische Universität Chicago, U.S. Berlin, Germany 4:55-5:15 Proportional Volume 5:20-5:40 A Tight Erdös-Pósa Function Sampling and Approximation for Planar Minors Algorithms for A-Optimal Design Jean-Florent Raymond, Technische Uthaipon Tantipongpipat and Mohit Singh, Universität Berlin, Germany; Wouter Georgia Institute of Technology, U.S.; Cames Van Batenburg, Tony Huynh, Aleksandar Nikolov, University of and Gwenaël Joret, Université Libre de Toronto, Canada Bruxelles, Belgium 5:20-5:40 Perron-Frobenius Theory 5:45-6:05 Polynomial Bounds for in Nearly Linear Time: Positive Centered Colorings on Proper Minor- Eigenvectors, M-Matrices, Graph Closed Graph Classes Kernels, and Other Applications Sebastian Siebertz, Humboldt University Amirmahdi Ahmadinejad, Arun Jambulapati, at Berlin, Germany; Michal Pilipczuk, Amin Saberi, and Aaron Sidford, Stanford University of Warsaw, Poland University, U.S. 6:10-6:30 Every Collinear Set in a 5:45-6:05 Iterative Refinement for Planar Graph is Free ℓp-Norm Regression Vida Dujmovic, University of Ottawa, Sushant Sachdeva and Deeksha Adil, Canada; Fabrizio Frati, Universita Roma University of Toronto, Canada; Rasmus Tre, Italy; Daniel Gonçalves, Université de Kyng, Yale University, U.S.; Richard Montpellier and CNRS, France; Pat Morin, Peng, Georgia Institute of Technology, Carleton University, Canada; Günter Rote, U.S. Freie Universität Berlin, Germany 6:10-6:30 Optimizing Quantum Optimization Algorithms via Faster Quantum Gradient Computation Andras Gilyen, QuSoft, CWI and University Intermission of Amsterdam, Netherlands; Srinivasan 6:35 PM-6:45 PM Arunachalam, Massachusetts Institute of Technology, U.S.; Nathan Wiebe, Microsoft Research, U.S. SODA Business Meeting and Awards Presentation 6:45 PM-7:45 PM Room: Emerald Ballroom - 2nd Floor Conference Program SODA, ALENEX, ANALCO and SOSA 2019 23

Tuesday, January 8 Tuesday, January 8 Tuesday, January 8 CP25 CP26 CP27 ALENEX Session 4 SODA Session 7A SODA Session 7B 9:00 AM-11:05 AM 9:00 AM-11:05 AM 9:00 AM-11:05 AM Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Chair: Stephen Kobourov, University of Chair: To Be Determined Chair: To Be Determined Arizona, U.S. 9:00-9:20 A 1.5-Approximation for Path 9:00-9:20 Coresets Meet EDCS: 9:00-9:20 Parallel Range, Segment TSP Algorithms for Matching and Vertex and Rectangle Queries with Rico Zenklusen, ETH Zürich, Switzerland Cover on Massive Graphs Augmented Maps 9:25-9:45 A New Dynamic Sepehr Assadi, University of Pennsylvania, Yihan Sun and Guy Blelloch, Carnegie Programming Approach for Spanning U.S.; MohammadHossein Bateni, Google Mellon University, U.S. Trees with Chain Constraints and Research, U.S.; Aaron Bernstein, Rutgers University, U.S.; Vahab Mirrokni, Google, 9:25-9:45 A Practical Algorithm for Beyond Martin Nagele and Rico Zenklusen, ETH Inc., U.S.; Cliff Stein, Columbia University, Spatial Agglomerative Clustering U.S. Thom Castermans, Bettina Speckmann, and Zürich, Switzerland Kevin Verbeek, Eindhoven University of 9:50-10:10 Lift and Project Algorithms 9:25-9:45 Sparsifying Distributed Technology, Netherlands for Precedence Constrained Algorithms with Ramifications in Scheduling to Minimize Completion Massively Parallel Computation and 9:50-10:10 Practical Methods for Centralized Local Computation Computing Large Covering Tours and Time Janardhan Kulkarni, Microsoft Research, Mohsen Ghaffari and Jara Uitto, ETH Zürich, Cycle Covers with Turn Cost Switzerland Sándor Fekete and Dominik M. Krupke, U.S.; Shashwat Garg, Eindhoven University Technische Universität Braunschweig, of Technology, Netherlands; Shi Li, State 9:50-10:10 Massively Parallel Germany University of New York at Buffalo, U.S. Approximation Algorithms for Edit Distance and Longest Common 10:15-10:35 A Polynomial Time 10:15-10:35 Faster Support Vector Subsequence Machines Constant Approximation For Minimizing Total Weighted Flow-time Saeed Seddighin, University of Maryland, Sebastian Schlag and Matthias Schmitt, College Park, U.S.; Xiaorui Sun, Janardhan Kulkarni, Microsoft Research, Karlsruhe Institute of Technology, University of Illinois at Chicago, U.S.; U.S.; Uriel Feige, Weizmann Institute of Germany; Christian Schulz, University of MohammadTaghi Hajiaghayi, University of Science, Israel; Shi Li, State University of Vienna, Austria and Karlsruhe Institute of Maryland, College Park, U.S. Technology, Germany New York at Buffalo, U.S. 10:15-10:35 Low Congestion Cycle 10:40-11:00 On Approximating 10:40-11:00 Scalable Edge Partitioning Covers and Their Applications Darren Strash, Colgate University, U.S.; (Sparse) Covering Integer Programs Eylon Yogev and Merav Parter, Weizmann Sebastian Schlag, Karlsruhe Institute Chandra Chekuri and Kent Quanrud, Institute of Science, Israel of Technology, Germany; Christian University of Illinois at Urbana-Champaign, Schulz, University of Vienna, Austria U.S. 10:40-11:00 Distributed Algorithms and Karlsruhe Institute of Technology, Made Secure: A Graph Theoretic Germany; Daniel Seemaier, Karlsruhe Approach Institute of Technology, Germany Eylon Yogev and Merav Parter, Weizmann Institute of Science, Israel 24 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Tuesday, January 8 Tuesday, January 8 Tuesday, January 8 CP28 IP3 CP29 SODA Session 7C Inherent Trade-Offs in SOSA Session 1 9:00 AM-11:05 AM Algorithmic Fairness 2:00 PM-4:05 PM Room: Diamond 1 - 2nd Floor 11:30 AM-12:30 PM Room: Diamond 2 - 2nd Floor Chair: To Be Determined Room: Emerald Ballroom - 2nd Floor Chair: To Be Determined 9:00-9:20 Interval Vertex Deletion Chair: To Be Determined 2:00-2:20 Isotonic Regression by Admits a Polynomial Kernel Recent discussion in the public sphere Dynamic Programming Akanksha Agrawal, Hungarian Academy of about classification by algorithms has Günter Rote, Freie Universität Berlin, Germany Sciences, Hungary involved tension between competing 9:25-9:45 Losing Treewidth by notions of what it means for such a 2:25-2:45 An Illuminating Algorithm for Separating Subsets classification to be fair to different the Light Bulb Problem Euiwoong Lee, New York University, U.S.; groups. We consider several of the key Josh Alman, Massachusetts Institute of Anupam Gupta and Jason M. Li, Carnegie fairness conditions that lie at the heart Technology, U.S. Mellon University, U.S.; Pasin Manurangsi, of these debates, and discuss recent 2:50-3:10 Simple Concurrent University of California, Berkeley, U.S.; research establishing inherent trade- Labeling Algorithms for Connected Michal Wlodarczyk, University of Warsaw, Components Poland offs between these conditions. We also consider a variety of methods for Sixue Liu, Princeton University, U.S.; Robert 9:50-10:10 On r-Simple k-Path and promoting fairness and related notions Tarjan, Princeton University and Intertrust Related Problems Parameterized by Technologies, U.S. for classification and selection problems k/r 3:15-3:35 A Framework for Searching Meirav Zehavi, Ben-Gurion University, Israel; that involve sets rather than just in Graphs in the Presence of Errors Gregory Gutin and Magnus Wahlstrom, individuals. This talk is based on joint Dariusz Dereniowski, Gdansk University Royal Holloway, University of London, work with Sendhil Mullainathan, Manish of Technology, Poland; Stefan Tiegel, United Kingdom Raghavan, and Maithra Raghu. Przemyslaw Uznanski, and Daniel Wolleb- 10:15-10:35 A Time and Space- Jon M. Kleinberg Graf, ETH Zürich, Switzerland Optimal Algorithm for the Many-Visits Cornell University, U.S. TSP 3:40-4:00 Selection from Heaps, Row- André Berger, Maastricht University, Sorted Matrices and X+Y Using Soft Netherlands; László Kozma, Eindhoven Heaps Uri Zwick, Haim Kaplan, and Or Zamir, Tel University of Technology, Netherlands; Lunch Break Aviv University, Israel Matthias Mnich, Maastricht University, 12:30 PM-2:00 PM Netherlands and Universität Bonn, Germany; Roland Vincze, Maastricht Attendees on their own University, Netherlands 10:40-11:00 Quantum Speedups for Exponential-Time Dynamic Programming Algorithms Jevgenijs Vihrovs, Andris Ambainis, Kaspars Balodis, Janis Iraids, Martins Kokainis, and Krisjanis Prusis, University of Latvia, Latvia

Coffee Break 11:05 AM-11:30 AM Room: Ballroom Foyer - 2nd Floor Conference Program SODA, ALENEX, ANALCO and SOSA 2019 25

Tuesday, January 8 Tuesday, January 8 Tuesday, January 8 CP30 CP31 CP32 SODA Session 8A SODA Session 8B SODA Session 8C 2:00 PM-4:05 PM 2:00 PM-4:05 PM 2:00 PM-4:05 PM Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 2:00-2:20 Optimal Las Vegas 3:40-4:00 Deterministically Maintaining 2:00-2:20 Prophet Secretary Through Approximate Near Neighbors in ℓp a (2 +ϵε)-Approximate Minimum Blind Strategies Alexander Wei, Harvard University, U.S. Vertex Cover in O(1/ε2) Amortized José Correa and Raimundo Saona, 2:25-2:45 The Andoni-Krauthgamer- Update Time Universidad de Chile, Chile; Bruno Ziliotto, Razenshteyn Characterization of Sayan Bhattacharya, University of Warwick, Universite Paris Dauphine and CNRS, Sketchable Norms Fails for Sketchable United Kingdom; Janardhan Kulkarni, France Microsoft Research, U.S. Metrics 2:25-2:45 Pricing for Online Resource Assaf Naor, Princeton University, U.S.; 2:00-2:20 (1 + Eps)-Approximate Allocation: Intervals and Paths Subhash Khot, New York University, U.S. Incremental Matching in Constant Shuchi Chawla, Benjamin Miller, and Yifeng Deterministic Amortized Time Teng, University of Wisconsin, Madison, 2:50-3:10 Tight Bounds for ℓp Oblivious Subspace Embeddings Chris Schwiegelshohn, Università di Roma U.S. Ruosong Wang and David Woodruff, Carnegie “La Sapienza”, Italy; Fabrizio Grandoni, 2:50-3:10 An Optimal Truthful Mellon University, U.S. IDSIA, Switzerland; Stefano Leonardi, Mechanism for the Online Weighted Università di Roma “La Sapienza”, Bipartite Matching Problem 3:15-3:35 Optimal Lower Bounds for Italy; Piotr Sankowski, University of Distributed and Streaming Spanning Rebecca Reiffenhaeuser, Università di Roma Warsaw, Poland; Shay Solomon, Tel Aviv “La Sapienza”, Italy Forest Computation University, Israel Huacheng Yu and Jelani Nelson, Harvard 3:15-3:35 Fully Polynomial-Time University, U.S. 2:25-2:45 A Deamortization Approach Approximation Schemes for Fair Rent for Dynamic Spanner and Dynamic Division 3:40-4:00 Communication-Rounds Maximal Matching Eshwar Ram Arunachaleswaran, Siddharth Tradeoffs for Common Randomness Aaron Bernstein, Rutgers University, U.S.; Barman, and Nidhi Rathi, Indian Institute and Secret Key Generation Sebastian Forster, University of Salzburg, of Science, India Mitali Bafna, Harvard University, U.S.; Germany; Henzinger Monika, University Badih Ghazi, Google Research, U.S.; Noah of Vienna, Austria 3:40-4:00 Communication Complexity Golowich and , Harvard of Discrete Fair Division University, U.S. 2:50-3:10 Fully Dynamic Maximal Benjamin Plaut and Tim Roughgarden, Independent Set with Sublinear in n Stanford University, U.S. Update Time Sepehr Assadi, University of Pennsylvania, U.S.; Krzysztof Onak, IBM Research, U.S.; Baruch Schieber, New Jersey Coffee Break Institute of Technology, U.S.; Shay Solomon, Tel Aviv University, Israel 4:05 PM-4:30 PM 3:15-3:35 Dynamic Edge Coloring with Room: Ballroom Foyer - 2nd Floor Improved Approximation Ran Duan, Haoqing He, and Tianyi Zhang, Tsinghua University, China 26 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Tuesday, January 8 Tuesday, January 8 Tuesday, January 8 CP33 CP34 CP35 SOSA Session 2 SODA Session 9A SODA Session 9B 4:30 PM-6:35 PM 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 4:30-4:50 Approximating Optimal 4:30-4:50 The I/O Complexity of 4:30-4:50 Analyzing Boolean Functions Transport with Linear Programs Toom-Cook Integer Multiplication on the Biased Hypercube Via Higher- Kent Quanrud, University of Illinois at Lorenzo De Stefani, Brown University, U.S.; Dimensional Agreement Tests Urbana-Champaign, U.S. Gianfranco Bilardi, University of Padova, Yuval Filmus, Technion Israel Institute of Technology, Israel; Irit Dinur, Weizmann 4:55-5:15 LP Relaxation and Tree Italy Institute of Science, Israel; Prahladh Packing for Minimum k-Cuts 4:55-5:15 I/O-Efficient Algorithms Harsha, Tata Institute of Fundamental Chandra Chekuri and Kent Quanrud, for Topological Sort and Related Research, India University of Illinois at Urbana-Champaign, Problems U.S.; Chao Xu, Yahoo! Research, U.S. Nairen Cao, Jeremy Fineman, Katina 4:55-5:15 List Decoding with Double Samplers 5:20-5:40 On Primal-Dual Circle Russell, and Eugene Yang, Georgetown Inbal R. Livni Navon and Irit Dinur, Representations University, U.S. Weizmann Institute of Science, Israel; Stefan Felsner, Technische Universität, Berlin, 5:20-5:40 On the Structure of Unique Prahladh Harsha, Tata Institute of Germany; Günter Rote, Freie Universität Shortest Paths in Graphs Fundamental Research, India; Tali Berlin, Germany Greg Bodwin, Georgia Institute of Kaufman, Massachusetts Institute of Technology, U.S. 5:45-6:05 Asymmetric Convex Technology, U.S.; Amnon Ta-Shma, Tel Intersection Testing 5:45-6:05 Near Optimal Algorithms For Aviv University, Israel Luis Barba, ETH Zürich, Switzerland; The Single Source Replacement Paths 5:20-5:40 Maximally Recoverable Wolfgang J. Mulzer, Freie Universität Problem LRCs: A Field Size Lower Bound and Berlin, Germany Sarel Cohen and Shiri Chechik, Tel Aviv Constructions for Few Heavy Parities University, Israel 6:10-6:30 Relaxed Voronoi: A Simple Sivakanth Gopi, Microsoft Research, U.S.; Framework for Terminal-Clustering 6:10-6:30 Exact Distance Oracles for Venkatesan Guruswami, Carnegie Mellon Problems Planar Graphs with Failing Vertices University, U.S.; Sergey Yekhanin, Arnold Filtser, Ben Gurion University, Israel; Panagiotis Charalampopoulos, King’s Microsoft, U.S. Robert Krauthgamer and Ohad Trabelsi, College London, United Kingdom; 5:45-6:05 Binary Robust Positioning Weizmann Institute of Science, Israel Shay Mozes and Benjamin Tebeka, Patterns with Low Redundancy and Interdisciplinary Center Herzliya, Israel Efficient Locating Algorithms Yeow Meng Chee, Duc Tu Dao, Han Mao Kiah, San Ling, and Hengjia Wei, Nanyang Technological University, Singapore 6:10-6:30 Synchronization Strings: Highly Efficient Deterministic Constructions over Small Alphabets Kuan Cheng, Johns Hopkins University, U.S.; Bernhard Haeupler, Carnegie Mellon University, U.S.; Xin Li, Johns Hopkins University, U.S.; Amirbehshad Shahrasbi, Carnegie Mellon University, U.S.; Ke Wu, Johns Hopkins University, U.S. Conference Program SODA, ALENEX, ANALCO and SOSA 2019 27

Tuesday, January 8 Wednesday, Wednesday, January 9 CP36 January 9 CP37 SODA Session 9C SOSA Session 3 4:30 PM-6:35 PM 9:00 AM-11:05 AM Registration Room: Diamond 1 - 2nd Floor Room: Diamond 2 - 2nd Floor 8:00 AM-5:00 PM Chair: To Be Determined Chair: To Be Determined 4:30-4:50 The Complexity of Room: Registration Desk - 2rd Floor 9:00-9:20 Towards a Unified Theory of Approximately Counting Retractions Sparsification for Matching Problems Jacob Focke, Leslie Ann Goldberg, and Sepehr Assadi, University of Pennsylvania, Stanislav Zivny, University of Oxford, Continental Breakfast U.S.; Aaron Bernstein, Rutgers University, United Kingdom U.S. 8:30 AM-9:00 AM 4:55-5:15 Improved Bounds for 9:25-9:45 A New Application of Randomly Sampling Colorings Via Room: Ballroom Foyer - 2nd Floor Orthogonal Range Searching for Linear Programming Computing Giant Graph Diameters Sitan Chen, Massachusetts Institute of Guillaume Ducoffe, ICI – National Institute Technology, U.S.; Michelle Delcourt, for Research and Development informatics, University of Waterloo, Canada; Ankur Romania Moitra, Massachusetts Institute of Technology, U.S.; Guillem Perarnau, 9:50-10:10 Simplified and Space-Optimal Semi-Streaming University of Birmingham, United (2+ )-Approximate Matching Kingdom; Luke Postle, University of ε Mohsen Ghaffari, ETH Zürich, Switzerland; Waterloo, Canada David Wajc, Carnegie Mellon University, 5:20-5:40 Algorithms for #{BIS}-Hard U.S. Problems on Expander Graphs 10:15-10:35 Simple Greedy Matthew Jenssen and Peter Keevash, 2-Approximation Algorithm for the University of Oxford, United Kingdom; Maximum Genus of a Graph Will Perkins, University of Illinois at Michal Kotrbcik and Martin Skoviera, Chicago, U.S. Comenius University, Bratislava, Slovakia 5:45-6:05 Approximability of the Six- 10:40-11:00 A Note on Max K-Vertex Vertex Model Cover: Faster Fpt-As, Smaller Jin-Yi Cai and Tianyu Liu, University of Approximate Kernel and Improved Wisconsin, Madison, U.S.; Pinyan Lu, Approximation Shanghai University of Finance and Pasin Manurangsi, University of California, Economics, China Berkeley, U.S. 6:10-6:30 Zeros of Holant Problems: Locations and Algorithms Heng Guo, University of Edinburgh, United Kingdom; Chao Liao, Shanghai Jiao Tong University, China; Pinyan Lu, Shanghai University of Finance and Economics, China; Chihao Zhang, Shanghai Jiaotong University, China

Intermission 6:35 PM-6:45 PM

SOSA Business Meeting 6:45 PM-7:45 PM Room: Diamond 2 - 2nd Floor 28 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Wednesday, January 9 Wednesday, January 9 Wednesday, January 9 CP38 CP39 CP40 SODA Session 10A SODA Session 10B SODA Session 10C 9:00 AM-11:05 AM 9:00 AM-11:05 AM 9:00 AM-11:05 AM Room: Emerald Ballroom - 2nd Floor Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 9:00-9:20 On Facility Location with 9:00-9:20 Theorems of Carathéodory, 9:00-9:20 Can We Overcome the n log n General Lower Bounds Helly, and Tverberg Without Barrier for Oblivious Sorting? Shi Li, State University of New York at Dimension Wei-Kai Lin and Elaine Shi, Cornell Buffalo, U.S. Karim Adiprasito, Hebrew University of University, U.S.; Tiancheng Xie, Shanghai Jerusalem, Israel; Imre Bárány, Alfréd Jiao Tong University, China 9:25-9:45 Hierarchical Clustering Rényi Institute of Mathematics, Budapest Better Than Average-Linkage 9:25-9:45 Lower Bounds for Oblivious and University College London, United Moses Charikar, Vaggos Chatziafratis, and Data Structures Kingdom; Nabil H. Mustafa, ESIEE, Rad Niazadeh, Stanford University, U.S. Riko Jacob, IT University of Copenhagen, France Denmark; Kasper G. Larsen and Jesper B. 9:50-10:10 The Threshold for SDP- 9:25-9:45 On the Spanning and Nielsen, Aarhus University, Denmark Refutation of Random Regular NAE- Routing Ratio of Theta-Four 3SAT 9:50-10:10 Foundations of Differentially Darryl R. Hill and Prosenjit Bose, Carleton Tselil Schramm, Massachusetts Institute of Oblivious Algorithms University, Canada; Jean-Lou De Carufel, Technology and Harvard University, U.S.; T-H. Hubert Chan, University of Hong Kong, University of Ottawa, Canada; Michiel Yash Deshpande, Massachusetts Institute Hong Kong; Kai-Min Chung, Academia Smid, Carleton University, Canada of Technology, U.S.; Andrea Montanari, Sinica, Taiwan; Bruce M. Maggs, Duke Stanford University, U.S.; Ryan O’Donnell, 9:50-10:10 Greedy Spanners Are University and Akamai Technologies, U.S.; Carnegie Mellon University, U.S.; Optimal in Doubling Metrics Elaine Shi, Cornell University, U.S. Subhabrata Sen, Massachusetts Institute of Glencora Borradaile and Hung Le, Oregon 10:15-10:35 Amplification by Shuffling: Technology, U.S. State University, U.S.; Christian Wulff- From Local to Central Differential Nilsen, University of Copenhagen, 10:15-10:35 Exponential Lower Bounds Privacy via Anonymity Denmark on Spectrahedral Representations of Ulfar Erlingsson, Vitaly Feldman, Ilya Hyperbolicity Cones 10:15-10:35 Viewing the Rings of a Mironov, Ananth Raghunathan, and Kunal Nick Ryder, Nikhil Srivastava, and Prasad Tree: Minimum Distortion Embeddings Talwar, Google, Inc., U.S.; Abhradeep Raghavendra, University of California, into Trees Thakurta, Google and University of Berkeley, U.S.; Benjamin Weitz, Pintrest, Benjamin A. Raichel, University of Texas at California, Santa Cruz, U.S. U.S. Dallas, U.S.; Amir Nayyeri, Oregon State 10:40-11:00 Towards Instance-Optimal University, U.S. 10:40-11:00 Universal Trees Grow Private Query Release Aleksandar Nikolov, University of Toronto, Inside Separating Automata: Quasi- 10:40-11:00 Minimizing Interference Polynomial Lower Bounds for Parity Potential Among Moving Entities Canada; Jaroslaw Blasiok, Harvard Games Daniel Busto, Ericsson, Montreal, Canada; University, U.S.; Mark Bun, Princeton Wojciech Czerwinski, University of Warsaw, William S. Evans, University of British University, U.S.; Thomas Steinke, IBM Poland; Laure Daviaud, University of Columbia, Canada; David Kirkpatrick, Research, U.S. Warwick, United Kingdom; Nathanael University of British Columbia, Canada Fijalkow, Université Bordeaux, France; Marcin Jurdzinski and Ranko Lazic, University of Warwick, United Kingdom; Coffee Break Pawel Parys, University of Warsaw, Poland 11:05 AM-11:30 AM Room: Ballroom Foyer - 2nd Floor Conference Program SODA, ALENEX, ANALCO and SOSA 2019 29

Wednesday, January 9 Wednesday, January 9 Wednesday, January 9 IP4 CP41 CP42 (Hardness of) Approximation SOSA Session 4 SODA Session 11A and Expansion 2:00 PM-4:05 PM 2:00 PM-4:05 PM 11:30 AM-12:30 PM Room: Diamond 2 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Room: Emerald Ballroom - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 2:00-2:20 Simple Contention 2:00-2:20 Non-Empty Bins with Simple Recently, there has been some exciting Resolution Via Multiplicative Weight Tabulation Hashing progress towards proving the unique Updates Anders Aamand and Mikkel Thorup, Yi-Jun Chang, Wenyu Jin, and Seth Pettie, games conjecture. Is the conjecture University of Copenhagen, Denmark University of Michigan, U.S. true? Experts are not sure. Still, 2:25-2:45 Derandomized Balanced it is clearly key to understanding 2:25-2:45 A Simple Near-Linear Allocation approximation algorithms for many Pseudopolynomial Time Randomized Xue Chen, Northwestern University, U.S. Algorithm for Subset Sum optimization problems, most notably 2:50-3:10 Optimal Ball Recycling Ce Jin and Hongxun Wu, Tsinghua constraint satisfaction. I will describe Michael A. Bender and Jake Christensen, University, China the background and consequences of Stony Brook University, U.S.; Alexander the conjecture and then focus on some 2:50-3:10 Submodular Optimization in Conway and Martin Farach-Colton, Rutgers interesting technical step pertaining to the MapReduce Model University, U.S.; Rob Johnson, Vmware the expansion of the so-called Grassman Paul Liu and Jan Vondrak, Stanford Research, U.S.; Meng-Tsung Tsai, National University, U.S. graph. I will then describe a more general Chiao Tung University, Taiwan phenomenon called high dimensional 3:15-3:35 Compressed Sensing with 3:15-3:35 A Fourier-Analytic Approach expansion (HDX). HDX is family of a Adversarial Sparse Noise Via L1 for the Discrepancy of Random Set generalizations of expansion in graphs to Regression Systems hypergraphs. This is a new area of study Sushrut Karmalkar and Eric Price, University Rebecca Hoberg and Thomas Rothvoss, of Texas at Austin, U.S. and has potential for algorithms, as I will University of Washington, U.S. try to show. 3:40-4:00 Approximating Maximin 3:40-4:00 On the Discrepancy of Share Allocations Random Low Degree Set Systems Jugal Garg, Peter McGlaughlin, and Setareh Nikhil Bansal, Centrum voor Wiskunde Irit Dinur Taki, University of Illinois at Urbana- en Informatica (CWI) and Eindhoven Weizmann Institute of Science, Israel Champaign, U.S. University of Technology, Netherlands; Raghu Meka, University of California, Los Angeles, U.S. Lunch Break 12:30 PM-2:00 PM Attendees on their own 30 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Wednesday, January 9 Wednesday, January 9 Wednesday, January 9 CP43 CP44 CP45 SODA Session 11B SODA Session 11C SODA Session 12A 2:00 PM-4:05 PM 2:00 PM-4:05 PM 4:30 PM-6:35 PM Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Room: Emerald Ballroom - 2nd Floor Chair: To Be Determined Chair: To Be Determined Chair: To Be Determined 2:00-2:20 Optimal Lower Bounds for 2:00-2:20 Constructive Polynomial 4:30-4:50 Dimension-independent Sketching Graph Cuts Partitioning for Algebraic Curves In~ Sparse Fourier Transform Charles A. Carlson and Alexandra Kolla, \reals3 with Applications Michael Kapralov, IBM T.J. Watson University of Colorado Boulder, U.S.; Esther Ezra, Georgia Institute of Technology, Research Center, U.S.; Ameya Velingker, Nikhil Srivastava and Luca Trevisan, U.S.; Boris Aronov, New York University, Google, Inc., U.S.; Amir Zandieh, École University of California, Berkeley, U.S. U.S.; Joshua Zahl, University of British Polytechnique Fédérale de Lausanne, Columbia, Canada Switzerland 2:25-2:45 Spectral Sparsification of Hypergraphs 2:25-2:45 Computing Height 4:55-5:15 Adaptive Sparse Recovery Tasuku Soma, University of Tokyo, Japan; Persistence and Homology Generators with Limited Adaptivity 3 Yuichi Yoshida, National Institute of in R Efficiently Akshay Kamath and Eric Price, University of Informatics, Japan Tamal K. Dey, Ohio State University, U.S. Texas at Austin, U.S. 2:50-3:10 Cheeger Inequalities for 2:50-3:10 Hardness of Approximation 5:20-5:40 Efficient Algorithms and Submodular Transformations for Morse Matching Lower Bounds for Robust Linear Yuichi Yoshida, National Institute of Abhishek J. Rathod and Ulrich Bauer, Regression Informatics, Japan Technische Universität München, Germany Weihao Kong, Stanford University, U.S.; Ilias Diakonikolas, University of Southern 3:15-3:35 Short Cycles via Low- 3:15-3:35 Improved Topological California, U.S.; Alistair Stewart, Stanford diameter Decompositions Approximations by Digitization University, U.S. Yang Liu, Stanford University, U.S.; Sushant Aruni Choudhary, Freie Universität Sachdeva and Zejun Yu, University of Berlin, Germany; Michael Kerber, Graz 5:45-6:05 High-Dimensional Robust Toronto, Canada University of Technology, Austria; Sharath Mean Estimation in Nearly-linear Time Raghvendra, Virginia Tech, U.S. Yu Cheng, Duke University, U.S.; Ilias 3:40-4:00 Expander Decomposition Diakonikolas, University of Southern and Pruning: Faster, Stronger, and 3:40-4:00 Full Tilt: Universal California, U.S.; Rong Ge, Duke Simpler. Constructors for General Shapes with University, U.S. Thatchaphol Saranurak, Toyota Technological Uniform External Forces Institute at Chicago, U.S.; Di Wang, Jose Balanza-Martinez, David Caballero, 6:10-6:30 Relative Error Tensor Low Georgia Institute of Technology, U.S. Angel Cantu, Luis Garcia, Austin Rank Approximation Luchsinger, and Rene Reyes, University Zhao Song, University of Texas at Austin, of Texas, Rio Grande Valley; Robert T. U.S.; David Woodruff, Carnegie Mellon Schweller, University of Texas - Pan University, U.S.; Peilin Zhong, Columbia American, U.S.; Tim Wylie, University of University, U.S. Texas, Rio Grande Valley

Coffee Break 4:05 PM-4:30 PM Room: Ballroom Foyer - 2nd Floor Conference Program SODA, ALENEX, ANALCO and SOSA 2019 31

Wednesday, January 9 Wednesday, January 9 CP46 CP47 SODA Session 12B SODA Session 12C 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room: Topaz - 2nd Floor Room: Diamond 1 - 2nd Floor Chair: To Be Determined Chair: To Be Determined 4:30-4:50 Popular Matchings and Limits 4:30-4:50 Seth Says: Weak Fréchet to Tractability Distance is Faster, But Only if it is Yuri Faenza, Columbia University, U.S.; Continuous and in One Dimension Telikepalli Kavitha, Tata Institute of Tim Ophelders, Michigan State University, Fundamental Research, India; Vladlena U.S.; Kevin Buchin and Bettina Powers and Xingyu Zhang, Columbia Speckmann, Eindhoven University of University, U.S. Technology, Netherlands 4:30-4:50 Popular Matching in 4:55-5:15 Fréchet Distance under Roommates Setting is Np-Hard Translation: Conditional Hardness and Pranabendu Misra and Sushmita Gupta, an Algorithm via Offline Dynamic Grid University of Bergen, Norway; Saket Reachability Saurabh, Institute of Mathematical Sciences, Karl Bringmann, Marvin Künnemann, and India and University of Bergen, Norway; André Nusser, Max Planck Institute for Meirav Zehavi, Ben-Gurion University, Informatics, Germany Israel 5:20-5:40 Approximating (k,l)-Center 4:55-5:15 A (1+1/e)-Approximation Clustering for Curves Algorithm for Maximum Stable Kevin Buchin, Eindhoven University of Matching with One-sided Ties and Technology, Netherlands; Anne Driemel, Incomplete Lists Universität Bonn, Germany; Joachim Chi-Kit Lam and C. Gregory Plaxton, Gudmundsson, University of Sydney, University of Texas at Austin, U.S. Australia; Michael Horton, New York University, U.S. and University of Sydney, 5:20-5:40 Beating Greedy for Stochastic Australia; Irina Kostitsyna, Eindhoven Bipartite Matching University of Technology, Netherlands; Buddhima Gamlath, Sagar Kale, and Ola Maarten Loffler, Utrecht University, Svensson, École Polytechnique Fédérale de Netherlands; Martijn Struijs, Eindhoven Lausanne, Switzerland University of Technology, Netherlands 5:45-6:05 Stochastic Matching with Few 5:45-6:05 Analysis of Ward’s Method Queries: New Algorithms and Tools Anna Großwendt, Heiko Röglin, Melanie Soheil Behnezhad and Alireza Farhadi, Schmidt, and Clemens Rösner, Universität University of Maryland, U.S.; Bonn, Germany MohammadTaghi Hajiaghayi, University of Maryland, College Park, U.S.; Nima 6:10-6:30 Exact Algorithms and Reyhani, University of Maryland, U.S. Lower Bounds for Stable Instances of Euclidean K-Means 6:10-6:30 Tight Competitive Ratios of Zachary Friggstad, Kamyar Khodamoradi, Classic Matching Algorithms in the Fully and Mohammad Salavatipour, University of Online Model Alberta, Canada Zhiyi Huang, University of Hong Kong, Hong Kong; Binghui Peng, Tsinghua University, China; Zhihao Gavin Tang, University of Hong Kong, Hong Kong; Runzhou Tao, Tsinghua University, China; Xiaowei Wu, City University of Hong Kong, Hong Kong; Yuhao Zhang, University of Hong Kong, Hong Kong 32 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Speaker Index

Symposium on Simplicity in Algorithms (SOSA19) Conference Program SODA, ALENEX, ANALCO and SOSA 2019 33

A Chatziafratis, Vaggos, CP38, 9:25 Wed Genitrini, Antoine, CP1, 9:25 Sun Aamand, Anders, CP42, 2:00 Wed Chechik, Shiri, CP14, 9:25 Mon Ghaffari, Mohsen, CP14, 9:50 Mon Abdelkader, Ahmed, CP7, 2:00 Sun Chechik, Shiri, CP34, 5:45 Tue Ghaffari, Mohsen, CP27, 9:25 Tue Adil, Deeksha, CP23, 5:45 Mon Chen, Lijie, CP2, 9:25 Sun Gilyen, Andras, CP23, 6:10 Mon Agarwal, Arpit, CP6, 3:15 Sun Chen, Sitan, CP36, 4:55 Tue Golowich, Noah, CP30, 3:40 Tue Agrawal, Akanksha, CP28, 9:00 Tue Chen, Xue, CP42, 2:25 Wed Gopi, Sivakanth, CP35, 5:20 Tue Ahmadinejad, Amirmahdi, CP23, 5:20 Cheng, Yu, CP45, 5:45 Wed Grossman, Ofer, CP11, 4:30 Sun Mon Choudhary, Aruni, CP44, 3:15 Wed Gurjar, Rohit, CP15, 9:00 Mon Alman, Josh, CP29, 2:25 Tue Conway, Alexander, CP42, 2:50 Wed Antoniadis, Antonios, CP18, 3:40 Mon H Hackl, Benjamin, CP1, 10:15 Sun Argue, C.J., CP3, 9:50 Sun D de Panafieu, Elie, CP1, 9:00 Sun Harms, Nathaniel, CP12, 4:55 Sun Assadi, Sepehr, CP14, 9:00 Mon De Stefani, Lorenzo, CP34, 4:30 Tue Harris, David G., CP14, 10:40 Mon Assadi, Sepehr, CP27, 9:00 Tue Del Giudice, Nicola, CP9, 5:20 Sun Hass, Nikolaj, CP13, 9:25 Mon Assadi, Sepehr, CP37, 9:00 Wed Deng, Yuan, CP4, 9:25 Sun Hatzel, Meike, CP24, 4:55 Mon Axiotis, Kyriakos, CP2, 10:15 Sun Dereniowski, Dariusz, CP29, 3:15 Tue Heuberger, Clemens, CP1, 9:50 Sun Azais, Romain, CP13, 10:15 Mon Desmarais, Colin, CP9, 4:55 Sun Hill, Darryl R., CP39, 9:25 Wed B Dey, Tamal K., CP44, 2:25 Wed Hoberg, Rebecca, CP42, 3:15 Wed Balkanski, Eric, CP6, 2:25 Sun Dinur, Irit, IP4, 11:30 Wed Hovarau, Artsiom, CP8, 2:50 Sun Ban, Frank, CP12, 6:10 Sun Dinur, Irit, CP35, 4:30 Tue Huynh, Tony, CP24, 5:20 Mon Barba, Luis, CP33, 5:45 Tue Driemel, Anne, CP47, 5:20 Wed Barth, Florian, CP17, 2:25 Mon Ducoffe, Guillaume, CP37, 9:25 Wed J Jabrayilov, Adalat, CP21, 4:30 Mon Beck, Moritz, CP17, 2:50 Mon Jenssen, Matthew, CP36, 5:20 Tue Behnezhad, Soheil, CP46, 5:45 Wed E Ene, Alina, CP6, 2:25 Sun Jiang, Shunhua, CP22, 5:45 Mon Bei, Xiaohui, CP4, 9:50 Sun Eppstein, David, CP10, 6:10 Sun Jin, Ce, CP41, 2:25 Wed Bernstein, Aaron, CP31, 2:25 Tue Evans, William S., CP39, 10:40 Wed Jin, Yaonan, CP4, 10:15 Sun Bhattacharya, Sayan, CP31, 3:40 Tue Ezra, Esther, CP44, 2:00 Wed Jindal, Gorav, CP11, 5:45 Sun Bhattiprolu, Vijay, CP23, 4:30 Mon Bibak, Ali, CP15, 9:50 Mon F K Blasiok, Jaroslaw, CP40, 10:40 Wed Faenza, Yuri, CP46, 4:30 Wed Kamath, Akshay, CP45, 4:55 Wed Bodwin, Greg, CP34, 5:20 Tue Fahrbach, Matthew, CP6, 2:25 Sun Kamath, Gautam, CP12, 4:30 Sun Brakensiek, Joshua, CP8, 2:00 Sun Farhadi, Alireza, CP18, 2:50 Mon Karmalkar, Sushrut, CP41, 3:15 Wed Bringmann, Karl, CP2, 9:50 Sun Fichtenberger, Hendrik, CP12, 5:20 Sun Kaski, Petteri, CP8, 3:15 Sun Bubeck, Sebastien, CP3, 9:00 Sun Fill, James Allen, CP5, 3:15 Sun Kempa, Dominik, CP22, 6:10 Mon Bun, Mark, CP11, 6:10 Sun Filtser, Arnold, CP33, 6:10 Tue Khodamoradi, Kamyar, CP47, 6:10 Wed Focke, Jacob, CP36, 4:30 Tue Kleer, Pieter, CP16, 9:50 Mon C Frieze, Alan, CP16, 9:00 Mon Klein, Philip, CP18, 3:15 Mon Carlson, Charles A., CP43, 2:00 Wed Kleinberg, Jon M., IP3, 11:30 Tue Castermans, Thom, CP25, 9:25 Tue G Klimczak, Mateusz, CP1, 10:40 Sun Charalampopoulos, Panagiotis, CP34, Gamlath, Buddhima, CP46, 5:20 Wed Knop, Alexander, CP22, 4:30 Mon 6:10 Tue Garg, Mohit, CP6, 2:00 Sun Kociumaka, Tomasz, CP19, 2:00 Mon 34 SODA, ALENEX, ANALCO and SOSA 2019 Conference Program

Kong, Weihao, CP45, 5:20 Wed Mitzenmacher, Michael, CP9, 6:10 Sun Rote, Günter, CP24, 6:10 Mon Krupke, Dominik M., CP25, 9:50 Tue Molinaro, Marco, CP3, 9:25 Sun Rote, Günter, CP29, 2:00 Tue Kulkarni, Janardhan, CP26, 9:50 Tue Molinaro, Marco, CP6, 3:40 Sun Rote, Günter, CP33, 5:20 Tue Kulkarni, Janardhan, CP26, 10:15 Tue Mustafa, Nabil H., CP39, 9:00 Wed Russell, Katina, CP34, 4:55 Tue Ryder, Nick, CP38, 10:15 Wed Kurpicz, Florian, CP13, 9:50 Mon N Kuszmaul, William, CP19, 3:15 Mon Nagele, Martin, CP26, 9:25 Tue S L Naor, Assaf, CP30, 2:25 Tue Sabin, Manuel, CP16, 10:15 Mon Lahn, Nathaniel, CP10, 5:45 Sun Nebel, Markus, CP5, 2:50 Sun Sales, Marcelo, CP7, 3:40 Sun Lam, Chi-Kit, CP46, 4:55 Wed Nederlof, Jesper, CP18, 2:00 Mon Salmasi, Ario, CP10, 4:55 Sun Lamm, Sebastian, CP21, 5:45 Mon Nguyen, Huy L., CP8, 3:40 Sun Saona, Raimundo, CP32, 2:00 Tue Langowski, Simon H., CP5, 2:25 Sun Nusser, André, CP47, 4:55 Wed Schirneck, Martin, CP21, 5:20 Mon Larsen, Kasper G., CP40, 9:25 Wed Schlag, Sebastian, CP25, 10:15 Tue O Schramm, Tselil, CP38, 9:50 Wed Lazic, Ranko, CP38, 10:40 Wed Oh, Eunjin, CP7, 2:50 Sun Schwiegelshohn, Chris, CP31, 2:00 Tue Le, Hung, CP39, 9:50 Wed Oliveira, Roberto, CP9, 5:45 Sun Seddighin, Saeed, CP19, 3:40 Mon Levy, Caleb, CP22, 5:20 Mon Ophelders, Tim, CP47, 4:30 Wed Li, Shi, CP38, 9:00 Wed Seddighin, Saeed, CP27, 9:50 Tue Liu, Paul, CP41, 2:50 Wed P Seemaier, Daniel, CP25, 10:40 Tue Pajor, Thomas, CP17, 2:00 Mon Liu, Sixue, CP29, 2:50 Tue Sering, Leon, CP15, 10:40 Mon Panigrahi, Debmalya, CP3, 10:40 Sun Liu, Tianyu, CP36, 5:45 Tue Shameli, Ali, CP4, 10:40 Sun Pettie, Seth, CP41, 2:00 Wed Liu, Yang, CP43, 3:15 Wed Shi, Elaine, CP40, 9:50 Wed Pilipczuk, Michal, CP20, 3:40 Mon Livni Navon, Inbal R., CP35, 4:55 Tue Siebertz, Sebastian, CP24, 5:45 Mon Plaut, Benjamin, CP32, 3:40 Tue Lodha, Neha, CP21, 4:55 Mon Skoviera, Martin, CP37, 10:15 Wed Polyanskii, Nikita, CP20, 2:25 Mon Luchsinger, Austin, CP44, 3:40 Wed Solomon, Shay, CP31, 2:50 Tue Prusis, Krisjanis, CP28, 10:40 Tue Lyu, Kaifeng, CP2, 9:00 Sun Soma, Tasuku, CP43, 2:25 Wed Q Starikovskaya, Tatiana, CP19, 2:50 Mon M Quanrud, Kent, CP6, 2:50 Sun Sun, Yihan, CP25, 9:00 Tue Mallmann-Trenn, Frederik, CP16, 9:25 Szpankowski, Wojciech, IP1, 11:30 Sun Mon Quanrud, Kent, CP26, 10:40 Tue Mandal, Ritankar, CP7, 3:15 Sun Quanrud, Kent, CP33, 4:30 Tue T Manurangsi, Pasin, CP37, 10:40 Wed R Taki, Setareh, CP41, 3:40 Wed Martinsson, Anders, CP9, 4:30 Sun Raghunathan, Ananth, CP40, 10:15 Tan, Li-Yang, CP11, 4:55 Sun Marx, Dániel, IP2, 11:30 Mon Wed Tan, Zihan, CP24, 4:30 Mon Mastrolilli, Monaldo, CP8, 2:25 Sun Raichel, Benjamin A., CP39, 10:15 Tang, Zhihao Gavin, CP46, 6:10 Wed Meka, Raghu, CP42, 3:40 Wed Wed Tantipongpipat, Uthaipon, CP23, 4:55 Misra, Pranabendu, CP46, 4:30 Wed Rathi, Nidhi, CP32, 3:15 Tue Mon Rathod, Abhishek J., CP44, 2:50 Wed Teng, Yifeng, CP32, 2:25 Tue Reiffenhaeuser, Rebecca, CP32, 2:50 Tengse, Anamay, CP11, 5:20 Sun Tue Tseng, Thomas, CP17, 3:15 Mon Rika, Havana, CP10, 4:30 Sun Rösner, Clemens, CP47, 5:45 Wed Rote, Günter, CP20, 2:00 Mon Conference Program SODA, ALENEX, ANALCO and SOSA 2019 35

V Y Velingker, Ameya, CP45, 4:30 Wed Yogev, Eylon, CP27, 10:15 Tue Vesely, Pavel, CP3, 10:15 Sun Yogev, Eylon, CP27, 10:40 Tue Vincze, Roland, CP28, 10:15 Tue Yoshida, Yuichi, CP43, 2:50 Wed W Yu, Huacheng, CP30, 3:15 Tue Wajc, David, CP37, 9:50 Wed Yuster, Raphael, CP20, 2:50 Mon Wang, Di, CP43, 3:40 Wed Z Wang, Ruosong, CP30, 2:50 Tue Zamir, Or, CP22, 4:55 Mon Wang, Yipu, CP10, 5:20 Sun Zamir, Or, CP29, 3:40 Tue Warode, Philipp, CP15, 10:15 Mon Zehavi, Meirav, CP18, 2:25 Mon Wegrzycki, Karol, CP2, 10:40 Sun Zehavi, Meirav, CP28, 9:50 Tue Wei, Alexander, CP30, 2:00 Tue Zenklusen, Rico, CP26, 9:00 Tue Wei, Hengjia, CP35, 5:45 Tue Zhang, Chihao, CP36, 6:10 Tue Weiß, Armin, CP13, 9:00 Mon Zhang, Fred, CP15, 9:25 Mon Wellnitz, Philip, CP19, 2:25 Mon Zhang, Hengjie, CP14, 10:15 Mon Wild, Sebastian, CP5, 2:00 Sun Zhang, Hongyang, CP12, 5:45 Sun Wlodarczyk, Michal, CP28, 9:25 Tue Zhang, Tianyi, CP31, 3:15 Tue Wu, Ke, CP35, 6:10 Tue Zhong, Mingxian, CP20, 3:15 Mon X Zhong, Peilin, CP45, 6:10 Wed Xie, Tiancheng, CP40, 9:00 Wed Zuo, Song, CP4, 9:00 Sun Xu, Chao, CP33, 4:55 Tue Xu, Jiaming, CP16, 10:40 Mon Xue, Jie, CP7, 2:25 Sun Westin San Diego DA19 Abstracts 1

IP1 and selection problems that involve sets rather than just TowardsAnalysisofInformationContentinDy- individuals. This talk is based on joint work with Sendhil namic Networks Mullainathan, Manish Raghavan, and Maithra Raghu.

Shannon information theory has served as a bedrock for Jon M. Kleinberg advances in communication and storage systems over the Cornell University past six decades. However, this theory does not handle well Dept of Computer Science higher order structures (e.g., graphs, geometric structures), [email protected] temporal aspects (e.g., real-time considerations), or seman- tics, which are essential aspects of data and information that underlie a broad class of current and emerging data IP4 science applications. In this talk, we present some recent results on structural and temporal information in dynamic (Hardness of) Approximation and Expansion networks/graphs, in which nodes and edges are added and removed over time. We focus on two related problems: (i) Recently, there has been some exciting progress towards compression of structures – for a given graph model, we ex- proving the unique games conjecture. Is the conjecture hibit an efficient algorithm for invertibly mapping network true? experts are not sure. Still, it is clearly key to under- structures (i.e., graph isomorphism types) to bit strings of standing approximation algorithms for many optimization minimum expected length, and (ii) node arrival order in- problems, most notably constraint satisfaction. I will de- ference – for a dynamic graph model, we determine the scribe the background and consequences of the conjecture extent to which the order of node arrivals can be inferred and then focus on some interesting technical step pertain- from a snapshot of the graph structure. For both prob- ingtotheexpansion of the so-called Grassman graph. I lems, we apply analytic combinatorics, probabilistic, and will then describe a more general phenomenon called high information-theoretic methods to find statistical limits and dimensional expansion (HDX). HDX is family of a gener- efficient algorithms for achieving those limits. alizations of expansion in graphs to hypergraphs. This is Wojciech Szpankowski a new area of study and has potential for algorithms, as I Purdue University will try to show. Depratment of Computer Science [email protected] Irit Dinur Weizmann Institute [email protected] IP2 Recent Advances on the Complexity of Parameter- ized Counting Problems CP1

Research in the past few decades revealed that a many Ranked Schr¨oder Trees of the basic algorithmic problems are fixed-parameter tractable with various parameterizations: they can be In biology, a phylogenetic tree is a tool to represent the solved in time f(k)nc,wherek is some parameter of the evolutionary relationship between species. Unfortunately, input instance. There have been significant progress both the classical Schr¨oder tree model is not adapted to take into in the design of parameterized algorithms and in under- account the chronology between the branching nodes. In standing the limitations of these techniques. However, up particular, it does not answer the question: how many dif- until recent years, there were relatively few algorithmic ferent phylogenetic stories lead to the creation of n species and complexity results on parameterized counting prob- and what is the average time to get there? In this pa- lems. Similarly to what one experiences in the area of per, we enrich this model in two distinct ways in order to polynomial-time computations, there are natural parame- obtain two ranked tree models for phylogenetics, i.e. mod- terized problems where finding a single solution is fixed- els coding chronology. For that purpose, we first develop parameter tractable, but counting the number of solutions a model of (strongly) increasing Schr¨oder trees, symbol- is hard. In this talk, I will give a survey of recent develop- ically described in the classical context of increasing la- ments, including new results that give a clean and unified beling trees. Then we introduce a generalization for the explanation for the complexity of #k-Path, #k-Matching, labeling with some unusual order constraint in Analytic and many other parameterized counting problems. Combinatorics (namely the weakly increasing trees). Al- though these models are direct extensions of the Schr¨oder D´aniel Marx tree model, it appears that they are also in one-to-one cor- Hungarian Academy of Sciences (MTA SZTAKI), respondence with several classical combinatorial objects. Budapest,Hungary Through the paper, we present these links, exhibit some [email protected] parameters in typical large trees and conclude the studies with efficient uniform samplers. IP3 Antoine Genitrini Inherent Trade-Offs in Algorithmic Fairness Sorbonne University / LIP6 Recent discussion in the public sphere about classification [email protected] by algorithms has involved tension between competing no- tions of what it means for such a classification to be fair Olivier Bodini to different groups. We consider several of the key fairness LIPN, Universit´e Paris 13 conditions that lie at the heart of these debates, and discuss [email protected] recent research establishing inherent trade-offs between these conditions. We also consider a variety of methods Mehdi Naima for promoting fairness and related notions for classification Universit´e Paris-Nord 2 DA19 Abstracts

[email protected] of computer simulations.

Zbigniew Golebiewski, Mateusz Klimczak CP1 Wroclaw University of Science and Technology Reducing Simply Generated Trees by Iterative Leaf [email protected], ma- Cutting [email protected]

We consider a procedure to reduce simply generated trees CP1 by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted Combinatorics of Nondeterministic Walks of the after applying this procedure a fixed number of times by Dyck and Motzkin Type using an additive tree parameter model combined with a This paper introduces nondeterministic walks,anewvari- recursive characterization. Our results include asymptotic ant of one-dimensional discrete walks. At each step, a formulas for mean and variance of this quantity as well as nondeterministic walk draws a random set of steps from a central limit theorem. a predefined set of sets and explores all possible extensions in parallel. We introduce our new model on Dyck steps Benjamin Hackl with the nondeterministic steps {−1}, {1}, {−1, 1} and Alpen-Adria-Universit¨at Klagenfurt Motzkin steps with the nondeterministic steps {−1}, {0}, [email protected] {1}, {−1, 0}, {−1, 1}, {0, 1}, {−1, 0, 1}. For general lists of step sets and a given length, we express the generating Clemens Heuberger function of nondeterministic walks where at least one of Alpen-Adria-Universit¨at Klagenfurt, Austria the walks explored in parallel is a bridge (ends at the ori- [email protected] gin). In the particular cases of Dyck and Motzkin steps, we also compute the asymptotic probability that at least one Stephan Wagner of those parallel walks is a meander (stays nonnegative) Stellenbosch University, South Africa or an excursion (stays nonnegative and ends at the ori- [email protected] gin). This research is motivated by the study of networks involving encapsulations and decapsulations of protocols. Our results are obtained using generating functions and CP1 analytic combinatorics. Esthetic Numbers and Lifting Restrictions on the Analysis of Summatory Functions of Regular Se- Elie de Panafieu quences Nokia Bell Labs France depanafi[email protected] When asymptotically analysing the summatory function of a q-regular sequence in the sense of Allouche and Shallit, Mohamed Lamine Lamali, Michael Wallner the eigenvalues of the sum of matrices of the linear repre- LaBRI - Universit´e de Bordeaux, France sentation of the sequence determine the “shape’ (in partic- [email protected], wall- ular the growth) of the asymptotic formula. Existing gen- [email protected] eral results for determining the precise behavior (including the Fourier coefficients of the appearing fluctuations) have previously been restricted by a technical condition on these CP2 eigenvalues. The aim of this work is to lift these restric- Fast Modular Subset Sum Using Linear Sketching tions by providing an insightful proof based on generating functions for the main pseudo Tauberian theorem for all Given n positive integers, the Modular Subset Sum prob- cases simultaneously. (This theorem is the key ingredi- lem asks if a subset adds up to a given target t modulo ent for overcoming convergence problems in Mellin–Perron a given integer m. This is a natural generalization of the summation in the asymptotic analysis.) One example is Subset Sum problem (where m =+∞) with ties to additive discussed in more detail: A precise asymptotic formula for combinatorics and cryptography. Recently, in [Bringmann, the amount of esthetic numbers in the first N natural num- SODA’17] and [Koiliaris and Xu, SODA’17], efficient algo- bers is presented. Prior to this only the asymptotic amount rithms have been developed for the non-modular case, run- of these numbers with a given digit-length was known. ning in near-linear pseudo-polynomial time. For the mod- ular case, however, the best known algorithm by Koiliaris Clemens Heuberger,DanielKrenn and Xu [Koiliaris and Xu, SODA’17] runs in time O(m5/4). Alpen-Adria-Universit¨at Klagenfurt, Austria In this paper, we present an algorithm running in time [email protected], [email protected] O(m), which matches a recent conditional lower bound of [Abboud et al.’17] based on the Strong Exponential Time Hypothesis. Interestingly, in contrast to most previous re- CP1 sults on Subset Sum, our algorithm does not use the Fast Protection Number of Recursive Trees Fourier Transform. Instead, it is able to simulate the “text- book’ Dynamic Programming algorithm much faster, using The protection number of a tree is the minimal distance ideas from linear sketching. This is one of the first appli- from its root to a leaf. In this paper we are interested in cations of sketching-based techniques to obtain fast algo- the protection number of a uniformly chosen random recur- rithms for combinatorial problems in an offline setting. sive tree of size n. Due to different construction of plane oriented and non-plane recursive trees we consider them Kyriakos Axiotis separately. We use the singularity analysis of derived gen- Massachusetts Institute of Technology erating functions to find out the number of relevant trees, [email protected] which leads us to the probability distribution of the protec- tion number. Our results are also compared to outcomes Arturs Backurs DA19 Abstracts 3

Toyota Technological Institute at Chicago Ryan Williams [email protected] Massachusetts Institute of Technology [email protected] Ce Jin Institute for Interdisciplinary Information Sciences Tsinghua University CP2 [email protected] Fine-grained Complexity Meets IP = PSPACE

Christos Tzamos In this paper we study the fine-grained complexity of find- University of Wisconsin, Madison ing exact and approximate solutions to problems in P. Our [email protected] main contribution is showing reductions from an exact to an approximate solution for a host of such problems. As one (notable) example, we show that the Closest-LCS- Hongxun Wu Pair problem (Given two sets of strings A and B, com- Institute for Interdisciplinary Information Sciences pute exactly the maximum LCS(a,b) with (a, b) ∈ A × B) Tsinghua University is equivalent to its constant approximation version under [email protected] near-linear time reductions. More generally, we identify a class of problems, which we call BP-SAT-Equivalence- Class, comprising both exact and approximate solutions, CP2 and show that they are all equivalent under near-linear Seth-Based Lower Bounds for Subset Sum and Bi- time reductions. Exploring this class and its properties, we criteria Path also show: 1. Under the NC-SETH assumption (a signifi- cantly more relaxed assumption than SETH), solving any Subset Sum and k-SAT are two of the most extensively of the problems in this class requires essentially quadratic studied problems in computer science, and conjectures time. 2. Modest improvements on the running time of about their hardness are among the cornerstones of fine- known algorithms (shaving log factors) would imply that grained complexity. An important open problem in this NEXP is not in non-uniform NC1. 3. Finally, we leverage area is to base the hardness of one of these problems on our techniques to show new barriers for deterministic ap- the other. Our main result is a tight reduction from k-SAT proximation algorithms for LCS. At the heart of these new to Subset Sum on dense instances, proving that Bellman’s ∗ results is a deep connection between interactive proof sys- 1962 pseudo-polynomial O (T )-time algorithm for Subset tems for bounded-space computations and the fine-grained Sum on n numbers and target T cannot be improved to complexity of exact and approximate solutions to problems − time T 1 ε · 2o(n) for any ε>0, unless the Strong Expo- in P. In particular, our results build on the proof techniques nential Time Hypothesis (SETH) fails. As a corollary, we from the classical IP = PSPACE result. prove a “Direct-OR” theorem for Subset Sum under SETH, offering a new tool for proving conditional lower bounds: Lijie Chen, Shafi Goldwasser It is now possible to assume that deciding whether one out MIT of N given instances of Subset Sum is a YES instance re- [email protected], shafi@theory.csail.mit.edu quires time (NT)1−o(1). As an application of this corollary, we prove a tight SETH-based lower bound for the classi- Kaifeng Lyu cal Bicriteria Path problem, which is extensively studied Tsinghua University in Operations Research. We separate its complexity from [email protected] that of Subset Sum: On graphs with m edges and edge lengths bounded by L, we show that the O(Lm) pseudo- Guy Rothblum polynomial time algorithm by Joksch from 1966 cannot be Microsoft Research improved to O˜(L+m), in contrast to a recent improvement [email protected] for Subset Sum (Bringmann, SODA 2017). Aviad Rubinstein Amir Abboud Harvard University IBM Research Almaden [email protected] [email protected]

Karl Bringmann CP2 Max Planck Institute for Informatics, A Subquadratic Approximation Scheme for Parti- Saarland Informatics Campus, Germany tion [email protected] The subject of this paper is the time complexity of approx- Danny Hermelin, Dvir Shabtay imating Knapsack, Subset Sum, Partition, and some other Ben-Gurion University related problems. The main result is an O(n +1/ε5/3) [email protected], [email protected] time randomized FPTAS for Partition, which is derived from a certain relaxed form of a randomized FPTAS for Subset Sum. To the best of our knowledge, this is the first CP2 NP-hard problem that has been shown to admit a sub- An Equivalence Class for Orthogonal Vectors quadratic time approximation scheme, i.e., one with time complexity of O((n +1/ε)2−δ )forsomeδ>0. To put Abstract not available. these developments in context, note that a quadratic FP- TAS for Partition has been known for 40 years. Our main Lijie Chen contribution lies in designing a mechanism that reduces an MIT instance of Subset Sum to several simpler instances, each [email protected] with some special structure, and keeps track of interactions 4 DA19 Abstracts

between them. This allows us to combine techniques from Microsoft Research approximation algorithms, pseudo-polynomial algorithms, [email protected] and additive combinatorics. We also prove several related results. Notably, we improve approximation schemes for Michael B. Cohen 3SUM, (min,+)-convolution, and Tree Sparsity. Finally, MIT we argue why breaking the quadratic barrier for approxi- [email protected] mate Knapsack is unlikely by giving an Ω((n +1/ε)2−o(1)) conditional lower bound. James R. Lee, Yin Tat Lee University of Washington Marcin Mucha [email protected], [email protected] University of Warsaw Faculty of Mathematics, Informatics and Mechanics [email protected] CP3 k-Servers with a Smile: Online Algorithms via Pro- Karol Wegrzycki,MichalWlodarczyk jections University of Warsaw [email protected], We consider the k-server problem on trees and HSTs. [email protected] We give finite algorithms based on the standard convex- programming primitive of Bregman projections. These al- gorithms have competitive ratios that match some of the CP3 recent results given by Bubeck et al. (STOC 2018), whose A Nearly-Linear Bound for Chasing Nested Convex algorithms were not finite, but were based using mirror- Bodies descent-based continuous dynamics prescribed via a differ- ential inclusion. Friedman and Linial introduced the convex body chas- ing problem to explore the interplay between geometry Marco Molinaro and competitive ratio in metrical task systems. In con- Georgia Institute of Technology vexbodychasing,ateachtimestept ∈ N, the online al- School of Industrial and System Engineering gorithm receives a request in the form of a convex body [email protected] d Kt ⊂ R and must output a point xt ∈ Kt. The goal is to minimize the total movement between consecutive output Niv Buchbinder points, where the distance is measured in some given norm. Statistics and Operations Research Dept. This problem is still far from being understood. Recently d 2 Tel Aviv University, Israel Bansal et al. gave an 6 (d!) -competitive algorithm for [email protected] the nested version, where each convex body is contained within the previous one. We propose a different strategy which is O(d log d)-competitive algorithm for this nested Anupam Gupta convex body chasing problem. Our algorithm works for Carnegie Mellon University any norm. This result is almost tight, given an Ω(d)lower [email protected] bound for the ∞ norm. Joseph Naor C.J. Argue Technion Carnegie Mellon University [email protected] Carnegie Mellon University [email protected] CP3 Sebastien Bubeck Elastic Caching Microsoft Research [email protected] Motivated by applications in cloud computing, we study the classical online caching problem for a cache of variable MichaelB.Cohen size, where the algorithm pays a maintenance cost that MIT monotonically increases with cache size. This captures not [email protected] only the classical setting of a fixed cache size, which cor- responds to a maintenance cost of 0 for a cache of size at most k and ∞ otherwise, but also other natural settings Anupam Gupta in the context of cloud computing such as a concave rental Carnegie Mellon University cost on cache size. We call this the elastic caching problem. [email protected] For this problem, we provide several results: Yin Tat Lee • we give a randomized algorithm with a competitive University of Washington ratio of O(log n); [email protected] • for concave, or more generally submodular mainte- nance costs, we give a deterministic algorithm with a CP3 competitive ratio of 2; Metrical Task Systems on Trees Via Mirror De- • when the cost function is any monotone non-negative scent and Unfair Gluing set function, we give a deterministic n-competitive on- line algorithm; Abstract not available • for the offline version of the problem, we give a ran- Sebastien Bubeck domized constant-factor approximation algorithm. DA19 Abstracts 5

Our algorithms are based on a configuration LP formula- [email protected]ff.cuni.cz tion of the problem, for which our main technical contri- bution is to maintain online a feasible fractional solution that can be converted to an integer solution using existing CP4 rounding techniques. Multi-unit Supply-monotone Auctions with Bayesian Valuations Debmalya Panigrahi Duke University We design multi-unit auctions for budget-constrained bid- [email protected] ders in the Bayesian setting. This extends the work of Dobzinski, Lavi, and Nisan (Games and Economic Behav- Anupam Gupta ior, 2012) and Goel, Mirrokni, and Paes Leme (Games Carnegie Mellon University and Economic Behavior, 2015) from the adversarial to [email protected] the Bayesian setting. Our auctions are supply-monotone, which allows the auction to be run online without know- ing the number of items in advance, and achieve asymp- Ravishankar Krishnaswamy totic revenue-optimality compared to the offline revenue- Microsoft Research India maximizing auction (Pai and Vohra, Journal of Economic [email protected] Theory, 2014). We also give an efficient algorithm for im- plementing our auction by using a succinct and efficiently Amit Kumar implementable characterization of supply-monotonicity in IIT Delhi the Bayesian setting. This provides a generalization of suc- [email protected] cinct characterizations for single unit allocations due to Border (Journal of Econometric Society, 1991; Economic Theory 2007) and Cai, Daskalakis, and Weinberg (STOC, CP3 2012) to the multi-unit setting. A φ-Competitive Algorithm for Scheduling Packets Yuan Deng, Debmalya Panigrahi with Deadlines Duke University [email protected], [email protected] In the online packet scheduling problem with deadlines (PacketScheduling, for short), the goal is to schedule trans- missions of packets that arrive over time in a network CP4 switch and need to be sent across a link. Each packet has Tight Revenue Gaps among Simple Mechanisms a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can We consider a fundamental problem in microeconomics: be transmitted in any time slot, so, if the system is over- Selling a single item among a number of buyers whose loaded, some packets will inevitably miss their deadlines values are drawn from known independent and regular and be dropped. In this scenario, the natural objective distributions. There are four widely used and stud- is to compute a transmission schedule that maximizes the ied mechanisms in this literature: Anonymous Posted- total weight of packets which are successfully transmitted. Pricing (AP), Second-Price Auction with Anonymous Re- The problem is inherently online, with the scheduling de- serve (AR), Sequential Posted-Pricing (SPM) and Myerson cisions made without the knowledge of future packet ar- Auction (OPT). Myerson Auction is optimal but compli- rivals. The central problem concerning PacketScheduling, cated, which also suffers a few issues in practice such as that has been a subject of intensive study since 2001, is fairness; AP is the simplest mechanism, but its revenue is to determine the optimal competitive ratio of online algo- also the lowest among these four; AR and SPM are of in- rithms, namely the worst-case ratio between the optimum termediate complexity and revenue. We study the revenue total weight of a schedule (computed by an offline algo- gaps among these four mechanisms, which is defined as the rithm) and the weight of a schedule computed by a (de- largest ratio between revenues from two mechanisms. We terministic) online algorithm. We solve this open problem establish two tight ratios and one tighter bound: by presenting a φ-competitive online algorithm for Pack- • etScheduling (where φ ≈ 1.618 is the golden ratio), match- SPM/AP. This ratio studies the power of discrimina- ing the previously established lower bound. tion in pricing schemes. We obtain the tight ratio of roughly 2.62, closing the previous known bounds − Pavel Vesely [e/(e 1),e]. Department of Computer Science, University of Warwick, • AR/AP. This ratio studies the relative power of auc- UK tion vs. pricing schemes, when no discrimination is [email protected]ff.cuni.cz allowed. We get the tight ratio of π2/6 ≈ 1.64, clos- ing the previous known bounds [e/(e − 1),e]. Marek Chrobak • OPT/AR. This ratio studies the power of discrimina- Department of Computer Science tion in auctions. Previously, the revenue gap is known University of California at Riverside, US to be in interval [2,e], and the lower-bound of 2 is con- [email protected] jectured to be tight. We disprove this conjecture by obtaining a better lower-bound of 2.15. Lukasz Jez Tel Aviv University Yaonan Jin University of Wroclaw, Institute of Computer Science The Hong Kong University of Science and Technology [email protected] [email protected]

Jiri Sgall Pinyan Lu Computer Science Institute Shanghai University of Finance and Economics Charles University, Czech Republic [email protected] 6 DA19 Abstracts

Zhihao Gavin Tang with common reserve price, and (ii) when the number of The University of Hong Kong bidders is large, SPM converges to optimum. In addition, [email protected] we extend some results on approximation and computa- tional tractability for lookahead auctions to the correlation- Tao Xiao robust framework. Shanghai Jiao Tong University xt [email protected] Xiaohui Bei Nanyang Technological University [email protected] CP4 Assignment Mechanisms under Distributional Con- Nick Gravin, Pinyan Lu straints Shanghai University of Finance and Economics [email protected], [email protected] We study the assignment problem of objects to agents with heterogeneous preferences under distributional con- Zhihao Gavin Tang straints. Each agent is associated with a publicly known The University of Hong Kong type and has a private ordinal ranking over objects. We [email protected] are interested in assigning as many agents as possible. Our first contribution is a generalization of the well-known and widely used serial dictatorship. Our mechanism maintains CP4 several desirable properties of serial dictatorship, includ- Dynamic Double Auctions: Towards First Best ing strategyproofness, Pareto efficiency, and computational tractability while satisfying the distributional constraints We study the problem of designing dynamic double auc- with a small error. We also propose a generalization of tions for two-sided markets in which a platform intermedi- the probabilistic serial algorithm, which finds an ordinally ates the trade between one seller offering independent items efficient and envy-free assignment, and also satisfies the to multiple buyers, repeatedly over a finite horizon. Mo- distributional constraints with a small error. We show, tivated by online advertising and ride-hailing markets, we however, that no ordinally efficient and envy-free mecha- seek to design mechanisms satisfying the following proper- nism is also weakly strategyproof. Both of our algorithms ties: no positive transfers, i.e., the platform never asks the assign at least the same number of students as the optimum seller to make payments nor buyers are ever paid and peri- fractional assignment. odic individual rationality, i.e., every agent should derive a non-negative utility from every trade opportunity. We pro- Itai Ashlagi vide simple mechanisms satisfying these requirements that Stanford University are asymptotically efficient and budget-balanced with high [email protected] probability as the number of trading opportunities grows. Moreover, we show that the average expected profit ob- Amin Saberi tained by the platform under these mechanisms asymptot- Management Science and Engineering ically approaches first-best (the maximum possible welfare Stanford University generated by the market) either in the case of one buyer [email protected] and one seller, or multiple buyers and one seller with de- terministic values. Ali Shameli Stanford University Santiago Balseiro [email protected] Columbia University [email protected]

CP4 Vahab Mirrokni Correlation-robust Analysis of Single Item Auction Google Inc. [email protected] We investigate the problem of revenue maximization in single-item auction within the new correlation-robust Renato Paes Leme, Song Zuo framework proposed by Carroll [2017] and further devel- Google Research oped by Gravin and Lu [2018]. In this framework the auc- [email protected], [email protected] tioneer is assumed to have only partial information about marginal distributions, but does not know the dependency structure of the joint distribution. The auctioneer’s rev- CP5 enue is evaluated in the worst-case over the uncertainty QuickSort: Improved Right-Tail Asymptotics for of possible joint distribution. For the problem of opti- the Limiting Distribution, and Large Deviations mal auction design in the correlation robust-framework we observe that in most cases the optimal auction does not We refine asymptotic logarithmic upper bounds – extend- admit a simple form like the celebrated Myerson’s auc- ing from one term to three – produced by Svante Janson tion for independent valuations. We analyze and com- (2015) on the right tail of the limiting QuickSort distri- pare performances of several DSIC mechanisms used in bution function F and by Fill and Hung (2018) on the practice. Our main set of results concern the sequen- right tails of the corresponding density f and of the abso- tial posted-price mechanism (SPM). We show that SPM lute derivatives of f of each order. All our results match achieves a constant (4.78) approximation to the optimal two-term lower bounds for the functions in question to correlation-robust mechanism. We also show that in the two terms and match conjectured asymptotic expansions symmetric (anonymous) case when all bidders have the to three terms. Using the refined asymptotic bounds on F , same marginal distribution, (i) SPM has almost match- we derive right-tail large deviation (LD) results for the dis- ing worst-correlation revenue as any second price auction tribution of the number of comparisons required by Quick- DA19 Abstracts 7

Sort that sharpen somewhat the two-sided LD results of eral pivots reduces overall memory transfers, we have seen McDiarmid and Hayward (1996). renewed interest in multiway Quicksort. Here, we ana- lyze in how far multiway partitioning helps in Quickse- James Allen Fill, Wei-Chun Hung lect. We compute the expected number of comparisons Johns Hopkins University and scanned elements (approximating memory transfers) jimfi[email protected], [email protected] for a generic class of (non-adaptive) multiway Quickselect and show that three or more pivots are not helpful, but two pivots are. Moreover, we consider “adaptive’ variants CP5 which choose partitioning and pivot-selection methods in Moments of Select Sets each recursive step from a finite set of alternatives depend- ing on the current (relative) sought rank. We show that We analyze a selection procedure introduced by Krieger, “Sesquickselect’, a new Quickselect variant that uses either Pollak, and Samuel–Cahn. It retains an item if it is among one or two pivots, makes better use of small samples w.r.t. the top 100p percent, as compared to the items that have memory transfers than other Quickselect variants. been accepted so far. Gaither and Ward analyzed the aver- age behavior of the number of items selected. We present the asymptotic properties of the higher moments of the Sebastian Wild number of items retained by the selection procedure. We David R. Cheriton School of Computer Science derive a general formula for the moments. To demonstrate University of Waterloo the complexity of these moments, we present the exact [email protected] first-order asymptotic growth of some of these moments, for various rational values of p. Conrado Mart´ınez Department of Computer Science Simon H. Langowski, Mark Daniel Ward Univ. Polit`ecnica de Catalunya Purdue University [email protected] Department of Statistics [email protected], [email protected] Markus Nebel Universit¨at Bielefeld [email protected] CP5 Median-of-K Jumplists and Dangling-Min BSTs

We extend randomized jumplists introduced by CP6 Br¨onnimann et al. (STACS 2003) to choose jump- pointer targets as median of a small sample for better Stochastic Submodular Cover with Limited Adap- search costs, and present randomized algorithms with tivity expected O(log n) time complexity that maintain the prob- ability distribution of jump pointers upon insertions and In the submodular cover problem, we are given a non- deletions. We analyze the expected costs to search, insert negative monotone submodular function f over a ground and delete a random element, and we show that omitting set E of items, and the goal is to choose a smallest sub- jump pointers in small sublists hardly affects search costs, set S ⊆ E such that f(S)=Q where Q = f(E). In the but significantly reduces the memory consumption. We stochastic version of the problem, we are given m stochas- use a bijection between jumplists and “dangling-min tic items which are different random variables that inde- BSTs’, a variant of (fringe-balanced) binary search trees pendently realize to some item in E, and the goal is to for the analysis. Despite their similarities, some standard find a smallest set of stochastic items whose realization R analysis techniques for search trees fail for dangling-min satisfies f(R)=Q. The problem captures as a special trees (and hence for jumplists). case the stochastic set cover problem and more generally, stochastic covering integer programs. We study the role Sebastian Wild of adaptivity in the stochastic submodular cover problem. David R. Cheriton School of Computer Science We define an r-round adaptive algorithm to be an algo- University of Waterloo rithm that chooses a permutation of all available items in [email protected] each round k ∈ [r], and a threshold τk, and realizes items in the order specified by the permutation until the func- Markus Nebel tion value exceeds τk. Our main result is that for any Universit¨at Bielefeld integer r, there exists a poly-time r-round adaptive algo- [email protected] rithm for stochastic submodular cover whose expected cost is O˜(Q1/r) times the expected cost of a fully adaptive algo- Elisabeth Neumann rithm. We complement this result by showing that for any Carl-Friedrich-Gauß-Fakult¨at r, there exist instances of the stochastic submodular cover Technische Universit¨at Braunschweig, Germany problem where no r-round adaptive algorithm can achieve [email protected] better than Ω(Q1/r) approximation to the expected cost of a fully adaptive algorithm. CP5 Sesquickselect: One and a Half Pivots for Cache- Arpit Agarwal Efficient Selection PhD Student University of Pennsylvania Because of unmatched improvements in CPU performance, [email protected] memory transfers have become a bottleneck of program execution. As discovered in recent years, this also affects Sepehr Assadi, Sanjeev Khanna sorting in internal memory. Since partitioning around sev- University of Pennsylvania 8 DA19 Abstracts

[email protected], [email protected] oracle in expectation. The approximation guarantee and query complexity are optimal, and the adaptivity is nearly optimal. Moreover, the number of queries is substantially CP6 less than in previous works. Last, we extend our results to An Exponential Speedup in Parallel Running Time the submodular cover problem to demonstrate the gener- for Submodular Maximization Without Loss in Ap- ality of our algorithm and techniques. proximation Matthew Fahrbach Abstract not available Georgia Institute of Technology [email protected] Eric Balkanski, Aviad Rubinstein, Yaron Singer Harvard University Vahab Mirrokni [email protected], [email protected], Google Inc. [email protected] [email protected]

Morteza Zadimoghaddam CP6 Google Submodular Maximization with Nearly-optimal [email protected] Approximation and Adaptivity in Nearly-linear Time CP6 In this paper, we study the tradeoff between the approxi- Deterministic (1/2 + )-Approximation for Sub- mation guarantee and adaptivity for the problem of maxi- modular Maximization over a Matroid mizing a monotone submodular function subject to a car- dinality constraint. The adaptivity of an algorithm is the In this talk, we will consider the problem of maximizing a number of sequential rounds of queries it makes to the monotone submodular function subject to a matroid con- evaluation oracle of the function, where in every round straint and present a deterministic algorithm that achieves the algorithm is allowed to make polynomially-many par- (1/2 + )-approximation for the problem. This algorithm allel queries. Adaptivity is an important consideration in is the first deterministic algorithm known to improve over settings where the objective function is estimated using the 1/2-approximation ratio of the classical greedy algo- samples and in applications where adaptivity is the main rithm proved by Nemhauser, Wolsely and Fisher in 1978. running time bottleneck. Previous algorithms achieving anearly-optimal1− 1/e −  approximation require Ω(n) rounds of adaptivity. In this work, we give the first al- Niv Buchbinder gorithm that achieves a 1 − 1/e −  approximation using Statistics and Operations Research Dept. O(ln n/2) rounds of adaptivity. The number of function Tel Aviv University, Israel evaluations and additional running time of the algorithm [email protected] are O(n poly(log n, 1/)). Moran Feldman, Mohit Garg Alina Ene Open University of Israel Boston University [email protected], [email protected] [email protected]

Huy Nguyen CP6 Northeastern University Stochastic p Load Balancing and Moment Prob- [email protected] lems via the L-Function Method

This paper considers stochastic optimization problems CP6 whose objective functions involve powers of random vari- Submodular Maximization with Nearly Optimal ables. For example, consider the classic Stochastic lp Load Approximation, Adaptivity and Query Complexity Balancing Problem (SLBp): There are m machines and n jobs, and known independent random variables Yij de- Submodular optimization generalizes many classic prob- cribe the load incurred on machine i if we assign job j to lems in combinatorial optimization and has recently found it. The goal is to assign each jobs to machines in order to a wide range of applications in machine learning (e.g., fea- minimize the expected lp-norm of the total load on the ma- ture engineering and active learning). For many large-scale chines. While convex relaxations represent one of the most optimization problems, we are often concerned with the powerful algorithmic tools, in problems such as SLBp the adaptivity complexity of an algorithm, which quantifies the main difficulty is to capture the objective function in a way number of sequential rounds where polynomially-many in- that only depends on each random variable separately. We dependent function evaluations can be executed in paral- show how to capture p-power-type objectives in such sep- lel. While low adaptivity is ideal, it is not sufficient for a arable way by using the L-function method, introduced by distributed algorithm to be efficient, since in many practi- Latala to relate the moment of sums of random variables to cal applications of submodular optimization the number the individual marginals. We show how this quickly leads of function evaluations becomes prohibitively expensive. to a constant-factor approximation for very general subset Motivated by these applications, we study the adaptivity selection problem with p-moment objective. Moreover, we and query complexity of adaptive submodular optimiza- give a constant-factor approximation for SLBp, improv- tion. Our main result is a distributed algorithm for max- ing on the recent O(p/ ln p)-approximation of [Gupta et imizing a monotone submodular function with cardinality al., SODA 18]. Here the application of the method is constraint k that achieves a (1 − 1/e − ε)-approximation much more involved. In particular, we need to sharply in expectation. This algorithm runs in O(log(n)) adaptive connect the expected lp-norm of a random vector with the rounds and makes O(n) calls to the function evaluation p-moments of its marginals (machine loads), taking into ac- DA19 Abstracts 9

count simultaneously the different scales of the loads that The Hong Kong University of Science and Technology are incurred by an unknown assignment. [email protected]

Marco Molinaro Guilherme D. da Fonseca Georgia Institute of Technology Universit´e Clermont Auvergne, LIMOS School of Industrial and System Engineering France [email protected] [email protected]

CP6 David M. Mount University of Maryland Submodular Function Maximization in Parallel via [email protected] the Multilinear Extension

Balkanski and Singer [5] recently initiated the study of adaptivity (or parallelism) for constrained submodular CP7 function maximization, and studied the setting of a car- New Lower Bounds for the Number of Pseudoline dinality constraint. Very recent improvements for this Arrangements problem by Balkanski, Rubinstein, and Singer [6] and Ene and Nguyen [21] resulted in a near-optimal (1 − 1/e − )- Arrangements of lines and pseudolines are fundamental ob- approximation in O(log n/2) rounds of adaptivity. Partly jects in discrete and computational geometry. They also motivated by the goal of extending these results to more appear in other areas of computer science, such as the general constraints, we describe parallel algorithms for ap- study of sorting networks. Let Bn be the number of ar- proximately maximizing the multilinear relaxation of a rangements of n pseudolines and let bn =log2 Bn.The monotone submodular function subject to packing con- problem of estimating Bn was posed by Knuth in 1992. ≤ n 2 straints. Formally our problem is to maximize F (x)over Knuth conjectured that bn 2 + o(n ) and also derived ∈ n ≤ 2 x [0, 1] subject to Ax 1whereF is the multilinear the first upper and lower bounds: bn ≤ 0.7924(n + n) 2 relaxation of a monotone submodular function. Our algo- and bn ≥ n /6 − O(n). The upper bound underwent sev- − − 2 rithm achieves a near-optimal (1 1/e )-approximation eral improvements, bn ≤ 0.6988n (Felsner, 1997), and 2 4 2 in O(log m log n/ ) rounds where n is the cardinality of bn ≤ 0.6571n (Felsner and Valtr, 2011), for large n.Here 2 the ground set and m is the number of packing constraints. we show that bn ≥ cn − O(n log n)forsomeconstant 2 For many constraints of interest, the resulting fractional c>0.2053. In particular, bn ≥ 0.2053 n for large n.This 2 solution can be rounded via known randomized rounding improves the previous best lower bound, bn ≥ 0.1887n , schemes that are oblivious to the specific submodular func- due to Felsner and Valtr (2011). Our arguments are ele- tion. We thus derive randomized algorithms with poly- mentary and geometric in nature. Further, our construc- logarithmic adaptivity for a number of constraints includ- tions are likely to spur new developments and improved ing partition and laminar matroids, matchings, knapsack lower bounds for related problems, such as in topological constraints, and their intersections. graph drawings.

Chandra Chekuri, Kent Quanrud Adrian Dumitrescu University of Illinois at Urbana-Champaign Department of Computer Science [email protected], [email protected] University of Wisconsin-Milwaukee [email protected] CP7 Ritankar Mandal Approximate Nearest Neighbor Searching with University of Wisconsin–Milwaukee, USA Non-euclidean and Weighted Distances [email protected] We present a new approach to ε-approximate nearest- neighbor searching in Rd for fixed d under a variety of dis- tance functions including the Bregman divergence, the Ma- CP7 halanobis distance, the Minkowski metric, multiplicative Optimal Algorithm for Geodesic Nearest-point weights, and convex scaling distance functions. The most Voronoi Diagrams in Simple Polygons efficient data structure previously known for the Euclidean metric resisted generalization because of its reliance on the Given a set of m point sites in a simple polygon, the lifting transformation, and the best known approaches for geodesic nearest-point Voronoi diagram of the sites par- other distance functions are far less efficient. We circum- titions the polygon into m Voronoi cells, one cell per site, vent the reliance on the lifting transformation by a careful such that every point in a cell has the same nearest site application of convexification. While this technique is well under the geodesic metric. In this paper, we present an known in the field of non-linear optimization, it appears to O(n + m log m)-time algorithm for computing the geodesic be relatively new to computational geometry. Under mild nearest-point Voronoi diagram of m points in a simple n- assumptions on the distance functions in question, the pro- gon. This matches the best known lower bound of Ω(n + posed data structures answer queries in logarithmic time m log m) as well as improving the previously best known with storage O(n log(1/ε)/εd/2), where n is the number of algorithms which take time O(n + m log m + m log2 n)and data points. This nearly matches the best known results O(n log n + m log m). This answers the longstanding ques- for the Euclidean metric. tion whether the geodesic nearest-point Voronoi diagram can be computed optimally, which was explicitly posed by Ahmed Abdelkader Aronov [Algorithmica, 1989] and Mitchell [Handbook of University of Maryland Computational Geometry, 2000]. [email protected] Eunjin Oh Sunil Arya Max Planck Institute for Informatics 10 DA19 Abstracts

[email protected] sign efficient (1 + ε)-approximate CRCP data structures for orthogonal queries in the plane, where ε>0isapre- specified parameter. The highlights are two data struc- CP7 tures for answering rectangle queries, one of which uses −1 4 4 −1 3 −2 Extremal and Probabilistic Results for Order O(ε n log n)spaceandO(log n + ε log n + ε log n) −1 3 Types query time while the other uses O(ε n log n)spaceand O(log5 n + ε−1 log4 n + ε−2 log2 n) query time. In addi- A configuration is a finite set of points in the plane. Two tion, we also apply our techniques to the CRCP problem configurations A and B have the same order type if there in higher dimensions, obtaining efficient data structures for exists a bijection between them preserving the orienta- slab, 2-box, and 3D dominance queries. tion of every ordered triple. We investigate extremal and probabilistic problems related to configurations in general Jie Xue position. We focus on problems involving forbidden con- University of Minnesota, Twin Cities figurations or monotone/hereditary properties. Given a [email protected] configuration B, we consider the property of being “B- free’: a configuration A is B-free if no subset of points of A has the same order type as B. We prove a signifi- CP8 cant bound on the number of B-free N-point configurations An Algorithmic Blend of LPs and Ring Equations containedinthem × m grid [m]2 for arbitrary configura- for Promise CSPs tions B. We consider random N-point configurations U in the unit square, in which each of the N points is cho- Promise CSPs are a relaxation of constraint satisfaction sen uniformly at random and independently of all other problems where the goal is to find an assignment satisfying points. The above-mentioned enumeration result for B- a relaxed version of the constraints. Promise CSPs in- free configurations in the grid is then used to prove strong clude approximate graph coloring, discrepancy minimiza- bounds for the probability that the random set U should be tion, and interesting variants of satisfiability. Similar to B-free for any given B. We also investigate the threshold CSPs, the tractability of promise CSPs can be tied to the function N0 = N0(n) for the property that U should be n- structure of operations on the solution space called poly- universal, that is, should contain all n-point configurations morphisms, though in the promise world these operations in general position. As it turns out, N0 = N0(n) is doubly are much less constrained. In previous work, we classified exponential in n. Our arguments are mostly geometric and Boolean promise CSPs when the constraint predicates are combinatorial, with the recent container method playing an symmetric. In this work, we vastly generalize these algo- important role. rithmic results. Specifically, we show that promise CSPs that admit a family of ”regional-periodic” polymorphisms Jie Han are in P, assuming that determining which region a point University of Rhode Island is in can be computed in polynomial time. Our algorithm jie [email protected] is based on a novel combination of linear programming and solving linear systems over rings. We also abstract a frame- Yoshiharu Kohayakawa work based on reducing a promise CSP to a CSP over an Instituto de Matematica e Estatistica infinite domain, solving it there, and then rounding the Universidade de S˜ao Paulo, Brazil solution to an assignment for the promise CSP instance. [email protected] The rounding step is intimately tied to the family of poly- morphisms and clarifies the connection between polymor- phisms and algorithms in this context. As a key ingredient, Marcelo Sales we introduce the technique of finding a solution to an LP Emory University with integer coefficients that lies in a different ring to by- [email protected] pass ad-hoc adjustments for lying on a rounding boundary.

Henrique Stagni Joshua Brakensiek, Venkatesan Guruswami University of Sao Paulo Carnegie Mellon University [email protected] [email protected], [email protected]

CP7 CP8 Colored Range Closest-Pair Problem under Gen- Perfect Matchings, Rank of Connection Tensors eral Distance Functions and Graph Homomorphisms

The range closest-pair (RCP) problem is the range-search We develop a theory of graph algebras over general fields. version of the classical closest-pair problem, which aims This is modeled after the theory developed by Freed- to store a given dataset of points in some data struc- man, Lov´asz and Schrijver in ”[Michael Freedman, L´aszl´o ture such that when a query range X is specified, the Lov´asz, Alexander Schrijver, Reflection positivity, rank closest pair of points contained in X can be reported ef- connectivity, and homomorphism of graphs]” for connec- ficiently. A natural generalization of the RCP problem tion matrices, in the study of graph homomorphism func- is the colored RCP (CRCP) problem in which the given tions over real edge weight and positive vertex weight. We data points are colored and the goal is to find the clos- introduce connection tensors for graph properties. This est bichromatic pair contained in the query range. All notion naturally generalizes the concept of connection ma- the previous work on the RCP problem was restricted to trices. It is shown that counting perfect matchings, and a the uncolored version and the Euclidean distance function. host of other graph properties naturally defined as Holant In this paper, we make the first progress on the CRCP problems (edge models), cannot be expressed by graph ho- problem. We investigate the problem under a general dis- momorphism functions over the complex numbers (or even tance function induced by a monotone norm; this covers more general fields). Our necessary and sufficient condi- all Lp-metrics for p>0andtheL∞-metric. We de- tion in terms of connection tensors is a simple exponential DA19 Abstracts 11

rank bound. It shows that positive semidefiniteness is not IDSIA, University of Lugano needed in the more general setting. [email protected]

Jin-Yi Cai University of Wisconsin, Madison CP8 [email protected] Fast Greedy for Linear Matroids

Artsiom Hovarau A fundamental algorithmic result for matroids is that the University of Wisconsin-Madison maximum weight base can be computed using the greedy [email protected] algorithm. For explicitly represented matroids an impor- tant question is the time complexity of computing such a base. It is known that one can compute it in time almost CP8 linear in the number of non-zero entries of the linear rep- Probabilistic Tensors and Opportunistic Boolean resentation plus rω,wherer is the rank of the matroid and Matrix Multiplication ω is the matrix multiplication exponent. In this work, we give an alternative algorithm for the same task. We introduce probabilistic extensions of classical determin- istic measures of algebraic complexity of a tensor, such Huy L. Nguyen as the rank and the border rank. We show that these Northeastern University probabilistic extensions satisfy various natural and algo- [email protected] rithmically serendipitous properties, such as submultiplica- tivity under taking of Kronecker products. Furthermore, the probabilistic extensions enable improvements over their CP9 deterministic counterparts for specific tensors of interest, Subcritical Random Hypergraphs, High-Order starting from the tensor 2, 2, 2 that represents 2×2matrix Components, and Hypertrees multiplication. While it is well known that the (determin- istic) tensor rank and border rank satisfy In the binomial random graph G(n, p), when p changes from (1−ε)/n (subcritical case) to 1/n andthento(1+ε)/n rk 2, 2, 2 =7 and rk 2, 2, 2 =7 (supercritical case) for ε>0, with high probability the [V. Strassen, Numer. Math. 13 (1969); J. E. Hopcroft and order of the largest component increases smoothly from L. R. Kerr, SIAM J. Appl. Math. 20 (1971); S. Winograd, O(ε−2 log(ε3n)) to Θ(n2/3) and then to (1 ± o(1))2εn.As Linear Algebra Appl. 4 (1971); J. M. Landsberg, J. AMS a natural generalisation of random graphs and connected- 19 (2006)], we show that the probabilistic tensor rank and ness, we consider the binomial random k-uniform hyper- border rank satisfy graph H k(n, p)(whereeachk-tupleofverticesispresent 6 2 as a hyperedge with probability p independently) and the rk 2, 2, 2 ≤6+ and rk 2, 2, 2 ≤6+ . 7 3 following notion of high-order connectedness. Given an integer 1 ≤ j ≤ k − 1, two sets of j vertices are called By submultiplicativity, this leads immediately to novel ran- j-connected if there is a walk of hyperedges between them domized algorithm designs, such as algorithms for Boolean such that any two consecutive hyperedges intersect in at matrix multiplication as well as detecting and estimating least j vertices. A j-connected component is a maximal the number of triangles and other subgraphs in graphs. collection of pairwise j-connected j-tuples of vertices. Re- cently, the threshold for the appearance of the giant j- Petteri Kaski, Matti Karppa k Aalto University connected component in H (n, p) and its order were deter- Department of Computer Science mined. In this article, we take a closer look at the subcrit- petteri.kaski@aalto.fi, matti.karppa@aalto.fi ical random hypergraph. We determine the structure and size (i.e. number of hyperedges) of the largest j-connected components, with the help of a certain class of ‘hypertrees’ CP8 and related objects. In our proofs, we combine various The Complexity of the Ideal Membership Problem probabilistic and enumerative techniques, such as generat- for Constrained Problems Over the Boolean Do- ing functions and couplings with branching processes. main Wenjie Fang, Oliver Cooley, Nicola Del Giudice Given an ideal I and a polynomial f the Ideal Membership Graz University of Technology Problem is to test if f ∈ I. This problem is a funda- [email protected], [email protected], mental algorithmic problem with important applications [email protected] and notoriously intractable. We study the complexity of the Ideal Membership Problem for combinatorial ideals Mihyun Kang that arise from constrained problems over the Boolean do- Technische Universitaet Graz main. As our main result, we identify the precise border- Institut fuer Optimierung und Diskrete Mathematik line of tractability. By using Gr¨obner bases techniques, [email protected] we generalize Schaefer’s dichotomy theorem [STOC, 1978] which classifies all Constraint Satisfaction Problems over the Boolean domain to be either in P or NP-hard. This CP9 paper is motivated by the pursuit of understanding the Degree Distributions of Generalized Hooking Net- recently raised issue of bit complexity of Sum-of-Squares works proofs [O’Donnell, ITCS, 2017]. Raghavendra and Weitz [ICALP, 2017] show how the Ideal Membership Problem A hooking network is grown from a set of graphs called tractability for combinatorial ideals implies bounded coef- blocks, each block with a labelled vertex called a hook. At ficients in Sum-of-Squares proofs. each step in the growth of the network, a vertex called a latch is chosen from the hooking network, and a block is Monaldo Mastrolilli attached by joining the hook of the block with the latch. 12 DA19 Abstracts

These graphs generalize trees, which are hooking networks randomly chosen hyperedges satisfy an appropriate notion grown from a single edge as the only block. Using P´olya limited independence. We leave several open problems re- urns, we show multivariate normal limit laws for the degree lated to these quasi-random hypergraphs and the thresh- distributions of hooking networks. We extend previous re- olds of associated problem variations. sults by allowing for more than one block in the growth of the network and by studying arbitrarily large degrees. Michael Mitzenmacher Harvard University Colin Desmarais [email protected] Uppsala University [email protected] CP9 Cecilia Holmgren Random Walks on Graphs: New Bounds on Hit- Uppsala University ting, Meeting, Coalescing and Returning Department of Mathematics [email protected] We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return prob- abilities P t(x, x) and the maximum expected hitting time CP9 thit, both in terms of the relaxation time. We also prove When Does Hillclimbing Fail on Monotone Func- a discrete-time version of the first-named author’s “Meet- tions? ing time lemma” that bounds the probability of a random walk hitting a deterministic trajectory in terms of hitting Hillclimbing is an essential part of optimization. An im- times of static vertices. The meeting time result is then portant benchmark for hillclimbing algorithms on functions used to bound the expected full coalescence time of mul- f : {0, 1}n → R are (strictly) montone functions, on which tiple random walks over a graph. This last theorem is a a surprising number of hillclimbers fail to be efficient. For discrete-time version of a result by the first-named author, example, the (1 + 1)-Evolutionary Algorithm is a standard which had been previously conjectured by Aldous and Fill. hillclimber which flips each bit independently with prob- Our bounds improve on recent results by Lyons and Oveis- ability c/n in each round. Perhaps surprisingly, this al- Gharan; Kanade et al; and (in certain regimes) Cooper et gorithm shows a phase transition: it optimizes any such al. monotone function in quasilinear time if c<1, while, on the other hand, it is known how to construct monotone Roberto Oliveira functions for which the algorithm needs exponential time IMPA, Rio de Janeiro if c is sufficiently large. As the previsouly known argument [email protected] for quasilinear running time breaks down at c =1,itis natural to suspect that the phase transition should occur Yuval Peres at this value. We here present a new runtime analysis for Microsoft Research, Redmond the (1 + 1)-EA which shows that this is not the case. More [email protected] precisely, there is a c0 > 1 such that the running time of the algorithm remains quasilinear for c

matching) in Kh-minor free graphs with h = O(1) and [email protected] integer edge weights having magnitude at most C.This improves upon the O˜(n10/7 log C) algorithm of Cohen et al. [SODA 2017] and the O(n3/2 log(nC)) algorithm of CP10 Gabow and Tarjan [SIAM J. Comput. 1989]. For a graph On Constant Multi-Commodity Flow-Cut Gaps for with m edges and n vertices, the Hopcroft-Karp [SIAM J. Families of Directed Minor-Free Graphs Comput. 1973], and Gabow-Tarjan algorithms compute, in each phase, a maximal set of vertex-disjoint shortest aug- The multi-commodity flow-cut gap is a fundamental pa- menting paths (for appropriately defined costs) in O(m) rameter that affects the performance of several divide & time.√ These algorithms arrive at an optimal matching√ af- conquer algorithms, and has been extensively studied for ter O( n) phases with a total execution time of O(m n). various classes of undirected graphs. It has been shown To obtain our speed-up, we relax the conditions on the by Linial, London and Rabinovich [1994] and by Aumann augmenting paths and compute, in each phase, a set of and Rabani [1998] that for general n-vertex graphs it is augmenting paths that are not restricted to be shortest or bounded by O(log n) and the Gupta-Newman-Rabinovich- vertex-disjoint. As a result, our algorithm computes sub- Sinclair conjecture [2004] asserts that it is O(1) for any stantially more augmenting paths√ in each phase, reducing family of graphs that excludes some fixed minor. The the number of phases from O( n)toO(n2/5). By using flow-cut gap is poorly understood for the case of directed small vertex separators, the execution of each phase takes graphs. We show that for uniform demands it is O(1) on O˜(m) time on average. For planar graphs, we combine our directed series-parallel graphs, and on directed graphs of algorithm with efficient shortest path data structures to ob- bounded pathwidth. These are the first constant upper tain a minimum-cost perfect matching in O˜(n6/5 log (nC)) bounds of this type for some non-trivial family of directed graphs. We also obtain O(1) upper bounds for the general time. This improves upon the recent O˜(n4/3 log (nC)) time multi-commodity flow-cut gap on directed trees and cycles. algorithm by Asathulla et al. [SODA 2018]. These bounds are obtained via new embeddings and Lip- schitz quasipartitions for quasimetric spaces, which gener- Nathaniel Lahn, Sharath Raghvendra alize analogous results form the metric case, and could be Virginia Tech of independent interest. Finally, we discuss limitations of [email protected], [email protected] methods that were developed for undirected graphs, such as random partitions, and random embeddings.

Ario Salmasi CP10 The Ohio State University [email protected] Flow-Cut Gaps and Face Covers in Planar Graphs Anastasios Sidiropoulos University of Illinois at Chicago The relationship between the sparsest cut and the maxi- [email protected] mum concurrent multi-flow in graphs has been studied ex- tensively. For general graphs with k terminal pairs, the flow-cut gap is O(log k), and this is tight. For planar Vijay Sridhar graphs, it has been conjectured that their flow-cut gap is Mathworks [email protected] O(1), while the known bounds place the gap somewhere√ between 2 (Lee and Raghavendra, 2003) and O( log k) (Rao, 1999). Okamura and Seymour (1981) show that CP10 when all the terminals of a planar network lie on a sin- gle face, the flow-cut gap is exactly 1. This setting can Maximum Integer Flows in Directed Planar be generalized by considering planar networks where the Graphs with Vertex Capacities and Multiple terminals lie on γ>1 faces in some fixed planar draw- Sources and Sinks ing. Lee and Sidiropoulos (2009) proved that the flow-cut gap is bounded by a function of γ, and Chekuri, Shep- We consider the problem of finding maximum flows in pla- herd, and Weibel (2013) showed that the gap is at most nar graphs with capacities on both vertices and arcs and 3γ. We prove that the flow-cut gap is O(log γ), by show- with multiple sources and sinks. We present three algo- ing that the edge-weighted shortest-path metric induced on rithms when the capacities are integers. The first algo- 3 the terminals admits a stochastic embedding into trees with rithm runs in O(n log n + kn) time when all capacities are distortion O(log γ), which is tight. For vertex-capacitated bounded, where n is the number of vertices in the graph networks, Lee, Mendel, and Moharrami (2015) showed that and k is the number of terminals. This algorithm is the first the vertex-capacitated flow-cut gap is O(1) on planar net- to solve the vertex-disjoint paths problem in near-linear works whose terminals lie on a single face. We prove that time when k is bounded but larger than 2. The second 5 the flow-cut gap is O(γ) for vertex-capacitated instances algorithm runs in O(k n polylog(nU)) time, where U is when the terminals lie on γ>1 faces. In fact, this result the largest finite capacity of a single vertex. Finally, when holds in the more general setting of submodular vertex ca- k = 3, we present an algorithm that runs in O(n log n) pacities. time; this algorithm works even when the capacities are arbitrary reals. Our algorithms improve on the fastest previously known algorithms when k is bounded and U Havana Rika, Robert Krauthgamer is bounded by a polynomial in n. Prior to this result, the Weizmann Institute of Science fastest algorithms ran in O(n2/ log n) time for real capaci- [email protected], ties, O(n3/2 log n log U) for integer capacities, and O˜(n10/7) [email protected] for unit capacities, even when k =3.

James R. Lee Yipu Wang University of Washington University of Illinois at Urbana-Champaign 14 DA19 Abstracts

[email protected] such graphs in log-space.

Yang Liu CP11 Stanford University Quantum Algorithms and Approximating Polyno- [email protected] mials for Composed Functions with Shared Inputs Ofer Grossman We give faster quantum algorithms for evaluating com- Berkeley posed functions whose inputs may be shared between [email protected] bottom-level gates. Let f be a Boolean function and con- sider a function F obtained by applying f to conjunc- tions of possibly overlapping subsets of n variables. If CP11 f has quantum query complexity Q(f), we give an al- A Deterministic PTAS for the Algebraic Rank of gorithm for evaluating F using O˜( Q(f) · n)√ quantum Bounded Degree Polynomials queries. This improves on the bound of O(Q(f) · n)that follows by treating each conjunction independently, and is We consider the problem of computing the algebraic rank tight for worst-case choices of f. Using completely different of a given set of multivariate polynomials over a field of techniques, we prove a similar tight composition theorem characteristic zero. The notion of algebraic rank natu- for the approximate degree of f. By recursively apply- rally generalizes the notion of rank in linear algebra. The ing our composition theorems, we obtain a nearly optimal decision version of the problem is equivalent to the cel- − −d ebrated Polynomial Identity Testing (PIT) problem. A O˜(n1 2 ) upper bound on the quantum query complexity randomized polynomial time algorithm for this problem is and approximate degree of linear-size depth-d AC0 circuits. known thanks to the classical Jacobian criterion, and the As a consequence, such circuits can be PAC learned in Schwartz-Zippel lemma. However, no deterministic algo- subexponential time, even in the challenging agnostic set- rithm is known. In fact, a deterministic algorithm would ting. Prior to our work, a subexponential-time algorithm imply a deterministic algorithm for the PIT problem which was not known even for linear-size depth-3 AC0 circuits. itself would imply circuit complexity lower bounds (Ka- We also show that any substantially faster learning algo- banets, Impagliazzo, STOC’03). We present a determin- rithm will require fundamentally new techniques. istic polynomial time approximation scheme (PTAS) for Mark Bun computing the algebraic rank of a set of bounded degree Simons Institute for the Theory of Computing polynomials. More specifically, we give an algorithm that { }⊂F [email protected] takes as input a set f := f1,...,fn [x1,...,xm]of polynomials with degrees bounded by d, and a rational d2 nmd O( ) · Robin Kothari number >0 and runs for time O((  ) M(n)), Microsoft Research where M(n) is the time required to compute the rank of [email protected] an n × n matrix (with field entries), and finally outputs a number r, such that r is at least (1 − ) times the algebraic Justin Thaler rank of f. Georgetown University Vishwas Bhargava [email protected] Rutgers University [email protected] CP11 Markus Bl¨aser Reproducibility and Pseudo-determinism in Log- Saarland University space [email protected] A curious property of randomized log-space search algo- rithms is that their outputs are often longer than their Gorav Jindal workspace. This leads to the question: how can we repro- Aalto University duce the results of a randomized log space computation [email protected] without storing the output or randomness verbatim? Run- ning the algorithm again with new random bits may result Anurag Pandey in a new (and potentially different) output. We show that Max-Planck-Institut fuer Informatik every problem in search-RL has a randomized log-space [email protected] algorithm where the output can be reproduced. Specifi- cally, we show that for every problem in search-RL, there are a pair of log-space randomized algorithms A and B CP11 where for every input x, A will output some string tx of Pseudorandomness for Read-k DNF Formulas size O(log n), such that B when running on (x, tx) will be pseudo-deterministic: that is, running B multiple times The design of pseudorandom generators and determinis- on the same input (x, tx) will result in the same output tic approximate counting algorithms for DNF formulas on all executions with high probability. Thus, by storing are important challenges in unconditional derandomiza- only O(log n) bits in memory, it is possible to reproduce tion. Numerous works on these problems have focused on the output of a randomized log-space algorithm. An algo- the subclass of small-read DNF formulas, which are for- rithm is reproducible without storing any bits in memory mulas in which each variable occurs a bounded number of (i.e., |tx| = 0) if and only if it is pseudo-deterministic. We times. Our first main result is a pseudorandom genera- show pseudo-deterministic algorithms for finding paths in tor which ε-fools M-term read-k DNFs using seed length undirected graphs and Eulerian graphs using logarithmic poly(k, log(1/ε)) · log M + O(log n). This seed length is ex- space. Our algorithms are substantially faster than the ponentially shorter, as a function of both k and 1/ε,than best known deterministic algorithms for finding paths in the best previous PRG for read-k DNFs. We also give a DA19 Abstracts 15

deterministic algorithm that approximates the number of the first (1 + )-approximation algorithm running in time satisfying assignments of an M-term read-k DNF to any npoly(k/).Further,forp = 0, we give the first almost-linear desired (1 + ε)-multiplicative accuracy in time time approximation scheme for what we call the General- ˜ ized Binary 0-Rank-k problem. Our algorithm computes · poly(k,log(k/ε)) O(log((k log M)/ε)) O(k) 2 poly(n) min (M/ε) , (M/ε) . (1 + )-approximation in time (1/)2 / · nd1+o(1).On the hardness of approximation side, for p ∈ (1, 2), assum- The common essential ingredients in these pseudorandom- ing the Small Set Expansion Hypothesis and the Expo- ness results are new analytic inequalities for read-k DNFs. nential Time Hypothesis (ETH), we show that there exists These inequalities may be of independent interest and util- δ := δ(α) > 0 such that the entrywise p-Rank-k problem δ ity; as an example application, we use them to obtain a k significant improvement on the previous state of the art has no α-approximation algorithm running in time 2 . for agnostically learning read-k DNFs. Frank Ban Rocco A. Servedio, Li-Yang Tan UC Berkeley Columbia University [email protected] [email protected], [email protected] Vijay Bhattiprolu CMU CP11 [email protected] Near-optimal Bootstrapping of Hitting Sets for Al- gebraic Circuits Karl Bringmann Max Planck Institute for Informatics, The classical lemma of Ore-DeMillo-Lipton-Schwartz- Saarland Informatics Campus, Germany Zippel states that any nonzero n-variate degree-s polyno- [email protected] mial f, will evaluate to a nonzero value at some point on a grid Sn with |S| >s. Thus, there is a deterministic poly- nomial identity test (PIT) for all degree-s size-s algebraic Pavel Kolev circuits in n variables that runs in time poly(s)(s +1)n. MPI-INF In a surprising recent result, Agrawal, Ghosh and Saxena [email protected] (STOC’18) showed any deterministic blackbox PIT algo- rithm for degree-s,size-s, n-variate circuits with running Euiwoong Lee 0.5−δ time as bad as sn ,whereδ>0,canbeusedtocon- Carnegie Mellon University struct blackbox PIT algorithms for degree-s size s circuits [email protected] ∗ with running time sexp(exp(O(log s))). The authors asked if a similar conclusion followed if their hypothesis was weak- David Woodruff CMU ened to having deterministic PIT with running time so(n). [email protected] In this paper, we answer their question in the affirmative. We show that, given a deterministic blackbox PIT that o(n) runs in time (s )H(n), where H(n) is an arbitrary func- CP12 tion, for all degree-s size-s algebraic circuits over n vari- ables, we can obtain a deterministic blackbox PIT that Every Testable (Infinite) Property of Bounded- ∗ degree Graphs Contains An Infinite Hyperfinite runs in time sexp(exp(O(log s))) for all degree-s size-s alge- Subproperty braic circuits over n variables. In other words, any black- box PIT with just a slightly non-trivial exponent of s com- One of the most fundamental questions in graph prop- O(n) pared to the trivial s test can be used to give a nearly erty testing is to characterize the combinatorial structure polynomial time blackbox PIT algorithm. of properties that are testable with a constant number of queries. We work towards an answer to this question for Mrinal Kumar the bounded-degree graph model, where the input graphs Simons Institute for the Theory of Computing, Berkeley, have maximum degree bounded by a constant d.Inthis USA model, it is known (among other results) that every hy- [email protected] perfinite property is constant-query testable, where, infor- mally, a graph property is hyperfinite, if for every δ>0 Ramprasad Saptharishi every graph in the property can be partitioned into small Tata Institute of Fundamental Research, Mumbai, India connected components by removing δn edges. In this paper [email protected] we show that hyperfiniteness plays a role in every testable property, i.e. we show that every testable property is either Anamay Tengse finite (which trivially implies hyperfiniteness and testabil- Tata Institute of Fundamental Research, Mumbai ity) or contains an infinite hyperfinite subproperty. A sim- [email protected] ple consequence of our result is that no infinite graph prop- erty that only consists of expander graphs is constant-query testable. Based on the above findings, one could ask if ev- CP12 ery infinite testable non-hyperfinite property might contain A Ptas for p-Low Rank Approximation an infinite family of expander (or near-expander) graphs. We show that this is not true. A number of recent works have studied algorithms for entrywise p-low rank approximation, namely, algorithms Hendrik Fichtenberger which given an n×d matrix A (with n ≥d), output a rank- TU Dortmund − p | − |p k matrix B minimizing A B p = i,j Ai,j Bi,j hendrik.fi[email protected] −  when p>0; and A B 0 = i,j [Ai,j = Bi,j ]for p = 0. On the algorithmic side, for p ∈ (0, 2), we give Pan Peng 16 DA19 Abstracts

University of Sheffield University of Wisconsin, Madison p.peng@sheffield.ac.uk [email protected]

Christian Sohler Department of Computer Science CP12 Technische Universitat Dortmund Testing Matrix Rank, Optimally [email protected] We show that for the problem of testing if a matrix A ∈ F n×n has rank at most d, or requires changing an -fraction CP12 of entries to have rank at most d,thereisanon-adaptive Testing Halfspaces over Rotation-invariant Distri- query algorithm making O(d2/) queries. Our algorithm butions works for any field F . This improves upon the previ- ous O(d2/2) bound (SODA’03), and bypasses an Ω(d2/2) We present an algorithm for testing halfspaces over ar- lower bound of (KDD’14) which holds if the algorithm is re- bitrary,√ unknown rotation-invariant distributions. Using quired to read a submatrix. Our algorithm is the first such O( n−7) random examples of an unknown function f,the algorithm which does not read a submatrix, and instead algorithm determines with high probability whether f is of reads a carefully selected non-adaptive pattern of entries − the form f(x)=sign( i wixi t)oris-far from all such in rows and columns of A. We complement our algorithm functions. This sample size is significantly smaller than with a matching query complexity lower bound for non- the well-known requirement of Ω(n) samples for learning adaptive testers over any field. We also give tight bounds halfspaces, and known lower bounds imply that our sample of Θ( d2) queries in the sensing model for which query access size is optimal up to logarithmic factors. The algorithm is  comes in the form of Xi,A := tr(Xi A); perhaps surpris- distribution-free in the sense that it requires no knowledge ingly these bounds do not depend on . We next develop of the distribution aside from the promise of rotation in- a novel property testing framework for testing numerical variance. To prove the correctness of this algorithm we properties of a real-valued matrix A more generally, which present a theorem relating the distance between a function includes the stable rank, Schatten-p norms, and SVD en- and a halfspace to the distance between their centers of tropy. Specifically, we propose a bounded entry model, mass, that applies to arbitrary distributions. where A is required to have entries bounded by 1 in ab- solute value. We give upper and lower bounds for a wide Nathaniel Harms range of problems in this model, and discuss connections University of Waterloo to the sensing model above. [email protected] Maria-Florina Balcan Carnegie Mellon University CP12 [email protected] Anaconda: A Non-adaptive Conditional Sampling Algorithm for Distribution Testing Yi Li Nanyang Technological University We investigate distribution testing with access to non- [email protected] adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a dis- David Woodruff, Hongyang Zhang tribution: it submits a query set S to an oracle, which Carnegie Mellon University returns a sample from the distribution conditioned on be- [email protected], [email protected] ing from S. In the non-adaptive setting, all query sets must be specified in advance of viewing the outcomes. Our main result is the first polylogarithmic-query algorithm for CP13 equivalence testing, deciding whether two unknown distri- butions are equal to or far from each other. This is an expo- Approximation of Trees by Self-nested Trees nential improvement over the previous best upper bound, and demonstrates that the complexity of the problem in The class of self-nested trees presents remarkable compres- this model is intermediate to the the complexity of the sion properties because of the systematic repetition of sub- problem in the standard sampling model and the adaptive trees in their structure. In this paper, we provide a bet- conditional sampling model. We also significantly improve ter combinatorial characterization of this specific family of the sample complexity for the easier problems of unifor- trees. In particular, we show from both theoretical and mity and identity testing. For the former, our algorithm practical viewpoints that complex queries can be quickly requires only O˜(log n) queries, matching the information- answered in self-nested trees compared to general trees. theoretic lower bound up to a O(log log n)-factor. Our al- We also present an approximation algorithm of a tree by a gorithm works by reducing the problem from 1-testing to self-nestedonethatcanbeusedinfastpredictionofedit ∞-testing, which enjoys a much cheaper sample complex- distance between two trees. ity. Necessitated by the limited power of the non-adaptive model, our algorithm is very simple to state. However, Romain Azais there are significant challenges in the analysis, due to the Inria complex structure of how two arbitrary distributions may [email protected] differ. Jean-Baptiste Durand Gautam Kamath Universit´e Grenoble Alpes MIT [email protected] [email protected] Christophe Godin Christos Tzamos Inria DA19 Abstracts 17

[email protected] Our new variant applies the median-of-medians algorithm for selecting pivots in order to circumvent the quadratic worst case. Indeed, we show that it uses at most n log n + CP13 1.6n comparisons for n large enough. We experimen- Simple and Fast BlockQuicksort using Lomuto’s tally confirm the theoretical estimates and show that the Partitioning Scheme new algorithm outperforms Heapsort by far and is only around 10% slower than Introsort (std::sort implementa- This paper presents simple variants of the BlockQuicksort tion of stdlibc++), which has a rather poor guarantee for algorithm described by Edelkamp and Weiss (ESA 2016). the worst case. We also simulate the worst case, which is The simplification is achieved by using Lomuto’s partition- only around 10% slower than the average case. In partic- ing scheme instead of Hoare’s crossing pointer technique ular, the new algorithm is a natural candidate to replace to partition the input. To achieve a robust sorting algo- Heapsort as a worst-case stopper in Introsort. rithm that works well on many different input types, the paper introduces a novel two-pivot variant of Lomuto’s par- Armin Weiß titioning scheme. A surprisingly simple twist to the generic Universit¨at Stuttgart two-pivot quicksort approach makes the algorithm robust. [email protected] The paper provides an analysis of the theoretical prop- erties of the proposed algorithms and compares them to Stefan Edelkamp their competitors. The analysis shows that Lomuto-based King’s College London approaches incur a higher average sorting cost than the [email protected] Hoare-based approach of BlockQuicksort. Moreover, the analysis is particularly useful to reason about pivot choices that suit the two-pivot approach. An extensive experi- CP14 mental study shows that, despite their worse theoretical Sublinear Algorithms for (Delta + 1) Vertex Col- behavior, the simpler variants perform as well as the orig- oring inal version of BlockQuicksort. Any graph with maximum degree Δ admits a proper vertex Martin Aum¨uller coloring with Δ + 1 colors that can be found via a simple IT University of Copenhagen sequential greedy algorithm in linear time and space. But [email protected] can one find such a coloring via a sublinear algorithm? We answer this fundamental question in the affirmative Nikolaj Hass for several canonical classes of sublinear algorithms includ- IT University Of Copenhagen ing graph streaming, sublinear time, and massively paral- [email protected] lel computation (MPC) algorithms. In particular, we de- sign (a) a single-pass semi-streaming algorithm in dynamic ˜ CP13 streams using O(n) space, (b) a sublinear-time algorithm in the standard query model√ that allows neighbor queries Lightweight Distributed Suffix Array Construction and pair queries using O˜(n n) time (which we also prove We present two new distributed suffix array construc- is optimal), and (c) a parallel algorithm in the massively ˜ tion algorithms. One of our algorithms requires parallel computation (MPC) model using O(n)memory only half as much memory as its competitor (PSAC) per machine and O(1) MPC rounds. At the core of our re- [Flick & Aluru, SC 2015], while achieving similar speed. In sults is a remarkably simple meta-algorithm for the (Δ+1) practice, we can compute on the same hardware suffix ar- coloring problem: Sample O(log n) colors for each vertex rays for text twice as large as PSAC. The other algorithm uniformly at random from the Δ + 1 colors; find a proper still requires less memory than PSAC but is faster on some coloring of the graph using the sampled colors. As our instances. As a by-product, we also engineered the first main result, we prove that the sampled set of colors with distributed string sorting algorithm. All of our algorithms high probability contains a proper coloring of the input are tested on text collections of up to 115 GB and running graph. The sublinear algorithms are then obtained by de- on 1280 cores. signing efficient algorithms for finding a proper coloring of the graph from the sampled colors in the corresponding Florian Kurpicz, Johannes Fischer models. TU Dortmund fl[email protected], johannes.fi[email protected] Sepehr Assadi, Yu Chen, Sanjeev Khanna dortmund.de University of Pennsylvania [email protected], [email protected], san- [email protected] CP13 Worst-case Efficient Sorting with QuickMergesort CP14 The two most prominent solutions for the sorting problem Optimal Distributed Coloring Algorithms for Pla- are Quicksort and Mergesort. While Quicksort is very fast nar Graphs in the Local Model on average, Mergesort additionally gives worst-case guar- antees, but needs extra space for a linear number of ele- In this paper, we consider distributed coloring for planar ments. Worst-case efficient in-place sorting, however, re- graphs with a small number of colors. Our main result is mains a challenge: the standard solution, Heapsort, suf- an optimal (up to a constant factor) O(log n) time algo- fers from a bad cache behavior and is also not overly fast rithm for 6-coloring planar graphs. Our algorithm is based for in-cache instances. In this work we present median- on a novel technique that in a nutshell detects small struc- of-medians QuickMergesort (MoMQuickMergesort), a new tures that can be easily colored given a proper coloring of variant of QuickMergesort, which combines Quicksort with the rest of the vertices and removes them from the graph Mergesort allowing the latter to be implemented in place. until the graph contains a small enough number of edges. 18 DA19 Abstracts

We believe this technique might be of independent inter- vious state-of-the-art bounds for Triangle Detection and est. In addition, we present a lower bound for 4-coloring Enumeration were O˜(n2/3)andO˜(n3/4), respectively, due planar graphs that essentially shows that any algorithm to Izumi and Le Gall (PODC 2017). The main nov- (deterministic or randomized) for 4-coloring planar graphs elty in this work is a distributed graph partitioning algo- requires Ω(n) rounds. We therefore completely resolve the rithm. We show that in O˜(n1−δ ) rounds we can partition problems of 4-coloring and 6-coloring for planar graphs in theedgesetofthenetworkG =(V,E) into three parts the LOCAL model. E = Em ∪ Es ∪ Er such that

Shiri Chechik • Each connected component induced by Em has mini- δ Tel-Aviv University, Israel mum degree Ω(n ) and conductance Ω(1/poly log(n)). [email protected] • The subgraph induced by Es has arboricity at most nδ. Doron Mukhtar •|E |≤|E|/6. Tel-Aviv University r [email protected] All our algorithms are based on the following generic frame- work, which we believe is of interest beyond this work. Roughly, we deal with Es by an algorithm that is efficient CP14 for low-arboricity graphs, and deal with Er using recursive Distributed Maximal Independent Set Using Small calls. For each connected component induced by Em,we Messagesu are able to simulate congested clique algorithms with small overhead by applying a routing algorithm due to Ghaffari, Abstract not available Kuhn, and Su (PODC 2017) for high conductance graphs.

Mohsen Ghaffari ETH Zurich Yi-Jun Chang, Seth Pettie ghaff[email protected] University of Michigan [email protected], [email protected]

CP14 Hengjie Zhang Oblivious Resampling Oracles and Parallel Algo- Tsinghua University rithms for the Lopsided Lov´asz Local Lemma [email protected] The Lov´asz Local Lemma (LLL) is a probabilistic tool which shows that, if a collection of “bad’ events B in a CP15 probability space are not too likely and not too interde- Improving the Smoothed Complexity of Flip for pendent, then there is a positive probability that no bad- Max-cut Problems events in B occur. Moser & Tardos (2010) gave sequential and parallel algorithms which transformed most applica- Finding locally optimal solutions for max-cut and max-k- tions of the variable-assignment LLL into efficient algo- cut are well-known PLS-complete problems. An instinctive rithms. A framework of Harvey & Vondr´ak (2015) based approach to finding such solutions is the FLIP method. on “resampling oracles’ extended this give very general se- Even though FLIP requires exponential time in worst- quential algorithms for other probability spaces satisfying case instances, it tends to terminate quickly in practical the Lopsided Lov´asz Local Lemma (LLLL). We describe a instances. To explain this discrepancy, the run-time of new structural property of resampling oracles which holds FLIP has been studied in the smoothed complexity frame- for all known resampling oracles, which we call “oblivious- work. Etscheid and R¨oglin (ACM Trans. Algorithms, ness.’ Essentially, it means that the interaction between 2017) showed that the smoothed complexity of FLIP for  two bad-events B,B depends only on the randomness used max-cut is quasi-polynomial. Angel, Bubeck, Peres and to resample B. This has two major consequences. First, it Wei (STOC 2017) showed that the smoothed complexity of is the key to achieving a unified parallel LLLL algorithm, FLIP for max-cut in complete graphs is O(φ5n15.1), where giving the first RNC algorithms for rainbow perfect match- φ is an upper bound on the random edge-weight density ings and rainbow hamiltonian cycles of Kn. Second, this and n is the number of vertices in the input graph. In this property allows us to build LLLL probability spaces out work, we improve the run-time bound for complete graphs. of a relatively simple “atomic’ set of events. Using this We prove that the smoothed complexity of FLIP in com- framework, we get the first sequential resampling oracle plete graphs is O(φn7.83). Our results are based on a care- for rainbow perfect matchings on the complete s-uniform fully chosen matrix whose rank captures the run-time of (s) hypergraph Kn , and the first commutative resampling or- the method along with improved rank bounds for this ma- acle for hamiltonian cycles of Kn. trix and an improved union bound based on this matrix. In addition, our techniques provide a general framework David G. Harris for analyzing FLIP in the smoothed framework. We illus- University of Maryland trate this general framework by showing that the smoothed [email protected] complexity of FLIP for max-3-cut in complete graphs is polynomial and for max-k-cut in arbitrary graphs is quasi- polynomial. CP14 Distributed Triangle Detection via Expander De- Ali Bibak composition University of Illinois, Urbana-Champaign [email protected] We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We Charles A. Carlson show that Triangle Detection, Counting, and Enumeration University of Colorado Boulder canbesolvedinO˜(n1/2) rounds. In contrast, the pre- [email protected] DA19 Abstracts 19

Karthekeyan Chandrasekaran [email protected] Department of Industrial and Enterprise Systems Engineering University of Illinois, Urbana-Champaign CP15 [email protected] Computing all Wardrop Equilibria Parametrized by the Flow Demand

CP15 We develop an algorithm that computes for a given undi- rected or directed network with flow-dependent piece-wise On the Number of Circuits in Regular Matroids linear edge cost functions all Wardrop equilibria as a func- (with Connections to Lattices and Codes) tion of the flow demand. Our algorithm is based on Katzenelson’s homotopy method for electrical networks. We show that for any regular matroid on m elements and The algorithm uses a bijection between vertex potentials any α ≥ 1, the number of α-minimum circuits, or circuits and flow excess vectors that is piecewise linear in the poten- whosesizeisatmostanα-multiple of the minimum size of tial space and where each linear segment can be interpreted 2 a circuit in the matroid is bounded by mO(α ). This gener- as an augmenting flow in a residual network. The algorithm alizes a result of Karger for the number of α-minimum cuts iteratively increases the excess of one or more vertex pairs in a graph. As a consequence, we obtain similar bounds until the bijection reaches a point of non-differentiability. on the number of α-shortest vectors in “totally unimod- Then, the next linear region is chosen in a simplex-like ular” lattices and on the number of α-minimum weight pivot step and the algorithm proceeds. We first show that codewords in “regular” codes. this algorithm correctly computes all Wardrop equilibria in undirected single-commodity networks along the chosen path of excess vectors. We then adapt our algorithm to also Rohit Gurjar work for discontinuous cost functions which allows to model Indian Institute of Technology Bombay directed edges and/or edge capacities. Our algorithm is [email protected] output-polynomial in non-degenerate instances where the solution curve never hits a point where the cost function of Nisheeth K. Vishnoi more than one edge becomes non-differentiable. For degen- EPFL erate instances we still obtain an output-polynomial algo- EPFL rithm computing the linear segments of the bijection by a [email protected] convex program. The latter technique also allows to handle multiple commodities.

CP15 Philipp Warode, Max Klimm School of Business and Economics, HU Berlin Nash Flows over Time with Spillback [email protected], [email protected]

Modeling traffic in road networks is a widely studied but challenging problem, especially under the assumption that CP15 drivers act selfishly. A common approach used in simula- Minimum Cut and Minimum k-Cut in Hyper- tion software is the deterministic queuing model, for which graphs via Branching Contractions the structure of dynamic equilibria has been studied exten- sively in the last couple of years. The basic idea is to model Random edge contractions (Karger, SODA ’93) provide a traffic by a continuous flow that travels over time from a particularly simple and elegant method for computing the source to a sink through a network, in which the arcs are minimum cut of a graph. Recent work (Chandrasekharan, endowed with transit times and capacities. Whenever the Xu, and Yu, SODA ’18; Ghaffari, Karger, and Panigrahi, flow rate exceeds the capacity a queue builds up and the SODA ’17) has extended the random contraction technique infinitesimally small flow particles wait in line in front of from graphs to finding minimum cuts and minimum k-cuts the bottleneck. It was not possible, until now, to repre- in hypergraphs. We further this line of work by providing sent spillback in this model, which was a big drawback, a branching randomized contraction technique for hyper- since spillback has a huge impact on travel times in highly graphs. Our algorithms perform branches as a random congested regions. We extend the model by introducing response to the size of a hyperedge selected for contrac- a storage capacity that bounds the total amount of flow tion. The analysis then hinges on being able to quantify on each arc. If an arc gets full, the inflow capacity is re- the (random) structure of the resulting computation tree duced to the current outflow rate, which can cause queues and the randomness of the contracted hypergraph. This on previous arcs, i.e., spillback. We carry over the main new technique leads to the following improvements in run- results of the original model to our generalization and char- ning time (m is the number of hyperedges, n the number acterize dynamic equilibria, called Nash flows over time, by of vertices, and p the total size of all hyperedges): sequences of particular static flows, we call spillback thin • We give an algorithm that runs in O mn2k−2 time flows. Furthermore, we give a constructive proof for the ex- for finding a minimum k-cut in hypergraphs of ar- istence of dynamic equilibria, which suggests an algorithm bitrary rank (maximum size of a hyperedge). This for their computation. This solves an open problem stated improves the best known running time for k>2. by Koch and Skutella in 2010. • We give another algorithm that runs in max{r,2k−2} Leon Sering O n time for finding a minimum Institute of Mathematics - Technische Universit¨at Berlin k-cut in hypergraphs of constant rank r. This betters [email protected] the best known running times for dense hypergraphs. Our techniques and results extend to the problems of min- Laura Vargas Koch imum hedge-cut and minimum hedge-k-cut as well. School of Business and Economics - RWTH Aachen University Kyle Fox 20 DA19 Abstracts

Department of Computer Science rapid mixing for degree sequences satisfying strong stabil- The University of Texas at Dallas ity, a notion closely related to P -stability. This results in a [email protected] much shorter proof that unifies and extends the currently known rapid mixing results for the switch chain. In partic- Debmalya Panigrahi ular, our work resolves an open problem posed by Greenhill Duke University (SODA, 2015). Secondly, in order to illustrate the power of [email protected] our approach, we study the problem of uniformly sampling graphs for which—in addition to the degree sequence—a Fred Zhang joint degree distribution is given. Although the problem Harvard University was formalized over a decade ago, small progress has been [email protected] made on the random sampling of such graphs. The case of a single degree class reduces to sampling of regular graphs, but beyond this almost nothing is known. We fully resolve CP16 the case of two degree classes, by showing that the switch Markov chain is always rapidly mixing. On the Rank of a Random Sparse Binary Matrix × Georgios Amanatidis, Pieter Kleer We study the rank of a random n m matrix An,m;k with Centrum Wiskunde & Informatica (CWI) entries from GF (2), and exactly k unit entries in each col- [email protected], [email protected] umn, the other entries being zero. The columns are chosen independently and uniformly at random from the set of n all k such columns. We obtain an asymptotically cor- CP16 rect estimate for the rank as a function of the number of On Coalescence Time in Graphs-When Is Coalesc- columns m in terms of c, n, k,andwherem = cn/k.The ingasFastasMeeting? matrix An,m;k forms the vertex-edge incidence matrix of a k-uniform random hypergraph H. The rank of An,m;k can Coalescing random walks is a fundamental stochastic pro- | | be expressed as follows. Let C2 be the number of vertices cess, where a set of particles perform independent discrete- of the 2-core of H,and|E(C2)| the number of edges. Let ∗ time random walks on an undirected graph. Whenever two m be the value of m for which |C2| = |E(C2)|. Then w.h.p. ∗ or more particles meet at a given node, they merge and con- for m

Wesley Pegden Varun Kanade Carnegie Mellon University University of Oxford [email protected] [email protected]

Frederik Mallmann-Trenn CP16 MIT Rapid Mixing of the Switch Markov Chain for [email protected] Strongly Stable Degree Sequences and 2-Class Joint Degree Matrices Thomas Sauerwald University of Cambridge The switch Markov chain has been extensively studied as [email protected] the most natural Markov Chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We use comparison arguments to show that the switch chain mixes CP16 rapidly in two different settings. We first study the clas- Xor Codes and Learning Sparse Parities with Noise sic problem of uniformly sampling simple undirected, as well as bipartite, graphs with a given degree sequence. We A k-LIN instance is a system of m equations over n vari- apply an embedding argument, involving a Markov chain ables of the form si1 + ···+ sik = 0 or 1 modulo 2. In defined by Jerrum and Sinclair (TCS, 1990) for sampling a noisy planted instance, the system is evaluated on a graphs that almost have a given degree sequence, to show random solution and independent noise is added, while DA19 Abstracts 21

in a random instance, the right-hand side is uniformly [email protected] random. Alekhnovich conjectured that the two are hard to distinguish when k =3andm = O(n). We give a sample-efficient reduction from solving noisy planted k- CP17 LIN instances to distinguishing them from random in- Alternative Multicriteria Routes stances. Suppose that m-equation, n-variable instances of the two types are efficiently distinguishable with advan- We consider the problem of computing a set of alterna- tage . Then, we show that O(m · (m/)2/k)-equation, n- tive routes in a multicriteria setting where several network variable noisy planted k-LIN instances are efficiently solv- metrics are available. Previous approaches for alternative able with probability exp −O˜((m/)6/k). The solver is route computation were based on relaxing a single met- based on a new approximate local list-decoding algorithm ric to obtain alternative routes whereas our approach for for the k-XOR code at large distances. The k-XOR encod- the multicriteria setting produces routes that are always ing of a function F :Σ→{−1, 1} is its k-th tensor power optimal for a convex combination of the metrics. For the F k(x ,...,x )=F (x ) ···F (x ). Given oracle access to a concrete example of route planning for bicycles with three 1 k 1 k natural metrics (distance, positive height difference, un- function G that μ-correlates with F k, our algorithm out- suitability for cycling) we show how to efficiently generate 1/k − puts the description of a message that (μ )-correlates very natural alternative bicycle routes. with F with probability exp −O˜(k2μ−2/k−2). Previous decoders have a worse dependence on μ (Levin, Combina- Florian Barth torica 1987) or do not apply to subconstant μ1/k. University of Stuttgart [email protected]

Andrej Bogdanov Stefan Funke Chinese University of Hong Kong FMI, University of Stuttgart, Germany Chinese University of Hong Kong [email protected] [email protected] Sabine Storandt Manuel Sabin, Prashant Nalini Vasudevan Universit¨at Konstanz University of California, Berkeley [email protected] [email protected], [email protected]

CP17 Concatenated k-Path Covers CP16 Given a directed graph G(V,E), a k-(Shortest) Path Cover Seeded Graph Matching via Large Neighborhood is a subset C of the nodes V such that every simple (or Statistics shortest) path in G consisting of k nodes contains at least onenodefromC. In this paper, we extend the notion of k-Path Covers such that the objects to be covered don’t We study a well known noisy model of the graph iso- have to be single paths but can be concatenations of up morphism problem. In this model, the goal is to per- to p simple (or shortest) paths. For the generalized prob- fectly recover the vertex correspondence between two edge- lem of computing concatenated k-(Shortest) Path Covers, correlated graphs, with an initial seed set of correctly we present theoretical results regarding the VC-dimension matched vertex pairs revealed as side information. For of the concatenated path set in dependency of p as well as seeded problems, our result provides a dramatic improve- (approximation) algorithms. Subsequently, we study inter- ment over previously known results. We show that it is esting special cases of concatenated k-Path Covers, in par- possible to achieve the information-theoretic limit of graph ticular, covers for piecewise shortest paths, round tours and sparsity in time polynomial in the number of vertices n. trees. For those, we show how the pruning algorithm for Moreover, we show the number of seeds needed for ex- k-Path Cover computation can be abstracted and modified act recovery in polynomial-time can be as low as n in in order to also solve concatenated k-Path Cover problems. the sparse graph regime with the average degree smaller An extensive experimental study on different graph types than n)andΩ(logn) in the dense graph regime. Our proves the applicability and efficiency of our approaches. results also shed light on the unseeded problem. In partic- Moritz Beck ular, we give (the first) sub-exponential time algorithms for O(log n) Universit¨at Konstanz sparse models and an n algorithm for dense models [email protected] for some parameters, including some that are not covered by recent results of Barak et al. Unlike previous work on graph matching, which used small neighborhoods or small Kam-Yiu Lam subgraphs with a logarithmic number of vertices in order to City University of Hong Kong match vertices, our algorithms match vertices if their large [email protected] neighborhoods have a significant overlap in the number of seeds. Joseph Kee Yin Ng Hong Kong Baptist University [email protected] Elchanan Mossel MIT Sabine Storandt [email protected] Universit¨at Konstanz [email protected] Jiaming Xu Duke University Chun Jiang Zhu 22 DA19 Abstracts

University of Conneticut [email protected] [email protected]

CP18 CP17 A PTAS for Euclidean TSP with Hyperplane Neighborhoods Fast and Exact Public Transit Routing with Re- stricted Pareto Sets In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum We present a novel exact journey planning approach to length that visits at least one point in each region. Even computing a reasonable subset of multi-criteria Pareto sets in the Euclidean plane, TSPN is known to be APX-hard, in public transit networks. Our restriction is well defined which gives rise to studying more tractable special cases and independent of the choice of algorithm. In order to of the problem. In this paper, we focus on the funda- compute the restricted Pareto set efficiently, we present mental special case of regions that are hyperplanes in the Bounded McRAPTOR, a new set of algorithms that ex- d-dimensional Euclidean space. While for d = 2 an exact tend the well-known McRAPTOR algorithm. The fastest algorithm with running time O(n5) is known, settling the variant employs a novel pruning scheme based on carefully exact approximability of the problem for d =3hasbeen computed bounds. Experiments on large metropolitan net- repeatedly posed as an open question. To date, only an ap- works show that a four-criteria restricted Pareto set can proximation algorithm with guarantee exponential in d is be computed faster by a factor of up to 65, while retaining known, and NP-hardness remains open. For arbitrary fixed the important journeys of the full Pareto set. This easily d, we develop a Polynomial Time Approximation Scheme enables interactive applications in practice, making multi- (PTAS) that works for both the tour and path version of criteria Pareto-optimal journey planning scalable without the problem. Our algorithm is based on approximating the need of a preprocessing-based speedup technique. the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as Daniel Delling, Julian Dibbelt, Thomas Pajor solutions of a sophisticated LP formulation, which we com- Apple Inc bine with the enumeration of crucial properties of the tour. [email protected], [email protected], tpa- As part of our analysis we develop a general sparsification [email protected] technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we CP17 maintain important properties of the polytope. Batch-Parallel Euler Tour Trees Antonios Antoniadis, Krzysztof Fleszar Max-Planck-Institut f¨ur Informatik [email protected], kfl[email protected] The dynamic trees problem is to maintain a forest undergo- ing edge insertions and deletions while supporting queries Ruben Hoeksma for information such as connectivity. Though many data Universit¨at Bremen structures for this problem exist, few can exploit paral- [email protected] lelism in the batch setting in which large batches of edges are inserted or deleted from the forest at once. We demon- strate that the Euler tour tree (ETT), an existing sequen- Kevin Schewior tial dynamic trees data structure, can be parallelized in Technische Universit¨at M¨unchen ´ the batch setting. Our ETTs process a batch of k updates Ecole Normale Sup´erieure over an n-vertex forest with O(k log(1 + n/k)) expected [email protected] work and O(log n) depth with high probability. Our work bound is asymptotically optimal, and we improve on the CP18 depth bound achieved by Acar et al. for the batch-parallel dynamic trees problem. A crucial building block for our Polynomial-time Approximation Scheme for Mini- ETTs is a batch-parallel skip list data structure, which may mum k-Cut in Planar and Minor-free Graphs be of independent interest. ETTs require a sequence data structure capable of joins and splits. We show that skip The k-cut problem asks, given a connected graph G and a lists support batches of joins or splits of size k over n ele- positive integer k, to find a minimum-weight set of edges ments with O(k log(1 + n/k)) expected work and O(log n) whose removal splits G into k connected components. We give the first polynomial-time algorithm with approxima- depth with high probability. We also achieve the same − efficiency bounds for augmented skip lists, which lets us tion factor 2  (with constant >0) for the k-cut prob- augment our ETTs to support subtree queries. Our data lem in planar and minor-free graphs. Applying more com- structures achieve between 67-96x self-relative speedup on plex techniques, we further improve our method and give a 72 cores with hyper-threading on large batch sizes, and polynomial-time approximation scheme for the k-cut prob- they also significantly outperform the fastest existing se- lem in both planar and minor-free graphs. Despite the quential alternatives empirically. persistent effort, to the best of our knowledge, this is the first improvement for the k-cut problem over standard ap- proximation factor of 2 in any major class of graphs. Thomas Tseng, Laxman Dhulipala Carnegie Mellon University Alireza Farhadi [email protected], [email protected] University of Maryland [email protected] Guy Blelloch Computer Science Department MohammadHossein Bateni Carnegie Mellon University Google Research DA19 Abstracts 23

[email protected] Complexity

MohammadTaghi Hajiaghayi We give a new decomposition theorem in unit disk graphs University of Maryland, College Park (UDGs) and demonstrate its applicability in the fields of [email protected] Structural Graph Theory and Parameterized Complexity. First, we show that the class of UDGs admits a Contrac- tion Decomposition Theorem. Prior studies on this topic CP18 exhibited that the classes of planar graphs [Klein, 2008], graphs of bounded genus [Demaine, Hajiaghayi and Mo- Embedding Planar Graphs into Low-treewidth har, 2010] and H-minor free graphs [Demaine, Hajiaghayi Graphs with Applications to Efficient Approxima- and Kawarabayashi, 2011] admit a Contraction Decompo- tion Schemes for Metric Problems sition Theorem. Additionally, this result answers an open question posed by Hajiaghayi. Second, we present a “pa- Abstract not available. rameteric version’ of our new decomposition theorem. We prove that there is an algorithm that given a UDG G and Eli Fox-Epstein a positive integer k, runs in polynomial time and outputs Tufts University a collection of O(k) tree decompositions of G with the fol- [email protected] lowing properties. Each bag in any of these tree decom- positions can be partitioned into O(k) connected “pieces’. Philip Klein Moreover, for any subset S of at most k edges in G,thereis Brown University a tree decomposition in the collection such that S is “well [email protected] preserved’ in the decomposition in the following sense. For any bag in the tree decomposition and any edge in S with Aaron Schild both endpoints in the bag, either its endpoints lie in differ- University of California, Berkeley ent pieces or they lie in a piece which is a clique. Having [email protected] this decomposition at hand, we show that the design of parameterized algorithms for some cut problems becomes elementary. CP18 Meirav Zehavi Nearly ETH-tight Algorithms for Planar Steiner Ben-Gurion University Tree with Terminals on Few Faces [email protected] The Steiner Tree problem is one of the most fundamental NP-complete problems as it models many network design Fahad Panolan problems. Recall that an instance of this problem consists University of Bergen, Norway of a graph with edge weights, and a subset of vertices (of- [email protected] ten called terminals); the goal is to find a subtree of the graph of minimum total weight that connects all termi- Saket Saurabh nals. A seminal paper by Erickson et al. [Math. Oper. IMSc +UiB Res., 1987] considers instances where the underlying graph [email protected] is planar and all terminals can be covered by the boundary of k faces. Erickson et al. show that the problem can be solved by an algorithm using nO(k) time and nO(k) space, CP19 where n denotes the number of vertices of the input graph. The Streaming k-Mismatch Problem In the past 30 years there has been no significant improve- ment of this algorithm, despite several efforts. In this work, We consider the streaming complexity of a fundamental we give an algorithm√ for Planar Steiner Tree with running task in approximate pattern matching: the k-mismatch time 2O(k)nO( k) using only polynomial space. Further- problem. In this problem, we must compute Hamming more, we show the running time of our algorithm√ is almost distances between a pattern of length n and all length-n tight: we prove that there is no f(k)no( k) algorithm for substrings of a text for which the Hamming distance does Planar Steiner Tree for any computable function f, unless not exceed a given threshold k. In our problem formula- the Exponential Time Hypothesis fails. tion, we report not only the Hamming distance but also, on demand, the full mismatch information, that is the list S´andor Kisfaludi-Bak of mismatched pairs of symbols and their indices. The twin Eindhoven University of Technology challenges of streaming pattern matching derive from the [email protected] need both to achieve small working space and to guarantee that every arriving input symbol is processed quickly. We present a streaming algorithm for the k-mismatch prob- Jesper Nederlof lem which uses O(k log n log n ) bits of space and spends TU Eindhoven √ k O(log n ( k log k +log3 n)) time on each symbol of the in- [email protected] k put stream. In our formulation, the pattern also arrives in the stream, directly before the text. The running time Erik Jan van Leeuwen almost matches the classic offline solution and the space Utrecht University usage is within a logarithmic factor of optimal. Our new [email protected] algorithm therefore effectively resolves and extends a prob- lem first introduced in FOCS’09. En route to this solution, n | | we also give a deterministic O(k(log k +log Σ ))-bit encod- CP18 ing of all the alignments with Hamming distance at most Contraction Decomposition in Unit Disk Graphs k of a length-n pattern within a text of length O(n). This and Algorithmic Applications in Parameterized secondary result provides an optimal solution to a natural 24 DA19 Abstracts

encoding problem. first nontrivial algorithm for approximating in linear time. Our main result is a linear time algorithm for the longest Raphael Clifford common subsequence which√ has an approximation factor University of Bristol, UK of O(n). This beats the n barrier for approximating in raphael.cliff[email protected] linear time.

Tomasz Kociumaka Saeed Seddighin, MohammadTaghi Hajiaghayi Institute of Informatics University of Maryland, College Park University of Warsaw [email protected], [email protected] [email protected] Masoud Seddighin Ely Porat Sharif University of Technology Bar Ilan University [email protected] [email protected] Xiaorui Sun University of Illinois at Chicago CP19 [email protected] Efficiently Approximating Edit Distance Between Pseudorandom Strings CP19 We present an algorithm for approximating the edit dis- Lower Bounds for Text Indexing with Mismatches tance ed(x, y) between two strings x and y in time param- and Differences eterized by the degree to which one of the strings x satis- fies a natural pseudorandomness property. The pseudoran- In this paper we study lower bounds for the fundamental domness model is asymmetric in that no requirements are problem of text indexing with mismatches and differences. placed on the second string y,whichmaybeconstructed In this problem we are given a long string of length n,the by an adversary with full knowledge of x.Wesaythatx is “text’, and the task is to preprocess it into a data structure (p, B)-pseudorandom if all pairs a and b of disjoint B-letter such that given a query string Q, one can quickly identify substrings of x satisfy ed(a, b) ≥ pB. Given parameters p substrings that are within Hamming or edit distance at and B, our algorithm computes the edit distance between most k from Q. This problem is at the core of various prob- a(p, B)-pseudorandom string x and an arbitrary string y lems arising in biology and text processing. We start by within a factor of O(1/p)intimeO˜(nB), with high prob- demonstrating conditional lower bounds for k =Θ(logn). ability. If x is generated at random, then with high prob- We show that assuming the Strong Exponential Time Hy- ability it will be (Ω(1),O(log n))-pseudorandom, allowing pothesis, any data structure for text indexing that can be us to compute ed(x, y) within a constant factor in near constructed in polynomial time cannot have (n1−δ )query linear time. For strings x of varying degrees of pseudo- time, for any δ>0. This bound also extends to the set- randomness, our algorithm offers a continuum of runtimes. tingwhereweonlyaskfor(1+)-approximate solutions Our algorithm is robust in the sense that it can handle a for text indexing. However, in many applications the value small portion of x being adversarial (i.e., not satisfying the of k is rather small, and one might hope that for small k pseudorandomness property). In this case, the algorithm we can develop more efficient solutions. We show that this incurs an additive approximation error proportional to the would require a radically new approach as using the cur- fraction of x which behaves maliciously. rent methods one cannot avoid exponential dependency on k either√ in the space, or in the time bound for all even William Kuszmaul √8 log n ≤ k = o(log n). Our lower bounds also apply 3 Massachusetts Institute of Technology to the dictionary look-up problem, where instead of a text [email protected] one is given a set of strings.

Tatiana Starikovskaya CP19 Ecole Normale Sup´erieure √Approximating Lcs in Linear Time: Beating the Paris n Barrier [email protected] Longest common subsequence () is one of the most fun- damental problems in combinatorial optimization. Apart Vincent Cohen-Addad from theoretical importance, has enormous applications Sorbonne Universit´es and CNRS in bioinformatics, revision control systems, and data com- [email protected] parison programs1. Although a simple dynamic program computes in quadratic time, it has been recently proven Laurent Feuilloley that the problem admits a conditional lower bound and IRIF, Univ Paris Diderot may not be solved in truly subquadratic time [?]. In addi- [email protected] tion to this, is notoriously hard with respect to approxima- tion algorithms. Apart from a trivial sampling technique that obtains a nx approximation solution in time O(n2−2x) CP19 nothing else is known for . This is in sharp contrast to its Few Matches or Almost Periodicity: Faster Pattern dual problem edit distance for which several linear time so- Matching with Mismatches in Compressed Texts lutions are obtained in the past two decades [?, ?, ?, ?, ?]. Whether or not a nontrivial approximation for is possible A fundamental problem on strings in the realm of ap- in linear time has been raised as an open question by ex- proximate string matching is pattern matching with mis- perts in the community [?]. In this work, we present the matches: Given a text t, a pattern p, and a number k, determine whether some substring of t has Hamming 1a notable example is the UNIX application diff distance at most k to p; such a substring is called a k- DA19 Abstracts 25

match. We study the case of searching for a small pat- [email protected]ff.cuni.cz tern p in a text t that is compressed by a straight-line program. This grammar compression is popular in the Marcin Pilipczuk string community as it unifies many well-known compres- University of Warsaw sion schemes such as the Lempel-Ziv family, dictionary Warsaw, Poland methods, and others. We denote by m the length of p [email protected] and by n the compressed size of t. While exact pat- tern matching, i.e., the case k =0,isknowntobesolv- able in near-linear time O˜(n + m)[Je˙z TALG’15], despite CP20 considerable interest in the string community, the fastest How to Guess an n-Digit Number known algorithm for√ pattern matching with mismatches runs in time O˜(n m poly(k)) [Gawrychowski, Straszak In a deductive game for two players, SF and PGOM, SF ISAAC’13], which is far from linear even for very small k. conceals an n-digit number x = x1,...,xn in base q,and In this paper, we obtain an algorithm for pattern matching PGOM, who knows n and q, tries to identify x by asking with mismatches running in time O˜((n+m)poly(k)). This a number of questions, which are answered by SF. Each is near-linear in the input size for any constant (or slightly question is an n-digit number y = y1,...,yn in base q; superconstant) k. Our algorithm is based on a new struc- each answer is the number of subscripts i such that xi = tural insight for approximate pattern matching, essentially yi. Moreover, we require PGOM send all the questions at showing that either the number of k-matches is very small once. We show that the minimum number of questions or both text and pattern must be almost periodic. required to determine x is (2 + oq (1))n/ logq n.Ourresult closes the gap between the lower bound attributed to Erd˝os Karl Bringmann and R´enyi and the upper bounds developed subsequently Max Planck Institute for Informatics, by Lindstr¨om, Chv´atal, Kabatianski, Lebedev and Thorpe. Saarland Informatics Campus, Germany A more general problem is to determine the asymptotic [email protected] formula of the metric dimension of Cartesian powers of a graph. We state the class of graphs for which the formula Marvin K¨unnemann can be determined, and the smallest graphs for which we Max-Planck-Institut f¨ur Informatik, Saarbr¨ucken, did not manage to settle. Germany Zilin Jiang [email protected] Technion - Israel Institute of Technology [email protected] Philip Wellnitz Max Planck Institute for Informatics, Nikita Polyanskii Saarland Informatics Campus, Germany Skolkovo Institute of Science and Technology [email protected] [email protected]

CP20 CP20 Polynomial-time Algorithm for Maximum Weight The Maximum Number of Minimal Dominating Independent Set on P6-Free Graphs Sets in a Tree

In the classic Maximum Weight Independent Set problem Atreewithn verticeshasatmost95n/√13 minimal domi- we are given a graph G with a nonnegative weight func- nating sets. The growth constant λ = 13 95 ≈ 1.4194908 is tion on vertices, and the goal is to find an independent set best possible. It is obtained as a kind of “dominant eigen- in G of maximum possible weight. While the problem is value” of a bilinear operation on sixtuples that is derived NP-hard in general, we give a polynomial-time algorithm from the dynamic-programming recursion for computing working on any P6-free graph, that is, a graph that has the number of minimal dominating sets of a tree. The no path on 6 vertices as an induced subgraph. This im- semi-automatic computer-assisted way in which the growth proves the polynomial-time algorithm on P5-free graphs of constant was derived might be interesting in its own right. Lokshtanov et al., and the quasipolynomial-time algorithm We also develop an output-sensitive algorithm for listing on P6-free graphs of Lokshtanov et al. The main technical all minimal dominating sets with linear set-up time and contribution leading to our main result is enumeration of linear delay between reporting successive solutions. a polynomial-size family F of vertex subsets with the fol- lowing property: for every maximal independent set I in G¨unter Rote the graph, F contains all maximal cliques of some mini- Freie Universit¨at Berlin mal chordal completion of G that does not add any edge Institut f¨ur Informatik incident to a vertex of I. [email protected] Michal Pilipczuk University of Warsaw CP20 [email protected] Vector Clique Decompositions

Andrzej Grzesik Let Fk be the set of k-vertex graphs. For a graph G,a Jagiellonian University k-decomposition is a set of induced subgraphs of G,each Cracow, Poland isomorphic to an element of Fk, such that each pair of [email protected] vertices of G is in exactly one element of the set. It is a fundamental result of Wilson that for all n = |V (G)| Tereza Klimoˇsov´a sufficiently large, G has a k-decomposition if and only if − − k Charles University G is k-divisible, namely k 1 divides n 1and 2 di- n ∈ |Fk| F Prague, Czech Republic vides 2 .Letv R be indexed by k.Forak- 26 DA19 Abstracts

v decomposition L,letν (L)= F ∈Fk vF dL,F where dL,F [email protected] is the fraction of elements of L isomorphic to F .Let νv(G)=maxL νv(L), νv(n)=min{νv(G):|V (G)| = n}, νv = limn→∞ νv(n). Replacing k-decompositions with CP21 their fractional relaxations, one obtains the fractional ana- Exactly Solving the Maximum Weight Independent ∗ ∗ ∗ logue νv(G) and the corresponding νv(n)andνv.Our Set Problem on Large Real-world Graphs main result is that for each v ∈ R|Fk| One powerful technique to solve NP-hard optimization ∗ problems in practice is branch-and-reduce search—which νv = νv . is branch-and-bound that intermixes branching with re- ductions to decrease the input size. While this technique Furthermore, there is a polynomial time algorithm that is known to be very effective in practice for unweighted produces a decomposition L of a k-decomposable graph problems, very little is known for weighted problems, in such that νv(L) ≥ νv − on(1). Similar results hold in the part due to a lack of known effective reductions. In this directed and edge-colored settings. We use these results to work, we develop a full suite of new reductions for the obtain new and improved bounds on several decomposition maximum weight independent set problem and provide ex- results. tensive experiments to show their effectiveness in practice on real-world graphs of up to millions of vertices and edges. Raphael Yuster Our experiments indicate that our approach is able to out- Department of Mathematics perform existing state-of-the-art algorithms, solving many University of Haifa instances that were previously infeasible. In particular, [email protected] we show that branch-and-reduce is able to solve a large number of instances up to two orders of magnitude faster than existing (inexact) local search algorithms—and is able CP20 to solve the majority of instances within 15 minutes. For

Four-Coloring P6-Free Graphs those instances remaining infeasible, we show that combin- ing kernelization with local search produces higher-quality In this paper we present a polynomial time algorithm for solutions than local search alone. the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced Darren Strash six-vertex path, thus proving a conjecture of Huang. Com- Department of Computer Science bined with previously known results this completes the Colgate University classification of the complexity of the 4-coloring problem [email protected] for graphs with a connected forbidden induced subgraph. Sebastian Lamm Maria Chudnovsky, Sophie Spirkl Karlsruhe Institute of Technology Princeton University [email protected] [email protected], [email protected] Christian Schulz Mingxian Zhong University of Vienna Columbia University Karlsruhe Institute of Technology [email protected] [email protected]

Robert Williger CP21 Karlsruhe Institute of Technology A New Integer Linear Program for the Steiner Tree [email protected] Problem with Revenues, Budget and Hop Con- straints Huashuo Zhang Colgate University The Steiner tree problem with revenues, budgets and hop [email protected] constraints (STPRBH) is a variant of the classical Steiner tree problem. This problem asks for a subtree in a given graph with maximum revenues corresponding to its nodes, CP21 where its total edge costs respect the given budget, and the SAT-Encodings for Treecut Width and Treedepth number of edges between each node and its root does not exceed the hop limit. We introduce a new binary linear Graph decompositions associated with so-called width pa- program with polynomial size based on partial ordering, rameters (such as treewidth) have been the focus of ex- which (up to our knowledge) for the first time solves all tensive theoretical research. Finding an optimal decom- STPRBH instances from the DIMACS benchmark set to position is usually an NP-hard task. In this paper we optimality. The set contains graphs with up to 500 nodes propose, implement, and test the first practical decompo- and 12500 edges. sition algorithms for the width parameters treecut width and treedepth, which have recently gained a lot of atten- Adalat Jabrayilov tion in the theoretical research community. However, one TU Dortmund University prominent obstacle for any practical or experimental use Department of Computer Science of these two width parameters is the lack of any practical [email protected] or implemented algorithm for actually computing the asso- ciated decompositions. Our approach for computing tree- Petra Mutzel cut width and treedepth decompositions is based on effi- Dortmund University cient encodings into the propositional satisfiability problem Germany (SAT). Once an encoding is generated, any satisfiability DA19 Abstracts 27

solver can be used to find the decomposition. This allows [email protected] us to leverage the surprising power of todays state-of-the art SAT solvers. The success of SAT-based decomposition methods crucially depends on the used characterisation of CP22 the decomposition method, as not every characterisation is A Faster External Memory Priority Queue with suitable for that task. For treecut width and treedepth, we DecreaseKeys propose new characterisations that are based on sequences of partitions of the vertex set, a method that was pio- A priority queue is a fundamental data structure that neered for clique-width. We implemented and systemati- maintains a dynamic set of (key, priority)-pairs and sup- cally tested our encodings on various benchmark instances, ports Insert, Delete, ExtractMin and DecreaseKey op- including famous named graphs and random graphs of var- erations. In the external memory model, the current ious density. best priority queue supports each operation in amortized 1 N O( B log B ) I/Os. If the DecreaseKey operation does not Robert Ganian need to be supported, one can design a more efficient data TU Wien structure that supports the Insert, Delete and Extract- 1 N M [email protected] Min operations in O( B log B / log B ) I/Os. A recent re- sult shows that a degradation in performance is inevitable 1 Neha Lodha by proving a lower bound of Ω( B log B/log log N)I/Os TU Wien, Vienna, Austria for priority queues with DecreaseKeys. In this paper we [email protected] tighten the gap between the lower bound and the upper bound by proposing a new priority queue which supports the DecreaseKey operation and has an expected amor- Sebastian Ordyniak tized I/O complexity of O( 1 log N / log log N). Our re- University of Sheffield, Sheffield, UK B B sult improves the external memory priority queue with De- [email protected] creaseKeys for the first time in over a decade, and also gives the fastest external memory single source shortest path al- Stefan Szeider gorithm. TU Wien [email protected] Shunhua Jiang Institute for Interdisciplinary Information Sciences, Pan Peng Tsinghua University University of Sheffield [email protected] p.peng@sheffield.ac.uk Kasper G. Larsen MADALGO, Aarhus University CP21 [email protected] Efficiently Enumerating Hitting Sets of Hyper- graphs Arising in Data Profiling CP22 Optimal Construction of Compressed Indexes for We devise an enumeration method for inclusion-wise∗ mini- mal hitting sets in hypergraphs. It has delay O(mk +1n2) Highly Repetitive Texts and uses linear space. Hereby, n is the number of ver- tices, m the number of hyperedges, and k∗ the rank of the We propose algorithms that, given the input string of transversal hypergraph. In particular, on classes of hyper- length n over integer alphabet of size σ,construct graphs for which the cardinality k∗ of the largest minimal the Burrows–Wheeler transform (BWT), the permuted hitting set is bounded, the delay is polynomial. The al- longest-common-prefix (PLCP) array, and the LZ77 pars- gorithm solves the extension problem for minimal hitting ing in O(n/ logσ n + r polylog n) time and working space, sets as a subroutine. We show that the extension problem where r is the number of runs in the BWT of the input. is W[3]-complete when parameterised by the cardinality of These are the essential components of many compressed the set which is to be extended. For the subroutine, we indexes such as compressed suffix tree, FM-index, and give an algorithm that is optimal under the exponential grammar and LZ77-based indexes, but also find numer- time hypothesis. Despite these lower bounds, we provide ous applications in sequence analysis and data compres- empirical evidence showing that the enumeration outper- sion. The value of r is a common measure of repetitiveness forms the theoretical worst-case guarantee on hypergraphs that is significantly smaller than n if the string is highly arising in the profiling of relational databases, namely, in repetitive. Since just accessing every symbol of the string the detection of unique column combinations. requires Ω(n/ logσ n) time, the presented algorithms are time and space optimal for inputs satisfying the assump- tion n/r ∈ Ω(polylog n) on the repetitiveness. For such in- Thomas Bl¨asius, Tobias Friedrich, Julius Lischeid puts our result improves upon the currently fastest general Hasso Plattner Institute algorithms of Belazzougui (STOC 2014) and Munro et al. University of Potsdam (SODA 2017) which run in O(n) time and use O(n/ log n) [email protected], [email protected], σ working space. We also show how to use our techniques to [email protected] obtain optimal solutions on highly repetitive data for other fundamental string processing problems such as: Lyndon Kitty Meeks factorization, construction of run-length compressed suf- University of Glasgow fix arrays, and some classical “textbook’ problems such as [email protected] computing the longest substring occurring at least some fixed number of times. Martin Schirneck Hasso Plattner Institute Dominik Kempa University of Potsdam Department of Computer Science 28 DA19 Abstracts

University of Helsinki Robert Tarjan [email protected] Princeton University Microsoft Research [email protected] CP22 Strategies for Stable Merge Sorting CP22 We introduce new stable natural merge sort algorithms, called 2-merge sort and α-merge sort. We prove upper ASortofanAdversary and lower bounds for several merge sort algorithms, in- cluding Timsort, Shiver’s sort, α-stack sorts, and our new We describe an efficient deterministic adversary that forces 2-merge and α-merge sorts. The upper and lower bounds any comparison-based sorting algorithm to perform at least 37 n n have the forms c · n log m and c · n log n for inputs of 64 log comparisons. This improves on previous efficient length n comprising m runs. For Timsort, we prove a adversaries of Atallah and Kosaraju (1981), Richards and lower bound of (1.5 − o(1))n log n. For 2-merge sort, we Vaidya (1988), and of Bordal et al. (1996) that force any 1 · n n prove optimal upper and lower bounds of approximately sorting algorithm to perform at least 2 log compar- (1.089 ± o(1))n log m. We prove similar asymptotically isons. matching upper and lower bounds for α-merge sort, when ϕ<α<2, where ϕ is the golden ratio. Our bounds are Or Zamir in terms of merge cost; this upper bounds the number of Tel Aviv University comparisons and accurately models runtime. The merge [email protected] strategies can be used for any stable merge sort, not just natural merge sorts. The new 2-merge and α-merge sorts Haim Kaplan have better worst-case merge cost upper bounds and are Tel-Aviv University slightly simpler to implement than the widely-used Tim- [email protected] sort; they also perform better in experiments. Uri Zwick Samuel Buss Tel Aviv University Deaprtment of Mathematics [email protected] UC San Diego [email protected] CP23 Alexander Knop Department of Mathematics Iterative Refinement for p-Norm Regression UC San Diego [email protected] We give improved algorithms for the p-regression prob- lem, minx ||x||p such that Ax = b, for all p ∈ (1, 2) ∪ (2, ∞). Our algorithms obtain a high accuracy solution in |p−2| CP22 2p+|p−2| 1/3 O˜p(m ) ≤ O˜p(m ) iterations, where each iteration A New Path from Splay to Dynamic Optimality requires solving a linear system. Incorporating a procedure for maintaining an approximate inverse of the linear sys- Consider the task of performing a sequence of searches in tems that we need to solve at each iteration, we give an a binary search tree. After each search, an algorithm is al- algorithm for solving p-regression to 1/poly(n)accuracy lowed to arbitrarily restructure the tree, at a cost propor- max{ω,7/3} that runs in time O˜p(m ), where ω is the matrix tional to the amount of restructuring performed. The cost multiplication constant. For the current best value of ω, of an algorithm’s execution is the sum of the time spent this means that we can solve  regression for all constant searching and the time spent optimizing those searches p p bounded away from 1 as fast as 2 regression. The it- with restructuring operations. This notion was introduced eration counts, as well as running times on general matri- by Sleator and Tarjan in 1985, along with an algorithm ces and sparse graphs improve up previous best result by and a conjecture. The algorithm, Splay, is an elegant pro- [Bubeck-Cohen-Lee-Li STOC’18], as well as other, more cedure for performing adjustments while moving searched general purpose convex optimization algorithms. At the items to the top of the tree. The conjecture, called “dy- core of our algorithms is an iterative refinement scheme for namic optimality,’ is that the cost of splaying is always p-norms, using the quadratically-smoothed p-norms in- within a constant factor of the optimal algorithm for per- troduced in the work of Bubeck et al. Formally, we specify forming searches. The conjecture stands to this day. We a minimization problem over the quadratically-smoothed offer the first systematic proposal for settling the dynamic  norms, such that a crude solution to this problem al- optimality conjecture. At the heart of our methods is what p lows us to improve the quality of an approximate p-norm we term a simulation embedding: a formula that maps ex- minimizer by constant factor, leading to algorithms with ecutions to lists of keys which induce a target algorithm to fast convergence. simulate the execution. We build a simulation embedding for Splay by inducing it to perform arbitrary subtree trans- Sushant Sachdeva, Deeksha Adil formations, and use this to show that if the cost of splaying University of Toronto a sequence of items upper bounds the cost of splaying ev- [email protected], [email protected] ery subsequence thereof, then splay is dynamically optimal. We call this the subsequence property. Building on this machinery, we further show that the subsequence property Rasmus Kyng is also a necessary condition for dynamic optimality. Yale University [email protected] Caleb Levy Princeton University Richard Peng [email protected] DA19 Abstracts 29

[email protected] hardness of approximation is known for these problems for any p

In this paper we provide nearly linear time algorithms for Vijay Bhattiprolu several problems closely associated with the classic Perron- CMU Frobenius theorem, including computing Perron vectors, [email protected] i.e. entrywise non-negative eigenvectors of non-negative matrices, and solving linear systems in asymmetric M- matrices, a generalization of Laplacian systems. The run- Mrinalkanti Ghosh ning times of our algorithms depend nearly linearly on the Toyota Technological Institute Chicago input size and polylogarithmically on the desired accuracy [email protected] and problem condition number. Leveraging these results we also provide improved running times for a broader range Venkatesan Guruswami, Euiwoong Lee of problems including computing random walk-based graph Carnegie Mellon University kernels, computing Katz centrality, and more. The running [email protected], [email protected] times of our algorithms improve upon previously known re- sults which either depended polynomially on the condition Madhur Tulsiani number of the problem, required quadratic time, or only TTI Chicago applied to special cases. We obtain these results by pro- [email protected] viding new iterative methods for reducing these problems to solving linear systems in Row-Column Diagonally Dom- inant (RCDD) matrices. Our methods are related to the classic shift-and-invert preconditioning technique for eigen- CP23 vector computation and constitute the first alternative to the result in Cohen et al. (2016) for reducing stationary Optimizing Quantum Optimization Algorithms via distribution computation and solving directed Laplacian Faster Quantum Gradient Computation systems to solving RCDD systems.

Amirmahdi Ahmadinejad, Arun Jambulapati We develop a quantum algorithm that computes the gra- Stanford University dient of a multi-variate real-valued function f : Rd → R [email protected], [email protected] by evaluating it only a logarithmic number of times in su- perposition. Our algorithm is an improved version of Jor- Amin Saberi dan’s gradient computation algorithm, providing an ap- Management Science and Engineering proximation of the gradient ∇f with quadratically better Stanford University dependence on the evaluation accuracy of f, for an impor- [email protected] tant class of smooth functions. Furthermore, we show that most objective functions arising during the training of vari- Aaron Sidford ational quantum circuits satisfy the necessary smoothness Stanford University conditions, hence our algorithm improves the complexity [email protected] of computing their gradient. We also show that in a con- tinuous phase-query model, our gradient computation algo- rithm has optimal query complexity up to poly-logarithmic CP23 factors, for a class of smooth functions. Moreover, we show Approximability of P -¿ Q Matrix Norms: Gen- that for low-degree multivariate polynomials our algorithm eralized Krivine Rounding and Hypercontractive can provide exponential speedups compared to Jordan’s Hardness algorithm in terms of the dimension d.Weprovideef- ficient subroutines for performing a delicate interconver- We study the problem of computing the p → q sion between probability and phase oracles incurring only mxn norm of a matrix A in R , defined as ||A||p→q := a logarithmic overhead, which might be of independent in- maxx∈Rn{0} ||Ax||q/||x||p. This problem generalizes the terest. Finally, using these tools we improve the runtime spectral norm of a matrix (p = q =2)andthe of prior approaches for training quantum auto-encoders, Grothendieck problem (p=infinity, q=1), and has been variational quantum eigensolvers (VQE), and quantum ap- widely studied in various regimes. When p>= q,the proximate optimization algorithms (QAOA). problem exhibits a dichotomy: constant factor approxima- tion algorithms are known if 2 is in [q,p], and the prob- lem is hard to approximate within almost polynomial fac- Andras Gilyen tors when 2 is not in [q,p]. For the case when 2 is in QuSoft, CWI and University of Amsterdam [q,p] we prove almost matching approximation and NP- [email protected] hardness results. The regime when p2 was studied by [Barak et. al., STOC’12] QuSoft / CWI who gave sub-exponential algorithms for a promise ver- [email protected] sion of the problem (which captures small-set expansion) and also proved hardness of approximation results based Nathan Wiebe on the Exponential Time Hypothesis. However, no NP- Station Q QuArC, Microsoft Research 30 DA19 Abstracts

[email protected] establish a polynomial bound for the directed grid theo- rem on planar digraphs. We think this will enable further applications of directed treewidth and directed grids. We CP23 also give a “treewidth sparsifier’ for directed graphs, which Proportional Volume Sampling and Approximation already was considered in undirected graphs. This allows Algorithms for A-Optimal Design us to obtain an Eulerian subgraph of bounded degree that still has high directed treewidth. We believe this result is We study the optimal design problems where the goal is to of independent interest for structure graph theory. choose a set of linear measurements to obtain the most ac- curate estimate of an unknown vector in d dimensions. We Meike Hatzel study the A-optimal design variant where the objective is Technische Universit¨at Berlin to minimize the average variance of the error in the max- [email protected] imum likelihood estimate of the vector being measured. The problem also finds applications in sensor placement Ken-ichi Kawarabayashi in wireless networks, sparse least squares regression, fea- National Institute of Informatics, Japan ture selection for k-means clustering, and matrix approx- k [email protected] imation. In this paper, we introduce proportional volume sampling to obtain improved approximation algorithms for Stephan Kreutzer A-optimal design. Our main result is to obtain improved Technical University Berlin approximation algorithms for the A-optimal design prob- [email protected] lem by introducing the proportional volume sampling al- gorithm. Our results nearly optimal bounds in the asymp- totic regime when the number of measurements done, k,is CP24 significantly more than the dimension d. We also give first approximation algorithms when k is small including when ATightErd˝os-P´osa Function for Planar Minors k = d. The proportional volume-sampling algorithm also Let H be a planar graph. By a classical result of Robertson gives approximation algorithms for other optimal design and Seymour, there is a function f :→ such that for all k ∈ objectives such as D-optimal design and generalized ra- and all graphs G,eitherG contains k vertex-disjoint sub- tio objective matching or improving previous best known graphs each containing H as a minor, or there is a subset X results. Interestingly, we show that a similar guarantee of at most f(k) vertices such that G − X has no H-minor. cannot be obtained for the E-optimal design problem. We We prove that this remains true with f(k)=ck log k for also show that the A-optimal design problem is NP-hard some constant c = c(H). This bound is best possible, up to approximate within a fixed constant when k = d. to the value of c, and improves upon a recent result of Uthaipon Tantipongpipat Chekuri and Chuzhoy [STOC 2013], who established this d Georgia Institute of Technology with f(k)=ck log k for some universal constant d.The Computer Science proof is constructive and yields a polynomial-time O(log)- [email protected] approximation algorithm for packing subgraphs containing an H-minor.

Mohit Singh Jean-Florent Raymond H. Milton Stewart School of Industrial & Systems TU Berlin Engineering [email protected] Georgia Institute of Technology [email protected] Wouter Cames Van Batenburg D´epartement d’Informatique, Universit´eLibrede Aleksandar Nikolov Bruxelles University of Toronto Brussels, Belgium [email protected] [email protected]

CP24 Tony Huynh Polynomial Planar Directed Grid Theorem Universit´e Libre de Bruxelles [email protected] The grid theorem [Robertson, Seymour 1986] is a central result in the study of graph minors and has found many Gwena¨el Joret algorithmic applications. The relation between treewidth D´epartement d’Informatique, Universit´eLibrede and grid minors is polynomial, even linear, for planar Bruxelles graphs [Robertson, Seymour and Thomas, 1994] enabling Brussels, Belgium many important consequences (e.g. sublinear separators [email protected] and subexponential algorithms). In the mid-90s, Reed and Johnson, Robertson, Seymour and Thomas proposed a no- tion of directed treewidth. They conjectured an excluded CP24 grid theorem for directed graphs, which was proved in 2015 Polynomial Bounds for Centered Colorings on by the latter two authors but the function relating directed Proper Minor-Closed Graph Classes treewidth and grid minors is big, even in the planar case. Directed grids have found algorithmic applications such as Centered colorings play an important role in the theory low-congestion routing. However, in the undirected case of sparse graph classes introduced by Neˇsetˇril and Os- the polynomial bound on the size of grid minors in pla- sona de Mendez, as they structurally characterize classes nar graphs have made this tool so successful. The lack of of bounded expansion: a class C has bounded expansion if such a bound has so far prevented further applications in and only if there is a function f : N → N such that every the directed setting. The main result of this paper is to graph G ∈Cfor every p ∈ N admits a p-centered coloring DA19 Abstracts 31

with at most f(p) colors. Unfortunately, known proofs of Theorem the existence of such colorings yield large upper bounds on the function f governing the number of colors needed, even We study the Excluded Grid Theorem, a fundamental for as simple classes as planar graphs. In this paper, we structural result in graph theory, that was proved by prove that every Kt-minor-free graph admits a p-centered Robertson and Seymour in their seminal work on graph coloring with O(pg(t)) colors for some function g.Thispro- minors. The theorem states that there is a function Z+ → Z+ vides the first polynomial upper bounds on the number of f : , such that for every integer g>0, every × colors needed in p-centered colorings of graphs drawn from graph of treewidth at least f(g)containsthe(g g)-grid proper minor-closed classes, which answers an open prob- as a minor. For every integer g>0, let f(g) be the small- lem posed by Dvoˇr´ak. As an algorithmic application, we est value for which the theorem holds. Establishing tight C bounds on f(g) is an important graph-theoretic question. use our main result to prove that if is a fixed proper 2 minor-closed class of graphs, then given graphs H and G, Robertson and Seymour showed that f(g)=Ω(g log g) on p and n vertices, respectively, where G ∈C,itcanbede- must hold. For a long time, the best known upper bounds cided whether H is a subgraph of G in time 2O(p log p) ·nO(1) on f(g) were super-exponential in g. The first polynomial upper bound of f(g)=O(g98 log g) was proved by Chekuri and space nO(1). and Chuzhoy. It was later improved to f(g)=O(g36 log g), and then to f(g)=O(g19 log g). In this paper we further Sebastian Siebertz improve this bound to f(g)=O(g9 log g). We believe that Technische Universit¨at Berlin our proof is significantly simpler than the proofs of the pre- [email protected] vious bounds. Moreover, while there are natural barriers that seem to prevent the previous methods from yielding Michal Pilipczuk tight bounds for the theorem, it seems conceivable that the University of Warsaw techniques proposed in this paper can lead to even tighter [email protected] bounds on f(g).

Marcin Pilipczuk Julia Chuzhoy University of Warsaw Toyota Technological Institute at Chicago Warsaw, Poland [email protected] [email protected] Zihan Tan The University of Chicago CP24 [email protected] Every Collinear Set in a Planar Graph is Free CP25 We show that if a planar graph G has a plane straight- A Practical Algorithm for Spatial Agglomerative line drawing in which a subset S of its vertices is collinear, Clustering then for any set of points X with |X| = |S|,thereisa plane straight-line drawing of G in which the vertices in We study an agglomerative clustering problem motivated S are mapped to the points in X.Thissolvesanopen by visualizing disjoint glyphs centered at specific locations problem posed by Ravsky and Verbitsky in 2008. In their on a geographic map. As we zoom out, the glyphs grow terminology, we show that every collinear set is free. This and start to overlap. We replace overlapping glyphs by one result has applications in graph drawing, including untan- larger merged glyph to maintain disjointness. Our goal is gling, column planarity, universal point subsets, and partial to compute the resulting hierarchical clustering efficiently simultaneous drawings. in practice. A straightforward algorithm for such spatial agglomerative clustering runs in O(n2 log n)time,where Vida Dujmovic n is the number of glyphs. This is not efficient enough University of Ottawa for many real-world datasets which contain up to tens or [email protected] hundreds of thousands of glyphs. Recently the theoretical upper bound was improved to O(nα(n)log7 n)time[?], Fabrizio Frati where α(n) is the inverse Ackermann function. Although Universit`aRomaTre this new algorithm is asymptotically much faster than the [email protected] naive algorithm, from a practical point of view, it does not perform better for n ≤ 106. In this paper we present a new Daniel Gon¸calves agglomerative clustering algorithm which works efficiently LIRMM (CNRS & Universit´e de Montpellier) in practice. Our algorithm relies on the use of quadtrees to [email protected] speed up spatial computations. Interestingly, even in non- pathological datasets we can encounter large glyphs that Pat Morin intersect many quadtree cells and that are involved in many Carleton University clustering events. We therefore devise a special strategy to [email protected] handle such large glyphs. We test our algorithm on several synthetic and real-world datasets and show that it performs well in practice. G¨unter Rote Freie Universit¨at Berlin Thom Castermans Institut f¨ur Informatik TU Eindhoven [email protected] [email protected]

Bettina Speckmann CP24 Dept. of Mathematics and Computer Science Towards Tight(er) Bounds for the Excluded Grid TU Eindhoven 32 DA19 Abstracts

[email protected] Karlsruhe Institute of Technology [email protected] Kevin Verbeek TU Eindhoven [email protected] CP25 Scalable Edge Partitioning

CP25 Edge-centric distributed computations have appeared as Practical Methods for Computing Large Covering a recent technique to improve the shortcomings of think- Tours and Cycle Covers with Turn Cost like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partition- We study the problem of computing provably optimal and ing—partitioning edges into roughly equally sized blocks— near-optimal solutions for the NP-hard problem of finding has emerged as an alternative to traditional (node-based) covering tours and cycle covers with turn cost, which are graph partitioning. In this work, we develop a fast paral- of practical importance for a variety of applications, such lel split-and-connect graph construction algorithm in the as pest control and precision farming. Previous work has distributed setting and show that combining our parallel largely focused on theoretical aspects, such as complexity construction with advanced parallel node partitioning algo- and approximation. We develop a number of algorithm rithms yields high-quality edge partitions in a scalable way. engineering techniques and refinements to make such theo- Our technique scales to networks with billions of edges, retical insights practically useful, resulting in a comprehen- and runs efficiently on thousands of PEs. Our extensive sive study for solving a wide spectrum of large instances. experiments show that our algorithm computes solutions We compute provably optimal solutions for instances with of high quality on large real-world networks and large hy- more than 1000 pixels, from the largest previous solved perbolic random graphs—which have a power law degree instance size of 76 (de Assis and de Souza 2011). Making distribution and are therefore specifically targeted by edge use of additional algorithm engineering techniques for han- partitioning. dling very large instances, we also compute near-optimal solutions for instances with up to 300000 pixels, for which Darren Strash we give solutions that are typically within a few percent Department of Computer Science of our computed lower bounds. We also provide an ex- Colgate University perimental comparison of a practically refined version of [email protected] our new theoretical approach with the approximation tech- nique of Arkin et al. that dates back to 2001; we show that Sebastian Schlag our new LP/IP-based approximation method closes 70% of Karlsruhe Institute of Technology the remaining optimality gap to the lower bound. Institute for Theoretical Informatics, Algorithmics II [email protected] S´andor Fekete, Dominik M. Krupke TU Braunschweig [email protected], [email protected] Christian Schulz University of Vienna Karlsruhe Institute of Technology CP25 [email protected] Faster Support Vector Machines Daniel Seemaier The time complexity of support vector machines (SVMs) Karlsruhe Institute of Technology prohibits training on huge data sets with millions of sam- [email protected] ples. Recently, multilevel approaches to train SVMs have been developed to allow for time efficient training on huge data sets. While regular SVMs perform the entire train- CP25 ing in one - time consuming - optimization step, multilevel Parallel Range, Segment and Rectangle Queries SVMs first build a hierarchy of problems decreasing in size with Augmented Maps that resemble the original problem and then train an SVM model for each hierarchy level benefiting from the solved The support of range, segment and rectangle queries are models of previous levels. We present a faster multilevel fundamental problems in computational geometry, and support vector machine that uses a label propagation algo- have extensive applications in many domains. Despite sig- rithm to construct the problem hierarchy. Extensive exper- nificant theoretical work on these problems, efficient imple- iments show that our new algorithm achieves speed-ups of mentations can be complicated, and most implementations up to two orders of magnitude while having similar or bet- do not have useful theoretical bounds. In this paper, we ter classification quality over state-of-the-art algorithms. focus on simple and efficient parallel algorithms and imple- mentations for range, segment and rectangle queries, which have worst-case bounds in theory and good performance in Sebastian Schlag practice. Our approach uses an abstract data type called Karlsruhe Institute of Technology augmented map, based on which we develop both multi- Institute for Theoretical Informatics, Algorithmics II level tree structures and sweepline algorithms supporting [email protected] range, segment and rectangle queries. For the sweepline algorithms, we propose a parallel paradigm and show cor- Matthias Schmitt responding cost bounds. Theoretically, the construction Karlsruhe Institute of Technology algorithms of all of our data structures are work-efficient [email protected] and highly parallelized. We implemented all the data struc- tures in the paper, ten in all, using a parallel augmented Christian Schulz map library. Based on the library, each data structure only University of Vienna requires about 100 lines of C++ code. We test their per- DA19 Abstracts 33

formance on large data sets and a machine with 72-cores ture many interesting problem settings and are important (144 hyperthreads). Our implementation achieves 32-68x building blocks in various approximation algorithms. We speedup in construction, and up to 126x in queries. Se- consider spanning trees subject to constraints on the edges quentially, our implementation outperforms or is compet- in a family of cuts forming a laminar family of small width. itive to existing libraries including the CGAL library and Our main contribution is a new dynamic programming ap- the Boost library. proach, where the value of a table entry does not only de- pend on the values of previous table entries, as is usually Yihan Sun the case, but also on a specific representative solution saved Carnegie Mellon University together with each table entry. This allows for handling [email protected] a broad range of constraint types. In combination with other techniques—including negatively correlated rounding Guy Blelloch and a polyhedral approach—we obtain several new results. Computer Science Department We first present a quasi-polynomial time algorithm for the Carnegie Mellon University Minimum Chain-Constrained Spanning Tree problem with [email protected] an essentially optimal guarantee: violation of chain con- straints is bounded by a 1+epsilon factor, and the cost is no larger than that of an optimal solution not violating any CP26 chain constraint. The best previous procedure is a bicrite- Lift and Project Algorithms for Precedence Con- ria approximation violating each chain constraint by up to strained Scheduling to Minimize Completion Time a constant factor and losing another factor in the objective. Moreover, our approach can naturally handle lower bounds We consider the classic problem of scheduling jobs with on the chain constraints. Furthermore, we show how our precedence constraints on a set of identical machines to approach can also handle parity constraints as used in the minimize the weighted completion time objective. Under- context of (path) TSP and a generalization thereof, and standing the exact approximability of the problem when discuss implications in this context. job lengths are uniform is a well known open problem in scheduling theory. In this paper, we show an optimal algo- Martin Nagele,RicoZenklusen rithm that runs in polynomial time and achieves an approx- ETH Zurich imation factor of (2+epsilon) for the weighted completion [email protected], [email protected] time objective when the number of machines is a constant. The result is obtained by building on the lift and project approach introduced in a breakthrough work by Levey and CP26 Rothvoss for the makespan minimization problem. On Approximating (Sparse) Covering Integer Pro- grams Janardhan Kulkarni Microsoft Research, Redmond We consider approximation algorithms for covering inte- [email protected] ger programs parametrized by column sparsity. First, we show that a simple algorithm based on randomized round- Shashwat Garg ing with alteration improves or matches the best known TU Eindhoven approximation algorithms in a wide range of parameter [email protected] settings, and these bounds are essentially optimal. As a byproduct of the simplicity of the alteration algorithm Shi Li and analysis, we can derandomize the algorithm with- Toyota Technological Institute at Chicago out any loss in the approximation guarantee or efficiency. shil@buffalo.edu Non-trivial approximation algorithms for covering integer programs are based on solving the natural LP relaxation strengthened with knapsack cover inequalities. Our second CP26 contribution is a fast (essentially near-linear time) approx- A Polynomial Time Constant Approximation For imation scheme for solving the strengthened LP with a Minimizing Total Weighted Flow-time factor of n speed up over the previous best running time.

Abstract not available. Chandra Chekuri, Kent Quanrud University of Illinois at Urbana-Champaign Janardhan Kulkarni [email protected], [email protected] Microsoft Research, Redmond [email protected] CP26 Uriel Feige A 1.5-Approximation for Path TSP Weizmann Institute, Israel [email protected] We present a 1.5-approximation for the Metric Path Trav- eling Salesman Problem (Path TSP). All recent improve- Shi Li ments on Path TSP crucially exploit a structural prop- Toyota Technological Institute at Chicago erty shown by An, Kleinberg, and Shmoys [Journal of the shil@buffalo.edu ACM, 2015], namely that narrow cuts with respect to a Held-Karp solution form a chain. We significantly deviate from these approaches by showing the benefit of dealing CP26 with larger s-t cuts, even though they are much less struc- A New Dynamic Programming Approach for Span- tured. More precisely, we show that a variation of the ning Trees with Chain Constraints and Beyond dynamic programming idea recently introduced by Traub and Vygen [SODA, 2018] is versatile enough to deal with Short spanning trees subject to additional constraints cap- larger size cuts, by exploiting a seminal result of Karger 34 DA19 Abstracts

on the number of near-minimum cuts. This avoids a recur- tions in Massively Parallel Computation and Cen- sive application of dynamic programming as used by Traub tralized Local Computation and Vygen, and leads to a considerably simpler algorithm avoiding an additional error term in the approximation Abstract not available. guarantee. We match the still unbeaten 1.5-approximation guarantee of Christofides’ algorithm for TSP. Hence, any Mohsen Ghaffari, Jara Uitto further progress on the approximability of Path TSP will ETH Zurich also lead to an improvement for TSP. Speaker: Martin ghaff[email protected], [email protected] Nagele, ETH Zrich, Switzerland

Rico Zenklusen CP27 ETH Zurich Low Congestion Cycle Covers and their Applica- [email protected] tions A cycle cover of a bridgeless graph G is a collection of sim- CP27 ple cycles in G such that each edge e appears on at least Coresets Meet EDCS: Algorithms for Matching one cycle. Motivated by applications to distributed com- and Vertex Cover on Massive Graphs putation, we introduce the notion of low-congestion cycle covers, in which all cycles in the cycle collection are both We present a single unified approach for designing im- short and nearly edge-disjoint. Formally, a (, )-cycle cover proved algorithms for matching and vertex cover across of a graph G is a collection of cycles in G in which each several models of computation for processing massive cycle is of length at most and each edge participates in graphs such as streaming, distributed communication, and at least one cycle and at most cycles. Perhaps quite sur- the massively parallel computation (MPC) models. For prisingly, we prove the following: Every bridgeless graph example, we give: of diameter D admits a (, )-cycle cover where = O˜(D)and ˜ • The first one pass, significantly-better-than-2- = O(1). That is, the edges of G can be covered by cycles approximation for matching in the random arrival such that each cycle is of length at most O(D)andeach order streaming model that uses subquadratic space, edge participates in at most O(1) cycles. These parame- namely a 1.5-approximation streaming algorithm ters are existentially tight up to polylogarithmic terms. We that uses O˜(n1.5)space. demonstrate the usefulness of low congestion cycle covers • The first 2 round, better-than-2-approximation for in different settings of resilient computation. For instance, matching in the MPC model that uses subquadratic we consider a Byzantine fault model where in each round, space per machine, namely a 1.5-approximation algo- the adversary chooses a single message and corrupt in an √ arbitrarily manner. We provide a compiler that turns any rithm with O˜( mn + n) memory per machine. r-round distributed algorithm for a graph G with diameter By building on our unified approach, we further develop D, into an equivalent fault tolerant algorithm with r · (D) parallel algorithms in the MPC model that give a (1 + )- rounds. approximation to matching and an O(1)-approximation to vertex cover in only O(log log n) MPC rounds and Merav Parter, Eylon Yogev O(n/polylog(n)) memory per machine. These results set- Weizmann Institute tle multiple open questions posed by Czumaj et.al [STOC merav,[email protected], [email protected] 2018]. We obtain our results by a novel combination of two previously disjoint set of techniques, namely random- ized composable coresets and edge degree constrained sub- CP27 graphs (EDCS). We significantly extend the power of these Massively Parallel Approximation Algorithms for techniques and prove several new structural results. Edit Distance and Longest Common Subsequence

Sepehr Assadi String similarity measures are among the most fundamen- University of Pennsylvania tal problems in computer science. The notable examples [email protected] are edit distance () and longest common subsequence (). These problems find their applications in various contexts MohammadHossein Bateni such as computational biology, text processing, compiler Google Research optimization, data analysis, image analysis, etc. In this [email protected] work, we revisit edit distance and longest common sub- sequence in the parallel settings. We present massively Aaron Bernstein parallel algorithms for both problems that are optimal in the following senses: Technical University of Berlin, Germany [email protected] • The approximation factor of our algorithms is 1 + . • The round complexity of our algorithms is constant. Vahab Mirrokni • The total running time of our algorithms over all ma- Google Inc. 2 [email protected] chines is (n ). This matches the running time of the best-known solutions for approximating edit distance and longest common subsequence within a 1+ factor Cliff Stein in the sequential setting. Columbia University cliff@ieor.columbia.edu Our main technical contribution is a novel parallel algo- rithm for computing a set of compositions, and recursively decomposing each function into a set of smaller iterative CP27 compositions (in terms of memory needed to solve the prob- Sparsifying Distributed Algorithms with Ramifica- lem). These two methods together give us a strong tool for DA19 Abstracts 35

approximating combinatorial problems. For instance, can [email protected] be formulated as a recursive composition of functions and therefore this tool enables us to approximate within a fac- tor 1 + . CP28 Quantum Speedups for Exponential-Time Dynamic Saeed Seddighin Programming Algorithms University of Maryland, College Park [email protected] In this paper we study quantum algorithms for NP- complete problems whose best classical algorithm is an ex- Xiaorui Sun ponential time application of dynamic programming. We University of Illinois at Chicago introduce the path in the hypercube problem that models [email protected] many of these dynamic programming algorithms. In this problem we are asked whether there is a path from 0n to n MohammadTaghi Hajiaghayi 1 in a given subgraph of the Boolean hypercube, where University of Maryland, College Park the edges are all directed from smaller to larger Hamming [email protected] weight. We give a quantum algorithm that solves path in the hypercube in time O∗(1.817n ). The technique com- bines Grover’s search with computing a partial dynamic programming table. We use this approach to solve a va- CP27 riety of vertex ordering problems on graphs in the same Distributed Algorithms Made Secure: A Graph time O∗(1.817n), and graph bandwidth in time O∗(2.946n). Theoretic Approach Then we use similar ideas to solve the travelling salesman problem and minimum set cover in time O∗(1.728n). An inherent property of most existing distributed algo- rithms is that throughout the course of their execution, the Jevgenijs Vihrovs, Andris Ambainis, Kaspars Balodis, nodes get to learn not only their own output but rather Janis Iraids, Martins Kokainis, Krisjanis Prusis learn quite a lot on the outputs of many other entities. University of Latvia This leakage of information might be a major obstacle in [email protected], [email protected], many settings. In this paper, we introduce a new frame- [email protected], [email protected], mar- work for secure distributed graph algorithms and provide [email protected], [email protected] the first general compiler that takes any “natural’ non- secure distributed algorithm that runs in r rounds, and CP28 turns it into a secure algorithm that runs in O(r · D · (Δ)) rounds where Δ is the maximum degree in the graph and D A Time and Space-Optimal Algorithm for the is its diameter. The security of the compiled algorithm is Many-Visits TSP information-theoretic but holds only against a semi-honest adversary that controls a single node in the network. This The many-visits traveling salesperson problem (MV-TSP) compiler is made possible due to a new combinatorial struc- asks for an optimal tour of n cities that visits each city ture called private neighborhood trees: a collection of n c a prescribed number kc of times. Travel costs may be trees T (u1),...,T(un), one for each vertex ui ∈ V (G), asymmetric, and visiting a city twice in a row may incur such that each tree T (ui) spans the neighbors of ui with- a non-zero cost. The MV-TSP problem finds applications out going through ui.Ina(, )-private neighborhood trees in scheduling, geometric approximation, and Hamiltonic- each tree T (ui) has depth at most and each edge e ∈ G ity of certain graph families. The fastest known algorithm appears in at most different trees. We show a construction for MV-TSP is due to Cosmadakis and Papadimitriou O(n) 3 where = O(Δ · D)and=O(D). (SICOMP, 1984). It runs in time n + O(n log c kc) and requires nΩ(n) space. The algorithm has a logarithmic Merav Parter, Eylon Yogev dependence on the total length c kc of the tour, allowing Weizmann Institute it to handle instances with very long tours, beyond what merav,[email protected], [email protected] is tractable in the standard TSP setting. In this paper we significantly improve on the said algorithm, giving an MV- TSP algorithm that runs in single-exponential time with CP28 polynomial space. More precisely, we obtain the run time O(n) 3 2 2 + O(n log c kc), with O(n log c kc) space. The Interval Vertex Deletion Admits a Polynomial Ker- space requirement of our algorithm is (essentially) the size nel of the output, and assuming the Exponential-time Hypoth- esis (ETH), the time requirement is optimal. Our algo- Given a graph G and an integer k,theInterval Ver- rithm is deterministic, and arguably both simpler and eas- tex Deletion (IVD) problem asks whether there exists ier to analyse than the original approach of Cosmadakis a subset S ⊆ V (G)ofsizeatmostk such that G − S is an and Papadimitriou. It involves an optimization over di- interval graph. This problem is known to be NP-complete rected spanning trees and a recursive, centroid-based de- [Yannakakis, STOC’78]. Originally in 2012, Cao and Marx composition of trees. showed that IVD is fixed parameter tractable: they ex- hibited an algorithm with running time 10knO(1) [Cao and Andr´eBerger Marx, SODA’14]. The existence of a polynomial kernel for Maastricht University IVD remained a well-known open problem in Parameter- Department of Quantitative Economics ized Complexity. In this paper, we settle this problem in [email protected] the affirmative. L´aszl´oKozma Akanksha Agrawal Eindhoven University of Technology Hungarian Academy of Sciences Department of Mathematics and Computer Science 36 DA19 Abstracts

[email protected] when parameterized by k/r only? We resolve the wider 2 question by (a) obtaining a 2O((k/r) log(k/r))·(n+log k)O(1)- Matthias Mnich time algorithm for r-Simple k-Pathondigraphsanda Maastricht University / Universit{ 2O(k/r) · (n +logk)O(1)-time algorithm for r-Simple k-Path Department of Quantitative Economics / Computer on undirected graphs, (b) showing that p-Set (r, q)-Packing Science is FPT (in contrast, we prove that p-Multiset (r, q)-Packing [email protected] is W[1]-hard), and (c) proving that (r, k)-Monomial Detec- tion is para-NP-hard even if only two distinct variables are Roland Vincze in polynomial P and the circuit is non-canceling. All our Maastricht University algorithms are deterministic. [email protected] Meirav Zehavi Ben-Gurion University CP28 [email protected] Losing Treewidth by Separating Subsets Gregory Gutin, Magnus Wahlstrom We study the problem of deleting the smallest set S of Royal Holloway, University of London vertices (resp. edges) from a given graph G such that [email protected], [email protected] the induced subgraph (resp. subgraph) G \ S belongs to some class H. We consider the case where graphs in H have treewidth bounded by t, and give a general frame- CP29 work to obtain approximation algorithms for both vertex An Illuminating Algorithm for the Light Bulb and edge-deletion settings from approximation algorithms Problem for certain natural graph partitioning problems called k- Subset Vertex Separator and k-Subset Edge Separator, re- The Light Bulb Problem is one of the most basic prob- spectively. For the vertex deletion setting, our framework lems in data analysis. One is given as input n vectors in combined with the current best result for k-Subset Vertex {−1, 1}d, which are all independently and uniformly ran- Separator, improves approximation ratios for basic prob- dom, except for a planted pair of vectors with inner product lems such as k-Treewidth Vertex Deletion and Planar-F at least ρ·d for some constant ρ>0. The task is to find the Vertex Deletion. Our algorithms are simpler than previous planted pair. The most straightforward algorithm leads to works and give the first deterministic and uniform approxi- aruntimeofΩ(n2). Algorithms based on techniques like mation algorithms under the natural parameterization. For Locality-Sensitive Hashing achieve runtimes of n2−O(ρ);as the edge deletion setting, we give improved approximation ρ gets small, these approach quadratic. Building on prior algorithms for k-Subset Edge Separator combining ideas work, we give a new algorithm for this problem which runs from LP relaxations and important separators. We present in time O(n1.582 + nd), regardless of how small ρ is. This their applications in bounded-degree graphs, and also give matches the best known runtime due to Karppa et al. Our an APX-hardness result for the edge deletion problems. algorithm combines techniques from previous work on the Light Bulb Problem with the so-called ‘polynomial method Euiwoong Lee, Anupam Gupta, Jason M. Li in algorithm design,’ and has a simpler analysis than previ- Carnegie Mellon University ous work. Our algorithm is also easily derandomized, lead- [email protected], [email protected], ing to a deterministic algorithm for the Light Bulb Prob- [email protected] lem with the same runtime of O(n1.582 + nd), improving previous results. Pasin Manurangsi UC Berkeley Josh Alman [email protected] MIT [email protected] Michal Wlodarczyk University of Warsaw [email protected] CP29 A Framework for Searching in Graphs in the Pres- ence of Errors CP28 On r-Simple k-Path and Related Problems Param- We consider a problem of searching for an unknown tar- eterized by k/r get vertex t in a graph. Each vertex-query points to a vertex v and the response either admits that v is the tar- In r-Simple k-Path, given a digraph G on n vertices and get or provides any neighbor s that lies on a shortest path positive integers r, k, the goal is to decide whether G has an from v to t. This model has been introduced for trees r-simple k-path, which is a walk where every vertex occurs by Onak and Parys [FOCS 2006] and for general graphs at most r times and the total number of vertex occurrences by Emamjomeh-Zadeh et al. [STOC 2016]. In the lat- is k. Abasi et al. (2014) obtained a randomized algorithm ter, the authors provide an algorithm for the independent of running time 4(k/r)logr · nO(1) for this problem and a re- noise model where each query independently receives an lated problem called (r, k)-Monomial Detection. Gabizon erroneous answer with probability p<1/2. We show an O((k/r)logr) O(1) log2 n et al. (2015) designed a deterministic 2 · n - algorithm that needs at most 1−H(r) queries under adver- time algorithm for these two problems and a related prob- sarial errors with error rate bounded by a constant r<1/2. lem called p-Set (r, q)-Packing. These results prove that We then show that our algorithm coupled with a Chernoff the three problems are single-exponentially fixed-parameter bound argument leads to a simpler algorithm for the in- tractable (FPT) when parameterized by the product of two dependent noise model and has query complexity that is parameters, that is, k/r and log r. We consider the ques- both simpler and asymptotically better than the one of tion from a wider perspective: are the above problems FPT Emamjomeh-Zadeh et al. [STOC 2016]. Our approach has DA19 Abstracts 37

a wide range of applications. First, it improves and simpli- Freie Universit¨at Berlin fies the Robust Interactive Learning framework proposed Institut f¨ur Informatik by Emamjomeh-Zadeh and Kempe [NIPS 2017]. Secondly, [email protected] analogous analysis for edge-queries, where query to edge e returns its endpoint that is closer to target, recovers an asymptotically optimal noisy binary search algorithm, CP29 matching the complexity of Feige et al. [SIAM J. Comput. Selection from Heaps, Row-Sorted Matrices and 1994]. Thirdly, we improve and simplify upon an algo- X+Y Using Soft Heaps rithm for searching in unbounded domains due to Aslam and Dhagat [STOC 1991]. We use soft heaps to obtain simpler optimal algorithms for selecting the k-th smallest item, and the set of k small- Dariusz Dereniowski est items, from a heap-ordered tree, from a collection of Gdansk University of Technology sorted lists, and from X + Y ,whereX and Y are two [email protected] unsorted sets. Our results match, and in some ways ex- tend and improve, classical results of Frederickson (1993) Stefan Tiegel and Frederickson and Johnson (1982). In particular, for Department of Computer Science selecting the k-th smallest item, or the set of k smallest ETH Zurich items, from a collection of m sorted lists we obtain a new [email protected] optimal“output-sensitive” algorithm that performs only m O(m+ i=1 log(ki +1)) comparisons, where ki is the num- Przemyslaw Uznanski ber of items of the i-th list that belong to the overall set ETH Zurich of k smallest items. [email protected] Uri Zwick Daniel Wolleb-Graf Tel Aviv University Department of Computer Science [email protected] ETH Zurich [email protected] Haim Kaplan Tel-Aviv University [email protected] CP29 Simple Concurrent Labeling Algorithms for Con- Or Zamir nected Components Tel Aviv University [email protected] We present some new concurrent labeling algorithms for finding connected components and study their theoreti- L´aszl´oKozma cal efficiency. Even though many such algorithms have Eindhoven University of Technology been proposed and many experiments with them have been Department of Mathematics and Computer Science done, our algorithms are simpler. We obtain an O(lg n) [email protected] step bound for two of our algorithms using a novel multi- round analysis. We conjecture that our other algorithms also take O(lg n) steps but are unable to fully analyze them. CP30 We also point out some gaps in previous analyses of simi- lar algorithms. Our results show that even a basic problem Communication-Rounds Tradeoffs for Common like connected components still has secrets to reveal. Randomness and Secret Key Generation Sixue Liu We study the role of interaction in the Common Random- Princeton University ness Generation (CRG) and Secret Key Generation (SKG) [email protected] problems. In the CRG problem, two players, Alice and Bob, respectively get samples X1,X2,... and Y1,Y2,... Robert Tarjan with the pairs (X1,Y1), (X2,Y2), ... being drawn indepen- Princeton University dently from some known probability distribution μ.They Microsoft Research wish to communicate so as to agree on L bits of random- [email protected] ness. The SKG problem is the restriction of the CRG prob- lem to the case where the key is required to be close to random even to an eavesdropper who can listen to their CP29 communication (but does not have access to the inputs of Isotonic Regression by Dynamic Programming Alice and Bob). In this work, we study the relationship between the amount of communication and the number of For a given sequence of n numbers, we want to find a mono- rounds of interaction in both the CRG and the SKG prob- tonically increasing sequence of the same length that best lems. Specifically, we construct a family of distributions approximates it in the sense of minimizing the weighted μ = μr,n,L , parametrized by integers r, n and L, such that sum of absolute values of the differences. A conceptually for every r there exists a constant b = b(r)forwhichCRG ∼ easy dynamic programming approach leads to an algorithm (respectively SKG) is feasible when (Xi,Yi) μr,n,L with with running time O(n log n). While other algorithms with r + 1 rounds of communication, each consisting of O(log n) the same running time are known, our algorithm is very bits, but when restricted to r/2 − 2 rounds of interaction, simple. The only auxiliary data structure that it requires the total communication must exceed Ω(n/ logb(n)) bits. is a priority queue. The approach extends to other error Prior to our work no separations were known for r ≥ 2. measures such as sum of squares. Mitali Bafna G¨unter Rote John A. Paulson School of Engineering and Applied 38 DA19 Abstracts

Sciences are nearly optimal tradeoffs in terms of the dimension, dis- Harvard University tortion, and sparsity, for the important case of 1 ≤ p<2, [email protected] much less was known. In this paper we obtain nearly op- timal tradeoffs for p oblivious subspace embeddings for Badih Ghazi every 1 ≤ p<2. Oblivious subspace embeddings are cru- Google Research cial for distributed and streaming environments, as well [email protected] as entrywise p low rank approximation. Our results give improved algorithms for these applications.

Noah Golowich Ruosong Wang, David Woodruff Harvard University Carnegie Mellon University [email protected] [email protected], [email protected] Madhu Sudan Harvard CP30 [email protected] Optimal Las Vegas Approximate Near Neighbors in p CP30 We show that approximate near neighbor search in high The Andoni-Krauthgamer-Razenshteyn Charac- dimensions can be solved in a Las Vegas fashion (i.e., terization of Sketchable Norms Fails for Sketchable without false negatives) for p (1 ≤ p ≤ 2) while match- Metrics ing the performance of optimal locality-sensitive hashing. Specifically, we construct a data-independent Las Vegas Andoni, Krauthgamer and Razenshteyn (AKR) proved data structure with query time O(dnρ) and space usage · that a finite-dimensional normed space (X, X )admits O(dn1+ρ)for(r, cr)-approximate near neighbors in Rd un- a O(1) sketching algorithm (namely, with O(1) sketch size der the  norm, where ρ =1/cp + o(1). Furthermore, we ∈ p and O(1) approximation) if and only if for every  (0, 1) give a Las Vegas locality-sensitive filter construction for ≥ → there exist α 1 and an embedding f : X 1− such the unit sphere that can be used with the data-dependent − ≤ − ≤ − that x y X f(x) f(y) 1− α x y X for all data structure of Andoni et al. (SODA 2017) to achieve ∈ x, y X. The ”if part” of this theorem follows from a optimal space-time tradeoffs in the data-dependent setting. sketching algorithm of Indyk. The contribution of AKR For the symmetric case, this gives us a data-dependent Las is therefore to demonstrate that the mere availability of Vegas data structure with query time O(dnρ) and space us- a sketching algorithm implies the existence of the afore- age O(dn1+ρ)for(r, cr)-approximate near neighbors in Rd mentioned geometric realization. Indyk’s algorithm shows under the  norm, where ρ =1/(2cp − 1) + o(1). that the ”if part” of the AKR characterization holds true p for any metric space whatsoever, i.e., the existence of an Alexander Wei embedding as above implies sketchability even when X is Harvard University not a normed space. Due to this, a natural question that [email protected] AKR posed was whether the assumption that the underly- ing space is a normed space is needed for their characteri- zation of sketchability. We resolve this question by proving CP30 ∈ N that for arbitrarily large n there is an n-point metric Optimal Lower Bounds for Distributed and space (M(n),dM(n))whichisO(1)-sketchable yet for every Streaming Spanning Forest Computation 1 ∈ ≥ → −  (0, 2 ), if α(n) 1andfn : M(n) 1  are such that dM(n)(x, y) ≤ fn(x) − fn(y) 1− ≤ α(n)dM(n)(x, y) for all We show optimal lower bounds for spanning forest com- x, y ∈ M(n), then necessarily limn→∞ α(n)=∞. putation in two different models: * One wants a data structure for fully dynamic spanning forest in which up- Assaf Naor dates can insert or delete edges amongst a base set of n Princeton University vertices. The sole allowed query asks for a spanning for- [email protected] est, which the data structure should successfully answer with some given (potentially small) constant probability Subhash Khot >0. We prove that any such data structure must use New York University Ω(n log3 n) bits of memory. * There is a referee and n [email protected] vertices in a network sharing public randomness, and each vertex knows only its neighborhood; the referee receives no input. The vertices each send a message to the referee CP30 who then computes a spanning forest of the graph with Tight Bounds for p Oblivious Subspace Embed- constant probability >0. We prove the average mes- dings sage length must be Ω(log3 n) bits. Both our lower bounds are optimal, with matching upper bounds provided by the An p oblivious subspace embedding is a distribution over AGM sketch [AGM12] (which even succeeds with proba- r × n matrices Π such that for any fixed n × d matrix A, bility 1-1/poly(n)). Furthermore, for the first setting we show optimal lower bounds even for low failure probability 1− Pr[for all x, Ax p ≤ ΠAx p ≤ κ Ax p] ≥ 9/10, −n Π δ,aslongasδ>2 . where r is the dimension of the embedding, κ is the distor- Huacheng Yu tion of the embedding, and for an n-dimensional vector y, Stanford University n | | 1/p [email protected] y p = i=1 yi is the p-norm. Another important property is the sparsity of Π, that is, the maximum num- ber of non-zero entries per column, as this determines the Jelani Nelson running time of computing Π · A. While for p =2there Harvard DA19 Abstracts 39

[email protected] rithm of Solomon [FOCS 2016] who gets an approximation ratio of 2 and an expected amortized update time of O(1). We derive our result by analyzing, via a novel technique, a CP31 variant of the algorithm by Bhattacharya et al. Specifically, A Deamortization Approach for Dynamic Spanner we consider an idealized setting where the update time of and Dynamic Maximal Matching an algorithm can take any arbitrary fractional value, and use insights from this setting to come up with an appro- Many dynamic graph algorithms have an amortized up- priate potential function. date time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real- Sayan Bhattacharya time systems, where each individual operation has to be University of Warwick executed quickly. For this reason, there exist many re- Coventry cent randomized results that aim to provide a guarantee [email protected] stronger than amortized expected. The strongest possi- ble guarantee for a randomized algorithm is that it is al- Janardhan Kulkarni ways correct (Las Vegas), and has high-probability worst- Microsoft Research, Redmond case update time, which gives a bound on the time for [email protected] each individual operation that holds with high probability. In this paper we present the first polylogarithmic high- probability worst-case time bounds for the dynamic span- CP31 ner and the dynamic maximal matching problem. 1. For (1 + Eps)-Approximate Incremental Matching in dynamic spanner, the only known o(n) worst-case bounds Constant Deterministic Amortized Time were O(n3/4) high-probability worst-case update time for We study the matching problem in the incremental setting, maintaining a 3-spanner and O(n5/9) for maintaining a 5- k 3 where we are given a sequence of edge insertions and aim at spanner. We give a O(1) log n high-probability worst- maintaining a near-maximum cardinality matching of the − case time bound for maintaining a (2k 1)-spanner, which graph with small update time. We present a deterministic yields the first worst-case polylog update time for all con- algorithm that, for any constant ε>0, maintains a (1 + stant k. 2. For dynamic maximal matching, or dynamic ε)-approximate matching with constant amortized update 2-approximate maximum matching, no algorithm with o(n) time per insertion. worst-case time bound was known and we present an al- gorithm with O(log5 n) high-probability worst-case time; Chris Schwiegelshohn similar worst-case bounds existed only for maintaining a Sapienza University of Rome matching that was (2+)-approximate, and hence not max- [email protected] imal. Fabrizio Grandoni Aaron Bernstein IDSIA Technical University of Berlin, Germany [email protected] [email protected] Stefano Leonardi Sebastian Forster Sapienza University of Rome University of Salzburg [email protected] [email protected] Piotr Sankowski Henzinger Monika Institute of Informatics, University of Warsaw University of Vienna [email protected] [email protected] Shay Solomon CP31 Tel Aviv University [email protected] Deterministically Maintaining a (2 + )- Approximate Minimum Vertex Cover in O(1/2) Amortized Update Time CP31 We consider the problem of maintaining an (approxi- Fully Dynamic Maximal Independent Set with mately) minimum vertex cover in an n-node graph G = Sublinear in n Update Time (V,E) that is getting updated dynamically via a sequence The first fully dynamic algorithm for maintaining a maxi- of edge insertions/deletions. We show how to maintain a mal independent set (MIS) with update time that is sub- (2 + )-approximate minimum vertex cover, deterministi- 2 linear in the number of edges was presented recently by cally, in this setting in O(1/ ) amortized update time. the authors of this paper [Assadi et.al., STOC’18]. The Prior to our work, the best known deterministic algorithm 3/4 for maintaining a (2 + )-approximate minimum vertex algorithm is deterministic and its update time is O(m ), cover was due to Bhattacharya, Henzinger and Italiano where m is the number of edges. Subsequently, Gupta and [SODA 2015]. Their algorithm has an update time of Khan and independently Du and Zhang [arXiv, April 2018] O(log n/2). Recently, Bhattacharya, Chakrabarty, Hen- presented deterministic algorithms for dynamic MIS with ˜ 2/3 zinger [IPCO 2017] and Gupta, Krishnaswamy, Kumar, update times of O(m ). Du and Zhang√ also gave a ran- Panigrahi [STOC 2017] showed how to maintain an O(1)- domized algorithm with update time O˜( m). Moreover, approximation in O(1)-amortized update time for the same they provided some partial (conditional) hardness results problem. Our result gives an exponential improvement over hinting that the update time of m1/2−, and in particular the update time of Bhattacharya et al. [SODA 2015], and n1− for n-vertex dense graphs, is a natural barrier for this nearly matches the performance of the randomized algo- problem for any constant >0, for both deterministic and 40 DA19 Abstracts

randomized algorithms that satisfy a certain property. In players, for both deterministic and randomized protocols. this paper, we break this natural barrier and present the first fully dynamic (randomized) algorithm for maintaining Benjamin Plaut Stanford University an MIS with update time that is√ always sublinear in the number of vertices, namely, an O˜( n)expectedamortized [email protected] update time. We also show that a simpler variant of our algorithm can achieve an O˜(m1/3) expected amortized up- Tim Roughgarden Stanford University date time,√ which results in an improved performance over our O˜( n) update time algorithm for sufficiently sparse Computer Science Department [email protected] graphs, and breaks the m1/2 barrier for all values of m.

Sepehr Assadi CP32 University of Pennsylvania [email protected] Fully Polynomial-time Approximation Schemes for Fair Rent Division

Krzysztof Onak We study the problem of fair rent division that entails split- IBM Research ting the rent and allocating the rooms of an apartment [email protected] among roommates in a fair manner. In this setup, a distri- bution of the rent and an accompanying allocation is said Baruch Schieber to be fair if it is envy free, i.e., under the imposed rents, New Jersey Institute of Technology no agent has a strictly stronger preference for any other [email protected] agent’s room. The cardinal preferences of the agents are expressed via functions which specify the utilities of the Shay Solomon agents for the rooms for every possible room rent/price. Tel Aviv University While envy-free solutions are guaranteed to exist under [email protected] reasonably general utility functions, efficient algorithms for finding them were known only for quasilinear utilities. This work addresses this notable gap and develops approxima- CP31 tion algorithms for fair rent division with minimal assump- Dynamic Edge Coloring with Improved Approxi- tions on the utility functions. Specifically, we show that mation if the agents have continuous, monotone decreasing, and piecewise-linear utilities, then the fair rent-division prob- Given an undirected simple graph G =(V,E) that under- lem admits a fully polynomial-time approximation scheme. goes edge insertions and deletions, we wish to efficiently That is, we develop algorithms that find allocations and maintain an edge coloring with only a few colors. The prices of the rooms such that for each agent a the utility of previous best dynamic algorithm by [?] could deterministi- the room assigned to it is within a factor of (1 + )ofthe cally maintain a valid edge coloring using 2Δ−1 colors with utility of the room most preferred by a; here, >0isan O(log Δ) update time, where Δ stands for the current max- approximation parameter. We complement the algorith- imum vertex degree of graph G. In this paper, we first pro- mic results by proving that the fair rent division problem pose a new static (1+)Δ edge coloring algorithm that runs lies in the intersection of the complexity classes PPAD and in near-linear time. Based on this static algorithm, we show PLS. that there is a randomized dynamic algorithm for this prob- lem that only uses (1 + )Δ colors with O(log8 n/4)amor- Eshwar Ram Arunachaleswaran tized update time when Δ ≥ Ω(log2 n/2), where >0is Indian Institute of Science an arbitrarily small constant. [email protected]

Ran Duan Siddharth Barman Tsinghua University, Beijing, China Department of Computer Sciences, [email protected] University of Wisconsin-Madison [email protected] Haoqing He, Tianyi Zhang IIIS, Tsinghua Nidhi Rathi [email protected], tianyi- Indian Institute of Science [email protected] [email protected]

CP32 CP32 Communication Complexity of Discrete Fair Divi- An Optimal Truthful Mechanism for the Online sion Weighted Bipartite Matching Problem

We initiate the study of the communication complexity of In the weighted bipartite matching problem, the goal is to fair division with indivisible goods. We focus on some find a maximum-weight matching in a bipartite graph with of the most well-studied fairness notions (envy-freeness, nonnegative edge weights. We consider its online version proportionality, and approximations thereof) and valua- where the first vertex set is known beforehand, but vertices tion classes (submodular, subadditive and unrestricted). of the second set appear one after another. Vertices of the Within these parameters, our results completely resolve first set are interpreted as items, and those of the second whether the communication complexity of computing a fair set as bidders. On arrival, each bidder vertex reveals the allocation (or determining that none exist) is polynomial weights of all adjacent edges and the algorithm has to de- or exponential (in the number of goods), for every combi- cide which of those to add to the matching. We introduce nation of fairness notion, valuation class, and number of an optimal, e-competitive truthful mechanism under the DA19 Abstracts 41

assumption that bidders arrive in random order (secretary This problem is closely related to the so-called prophet- model). It has been shown that the upper and lower bound inequality and its extensions in recent literature. Moti- of e for the original secretary problem extends to various vated by applications to cloud economics, we consider two other problems even with rich combinatorial structure, one kinds of buyer preferences. In the first, items correspond of them being weighted bipartite matching. But truthful to different units of time at which a resource is available; mechanisms so far fall short of reasonable competitive ra- the items are arranged in a total order and buyers desire tios once respective algorithms deviate from the original, intervals of items. The second corresponds to bandwidth simple threshold form. The best known mechanism for allocation over a tree network; the items are edges in the weighted bipartite matching offers only a ratio logarith- network and buyers desire paths. For the interval pref- mic in the number of online vertices. We close this gap, erences setting, we show that static, anonymous bundle showing that truthfulness does not impose any additional pricings achieve a sublogarithmic competitive ratio, which bounds. The proof technique is new in this surrounding, is optimal (within constant factors) over the class of all and based on the observation of an independency inherent online allocation algorithms, truthful or not. For the path to the mechanism. The insights provided hereby are in- preferences setting, we obtain a nearly-tight logarithmic teresting in their own right and appear to offer promising competitive ratio. Both results exhibit an exponential im- tools for other problems, with or without truthfulness. provement over item pricings for these settings. Our results extend to settings where the seller has multiple copies of Rebecca Reiffenhaeuser each item, with the competitive ratio decreasing linearly RWTH Aachen University with supply. Such a gradual tradeoff between supply and [email protected] the competitive ratio for welfare was previously known only for the single item prophet inequality.

CP32 Shuchi Chawla, Benjamin Miller, Yifeng Teng Prophet Secretary Through Blind Strategies Department of Computer Sciences University of Wisconsin-Madison In the classic prophet inequality, a problem in optimal stop- [email protected], [email protected], ping theory, samples from independent random variables [email protected] arrive online. A gambler that knows the distributions, but cannot see the future, must decide at each point in time whether to stop and pick the current sample or to continue CP33 and lose that sample forever. The goal of the gambler is Asymmetric Convex Intersection Testing to maximize the expected value of what she picks and the performance measure is the worst case ratio between the We consider asymmetric convex intersection testing expected value the gambler gets and what a prophet, that (ACIT). Let P ⊂ Rd be a set of n points and H aset sees all the realizations in advance, gets. We study when of n halfspaces in d dimensions. We denote by P the poly- the samples arrive in a uniformly random order, deriving a tope obtained by taking the convex hull of P ,andbyH the way of analyzing multi-threshold strategies that basically polytope obtained by taking the intersection of the halfs- sets a nonincreasing sequence of thresholds to be applied paces in H. Our goal is to decide whether the intersection at different times. The gambler will thus stop the first time of H and the convex hull of P are disjoint. Even though a sample surpasses the corresponding threshold. We con- ACIT is a natural variant of classic LP-type problems that sider a class of robust strategies that we call blind quantile have been studied at length in the literature, and despite its strategies. These constitute a clever generalization of sin- applications in the analysis of high-dimensional data sets, gle threshold strategies. Our main result shows that these it appears that the problem has not been studied before. strategies can achieve a constant of 0.669 in the prophet We discuss how known approaches can be used to attack secretary problem, done by a sharp analysis of the under- the ACIT problem, and we provide a very simple strategy lying stopping time distribution for the gambler’s strategy that leads to a deterministic algorithm, linear on n and m, that is inspired by the theory of Schur-convex functions. whose running time depends reasonably on the dimension We further prove that our family of blind strategies cannot d. lead to a constant better that 0.675. Finally we prove that no nonadaptive algorithm for the gambler can achieve a Luis Barba constant better than 0.732. ETH Z¨urich [email protected] Jos´e Correa, Raimundo Saona Universidad de Chile Wolfgang J. Mulzer [email protected], [email protected] Freie Universit¨at Berlin [email protected] Bruno Ziliotto Universit´e Paris Dauphine CNRS CP33 [email protected] Relaxed Voronoi: A Simple Framework for Terminal-Clustering Problems

CP32 We reprove three known algorithmic bounds for terminal- Pricing for Online Resource Allocation: Intervals clustering problems, using a single framework that leads and Paths to simpler proofs. In this genre of problems, the input is ametricspace(X, d) and a subset of terminals K ⊂ X, We present pricing mechanisms for several online resource and the goal is to partition the points X such that each allocation problems which obtain tight or nearly tight ap- part, called a cluster, contains exactly one terminal (possi- proximations to social welfare. In our settings, buyers bly with connectivity constraints) so as to minimize some arrive online and purchase bundles of items; buyers’ val- goal. The bounds we reprove are for Steiner Point Removal ues for the bundles are drawn from known distributions. on trees [Gupta, SODA 2001], for Metric 0-Extension in 42 DA19 Abstracts

bounded doubling dimension [Lee and Naor, unpublished problem as well as a bound on the number of approxi- 2003], and for Connected Metric 0-Extension [Englert et mate minimum cuts. This is a different approach from his al., SICOMP 2014]. A natural approach is to cluster each well-known random contraction algorithm. Thorup devel- point with its closest terminal, which would partition X oped a fast deterministic algorithm for the minimum k-cut into so-called Voronoi cells, but this approach can fail mis- problem via greedy recursive tree packings. In this pa- erably due to its stringent cluster boundaries. A now- per, we revisit the properties of an LP relaxation for k-cut standard fix, which we call the Relaxed-Voronoi frame- proposed by Naor and Rabani, and analyzed by Chekuri, work, is to use enlarged Voronoi cells, but to obtain disjoint Guha and Naor. We show that the dual of the LP yields clusters, the cells are computed greedily according to some a tree packing, that when combined with an upper bound order. This method, first proposed by Calinescu, Karloff on the integrality gap for the LP, easily and transparently and Rabani [SICOMP 2004], was employed successfully extends Karger’s analysis for mincut to the k-cut prob- to provide state-of-the-art results for terminal-clustering lem. In addition to the simplicity of the algorithm and problems on general metrics. However, for restricted fam- its analysis, this allows us to improve the running time of ilies of metrics, only more complicated, ad-hoc algorithms Thorup’s algorithm by a factor of n.Wealsoimprovethe are known. Our main contribution is to demonstrate that bound on the number of α-approximate k-cuts. Second, the Relaxed-Voronoi algorithm is applicable to restricted we give a simple proof that the integrality gap of the LP is metrics, and leads to simple algorithms and analyses. 2(1−1/n). Third, we show that an optimum solution to the LP relaxation, for all values of k, is fully determined by the Arnold Filtser principal sequence of partitions of the input graph. This Ben-Gurion University of the Negev allows us to relate the LP relaxation to the Lagrangean re- [email protected] laxation approach of Barahona and Ravi and Sinha; it also shows that the idealized recursive tree packing considered Robert Krauthgamer, Ohad Trabelsi by Thorup gives an optimum dual solution to the LP. Weizmann Institute of Science [email protected], Chandra Chekuri, Kent Quanrud [email protected] University of Illinois at Urbana-Champaign [email protected], [email protected]

CP33 Chao Xu Approximating Optimal Transport with Linear Yahoo! Research NYC Programs [email protected]

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are re- CP34 duced (rather simply) to relative approximations for pos- On the Structure of Unique Shortest Paths in itive linear programs, resulting in faster additive approxi- Graphs mation algorithms for optimal transport. This paper develops a structural theory of unique shortest Kent Quanrud paths in real-weighted graphs. Our main goal is to char- University of Illinois at Urbana-Champaign acterize exactly which sets of node sequences, which we [email protected] call path systems, can appear as unique shortest paths in a graph with arbitrary real edge weights. We say that such a path system is strongly metrizable. An easy fact implicit CP33 in the literature is that a strongly metrizable path system On Primal-Dual Circle Representations must be consistent, meaning that no two of its paths may intersect, split apart, and then intersect again. Our main The Koebe-Andreev-Thurston Circle Packing Theorem result characterizes strong metrizability via forbidden in- states that every triangulated planar graph has a contact tersection patterns along these lines. In other words, we representation by circles. The theorem has been general- describe a new family of forbidden patterns beyond consis- ized in various ways. The most prominent generalization tency, and we prove that a path system is strongly metriz- assures the existence of a primal-dual circle representation able if and only if it consistent and it avoids all of these for every 3-connected planar graph. We present a simple new patterns. We offer separate (but closely related) char- and elegant elementary proof of this result. acterizations in this way for the settings of directed, undi- rected, and directed acyclic graphs. Our characterizations Stefan Felsner are based on a new connection between shortest paths and Technical University of Berlin certain boundary operators used in homology, which is used Institute for Mathematics to prove several additional structural corollaries and seems [email protected] to suggest new and possibly deep-rooted connections be- tween shortest paths and topology. G¨unter Rote Freie Universit¨at Berlin Greg Bodwin Institut f¨ur Informatik MIT [email protected] [email protected]

CP33 CP34 LP Relaxation and Tree Packing for Minimum k- Exact Distance Oracles for Planar Graphs with Cuts Failing Vertices

Karger used spanning tree packings to derive a near linear- We consider exact distance oracles for directed weighted time randomized algorithm for the global minimum cut planar graphs in the presence of failing vertices. Given a DA19 Abstracts 43

source vertex u, a target vertex v and a set X of k failed ity is established, by a technique that combines an analy- vertices, such an oracle returns the length of a shortest u- sis of the size of the dominators of suitable sub-CDAGs of to-v path that avoids all vertices in X. We propose oracles the Toom-Cook-k CDAG (Computational Directed Acyclic that can handle any number k of failures. More specif- Graph) and the analysis of a function, which we call “Par- ically, for a directed weighted planar graph√ with n ver- tial Grigoriev’s flow’, which captures the amount of infor- tices, any constant k,andforanyq ∈ [1, n], we propose mation to be transferred between specific subsets of input k+3/2 n and output variables, by any algorithm that solves the inte- an oracle of size O˜( 2k+1 ) that answers queries in O˜(q) q √ ger multiplication problem. The lower bound applies even O˜ O˜ time. In particular, we show an (n)-size, ( n)-query- if the recomputation of partial results is allowed. A careful time oracle for any constant k. This matches, up to poly- implementation of the Toom-Cook-k algorithm, assuming logarithmic factors, the fastest failure-free distance oracles that M =Ω k3 log k , is also developed and analyzed, with nearly linear space. For single vertex failures (k =1), s 5/2 leading to an I/O complexity upper bound that is within O˜ n O˜ afactorO(k2) of the corresponding lower bound, hence our ( q3 )-size, (q)-query-time oracle improves over the previously best known tradeoff of Baswana et al. [SODA asymptotically optimal for fixed k. All bounds are actu- 2012] by polynomial factors for q =Ω(nt), t ∈ (1/4, 1/2]. ally derived in the more general case where the value of k For multiple failures, no planarity exploiting results were is allowed to vary with the level of recursion. Extensions previously known. of the lower bound for a parallel model with P processors are also discussed. Panagiotis Charalampopoulos Department of Informatics, Kings College London Lorenzo De Stefani [email protected] Brown University lorenzo [email protected] Shay Mozes IDC Herzliya, Israel Gianfranco Bilardi [email protected] University of Padova [email protected] Benjamin Tebeka Efi Arazi School of Computer Science, The CP34 Interdisciplinary I/O-Efficient Algorithms for Topological Sort and Center Herzliya Related Problems [email protected] This paper presents I/O-efficient algorithms for topolog- ically sorting a directed acyclic graph and for the more CP34 general problem identifying and topologically sorting the Near Optimal Algorithms For The Single Source strongly connected components of a directed graph G = Replacement Paths Problem (V,E). Both algorithms are randomized and have I/O- costs O(sort(E) · poly(lg V )), with high probability, where The Single Source Replacement Paths (SSRP) problem is E sort(E)=O( B logM/B(E/B)) is the I/O cost of sorting as follows; Given a graph G =(V,E), a source vertex s and an |E|-element array on a machine with size-B blocks and a shortest paths tree Ts rooted in s, output for every vertex size-M cache/internal memory. These are the first algo- ∈ t V and for every edge e in Ts the length of the shortest rithms for these problems that do not incur at least one path from s to t avoiding e.√ We present near optimal upper I/O per vertex, and as such these are the first I/O-efficient ˜ 2 bounds, by providing O(m n + n ) time randomized com- algorithms for sparse graphs. By applying the technique of binatorial algorithm (where n is the number of vertices, m time-forward processing, these algorithms also imply I/O- is the number of edges and the O˜ notation suppresses poly- efficient algorithms for most problems on directed acyclic logarithmic factors) for unweighted undirected graphs, and graphs, such as shortest paths, as well as the single-source matching conditional lower bounds for the SSRP problem. reachability problem on arbitrary directed graphs.

Nairen Cao, Jeremy Fineman, Katina Russell,Eugene Sarel Cohen Yang Tel-Aviv University Georgetown University [email protected] [email protected], jfi[email protected], [email protected], eu- Shiri Chechik [email protected] Tel-Aviv University, Israel [email protected] CP35 Analyzing Boolean Functions on the Biased Hyper- CP34 cube Via Higher-Dimensional Agreement Tests The I/O Complexity of Toom-Cook Integer Multi- We propose a new paradigm for studying the structure of plication Boolean functions on the biased Boolean hypercube, i.e. when the measure is μ and p is potentially very small, Nearly matching upper and lower bounds are derived for p e.g. as small as O(1/n). Our paradigm is based on the the I/O complexity of the Toom-Cook-k algorithm com- following simple fact: the p-biased hypercube is express- puting the products of two integers, each represented with ible as a convex combination of many small-dimensional n digits in a given base s, in a two-level storage hier- copies of the uniform hypercube. To uncover structure for archy with M words of fast memory, with different dig- μp, we invoke known structure theorems for μ1/2, obtain- its stored in different memory words. An IOA (n, M)= k ing a structured approximation for each copy separately. − Ω (n/M)logk 2k 1 M lower bound on the I/O complex- We then sew these approximations together using a novel 44 DA19 Abstracts

“agreement theorem”. This strategy allows us to lift struc- [email protected] ture theorems from μ1/2 to μp. Our main application is a structure theorem for functions that are nearly low degree in the Fourier sense. The structure we uncover in the bi- CP35 ased hypercube is notatallthe same as for the uniform hypercube, despite using the structure theorem for the uni- List Decoding with Double Samplers form hypercube as a black box. Rather, new phenomena emerge: whereas nearly low degree functions on the uni- Samplers are bipartite graphs with nice pseudo-random form hypercube are close to juntas, when p becomes small, properties. A classical construction of ABNNR uses sam- non-juntas arise as well. A key component of our proof is pler graphs for amplifying the distance of an error correct- a new local-to-global agreement theorem for higher dimen- ing code. This construction has an algorithm for unique sions, which extends the work of Dinur and Steurer [Proc. decoding, but no efficient list decoding algorithm is known. 29th CCC, 2014]. Whereas their result sews together vec- In this talk, I will introduce ”double samplers”, which ex- tors, our agreement theorem sews together labeled graphs tend sampler graphs to three layers, and show a polyno- and hypergraphs. mial time algorithm which list decodes the ABNNR code Yuval Filmus construction on a double sampler. Double samplers can Technion be constructed from high dimensional expanders, and cur- yuvalfi@cs.technion.ac.il rently no other method is known.

Irit Dinur InbalR.LivniNavon,IritDinur Weizmann Institute Weizmann Institute [email protected] [email protected], [email protected]

Prahladh Harsha Prahladh Harsha Tata institute Tata institute [email protected] [email protected]

Tali Kaufman CP35 MIT Maximally Recoverable LRCs: A Field Size Lower [email protected] Bound and Constructions for Few Heavy Parities Amnon Ta-Shma The explosion in the volumes of data being stored online Tel-Aviv University has resulted in distributed storage systems transitioning to [email protected] erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these appli- cations. These codes can correct a small number of erasures by accessing only a small number of remaining coordinates. CP35 An (n, r, h, a, q)-LRC is a linear code over Fq of length n, whose codeword symbols are partitioned into g = n/r lo- Binary Robust Positioning Patterns with Low Re- cal groups each of size r.Ithash global parity checks and dundancy and Efficient Locating Algorithms each local group has a local parity checks. Such an LRC is Maximally Recoverable (MR), if it corrects all erasure pat- A robust positioning pattern is a large array that allows terns which are information-theoretically correctable given a mobile device to locate its position by reading a possi- the structure of local and global parity checks. We show bly corrupted small window around it. This paper provides that when a and h are constant and r may grow with n, constructions of binary positioning patterns, equipped with for every MR LRC with g = n/r local groups, efficient locating algorithms, that are robust to a con- stant number of errors and have redundancy within a con- { −  } α min a, h 2 h/g stant factor of optimality. Our construction of binary ro- q ≥ Ωa,h (n · r )whereα = . h/g bust positioning sequences has the least known redundancy amongst those explicit constructions with efficient locating No superlinear (in n) lower bounds were known prior to this algorithms. On the other hand, for binary robust position- work for any setting of parameters. MR LRCs deployed in ing arrays, our construction is the first explicit construction practice have a small number of global parities, typically whose redundancy is within a constant factor of optimality. h =2, 3. We complement our lower bounds by giving con- ≤ The locating algorithms accompanying our constructions structions with small field size for h 3. For h =2,we run in time cubic in sequence length or array dimensions. give a linear field size construction. We also show a surpris- ing application of elliptic curves and arithmetic progression free sets in the construction of MR LRCs. Yeow Meng Chee, Duc Tu Dao School of Physical and Mathematical Sciences Sivakanth Gopi Nanyang Technological University Microsoft Research [email protected], [email protected] [email protected] Han Mao Kiah Venkatesan Guruswami NTU, Singapore Carnegie Mellon University [email protected] [email protected] San Ling, Hengjia Wei Sergey Yekhanin School of Physical and Mathematical Sciences Microsoft Nanyang Technological University DA19 Abstracts 45

≥ 11 − [email protected], [email protected] is rapidly mixing for any k ( 6 0)Δ for some ab- solute constant 0 > 0. This is the first improvement to Vigoda’s result that holds for general graphs. Our first ap- CP35 proach analyzes a variable-length coupling in which these Synchronization Strings: Highly Efficient Deter- configurations break apart with high probability before the ministic Constructions over Small Alphabets coupling terminates, and our other approach analyzes a one-step path coupling with a new metric that counts the Synchronization strings are recently introduced by Haeu- extremal configurations. Additionally, our results extend pler and Shahrasbi (STOC17) in the study of codes for to list coloring, a widely studied generalization of coloring, correcting insertion and deletion errors. A synchroniza- where the previously best known results required k>2Δ. tion string is an encoding of the indices of the symbols in a string, and together with an appropriate decoding algo- rithm it can transform insertion and deletion errors into Sitan Chen standard symbol erasures and corruptions. This reduces MIT the problem of constructing insdel codes to the problem of [email protected] constructing standard error correcting codes. Besides this, synchronization strings are also useful in other applications Michelle Delcourt such as synchronization sequences and interactive coding University of Waterloo schemes. For all such applications, synchronization strings [email protected] are desired to be over alphabets that are as small as possi- ble. Haeupler and Shahrasbi showed that for any parame- Ankur Moitra ter ε>0, synchronization strings of arbitrary length exist MIT over an alphabet whose size depends only on ε. Specifically, [email protected] they obtained an alphabet size of O(ε−4), which left an open question on where the minimal size of such alphabets Guillem Perarnau −1 −4 lies between Ω(ε )andO(ε ). In this work, we partially University of Birmingham bridge this gap by providing an improved lower bound of [email protected] Ω ε−3/2 , and an improved upper bound of O ε−2 .We also provide fast explicit constructions of synchronization Luke Postle strings over small alphabets. University of Waterloo [email protected] Kuan Cheng Johns Hopkins University [email protected] CP36 Bernhard Haeupler The Complexity of Approximately Counting Re- Carnegie Mellon U. tractions [email protected]

Xin Li Let G be a graph that contains an induced subgraph H.A Johns Hopkins University retraction from G to H is a homomorphism from G to [email protected] H that is the identity function on H.Retractionsare very well-studied: Given H, the complexity of deciding Amirbehshad Shahrasbi whether there is a retraction from an input graph G to H Carnegie Mellon University is completely classified, in the sense that it is known for [email protected] which H this problem is tractable (assuming P =NP). Similarly, the complexity of (exactly) counting retractions  Ke Wu from G to H is classified (assuming FP =#P).How- Johns Hopkins University ever, almost nothing is known about approximately count- [email protected] ing retractions. Our first contribution is to give a com- plete trichotomy for approximately counting retractions to trees. Our second contribution is to locate the retraction CP36 counting problem in the complexity landscape of related approximate counting problems. Interestingly, our results Improved Bounds for Randomly Sampling Color- are in contrast to the situation in the exact counting con- ings Via Linear Programming text. We show that the problem of approximately counting retractions is separated both from the problem of approx- A well-known conjecture in computer science and statis- imately counting homomorphisms and from the problem tical physics is that Glauber dynamics on the set of k- of approximately counting list homomorphisms — whereas colorings of a graph G on n vertices with maximum degree ≥ for exact counting all three of these problems are interre- Δ is rapidly mixing for k Δ + 2. In FOCS 1999, Vigoda ducible. We also show that the number of retractions is at showed that the flip dynamics (and therefore also Glauber 11 least as hard to approximate as both the number of sur- dynamics) is rapidly mixing for any k> 6 Δ. It turns out 11 jective homomorphisms and the number of compactions. that there is a natural barrier at 6 , below which there is In contrast, exactly counting compactions is the hardest of no one-step coupling that is contractive with respect to the these problems. Hamming metric, even for the flip dynamics. We use linear programming and duality arguments to fully characterize 11 the obstructions to going beyond 6 . These extremal con- Jacob Focke, Leslie Ann Goldberg, Stanislav Zivny figurations turn out to be quite brittle, and in this paper University of Oxford we use this to give two proofs that the Glauber dynamics [email protected], [email protected], 46 DA19 Abstracts

[email protected] generalised second order recurrence modulo a couple of exceptional cases. As a consequence, any non-negative Holant problem on cubic graphs has an efficient approxima- CP36 tion algorithm unless the problem is equivalent to approxi- Algorithms for #BIS-Hard Problems on Expander mately counting perfect matchings, a central open problem Graphs in the area. This is in sharp contrast to the computa- tional phase transition shown by 2-state spin systems on We give an FPTAS and an efficient sampling algorithm cubic graphs. Our main technique is the recently estab- for the high-fugacity hard-core model on bounded-degree lished connection between zeros of graph polynomials and bipartite expander graphs and the low-temperature ferro- approximate counting. We also use the winding technique magnetic Potts model on bounded-degree expander graphs. to deduce the second result on cubic graphs. The results apply, for example, to random (bipartite) Δ-regular graphs, for which no efficient algorithms were Heng Guo known for these problems (with the exception of the Ising University of Edinburgh model) in the non-uniqueness regime of the infinite Δ- [email protected] regular tree. Chao Liao Matthew Jenssen, Peter Keevash Shanghai Jiao Tong University University of Oxford [email protected] [email protected], [email protected] Pinyan Lu Will Perkins Shanghai University of Finance and Economics University of Birmingham [email protected] [email protected] Chihao Zhang CP36 Shanghai Jiaotong University Approximability of the Six-Vertex Model [email protected]

Six-vertex models originate in statistical mechanics, as a family of vertex models for crystal lattices with hydro- CP37 gen bonds. In the language of graph theory and theory Towards a Unified Theory of Sparsification for of computing, it is a sum-of-product computation. On a Matching Problems 4-regular graph, we compute the partition function which is a weighted sum of Eulerian orientations, where at every We present a construction of a “matching sparsifier’, that vertex the orientation must be two-in-two-out (called the is, a sparse subgraph of the given graph that preserves large ice rule). There are thousands of papers on the six-vertex matchings approximately and is robust to modifications model, making it one of the three most studied models in of the graph. We use this matching sparsifier to obtain statistical physics, together with ferromagnetic Ising and several new algorithmic results for the maximum matching monomer-dimer models. In this paper, we take the first problem: step toward a classification of the approximation complex- • An almost (3/2)-approximation one-way communica- ity of the six-vertex model. Our complexity results con- tion protocol for the maximum matching problem, form to the phase transition phenomenon from physics. We simplifying the (3/2)-approximation protocol of Goel, show that the approximation complexity of the six-vertex Kapralov, and Khanna (SODA 2012) and extending model behaves dramatically differently on the two sides it from bipartite graphs to general graphs. separated by the phase transition threshold. Furthermore, we present structural properties of the six-vertex model on • An almost (3/2)-approximation algorithm for the planar graphs for parameter settings that have known re- stochastic matching problem, improving upon and lations to the Tutte polynomial T (G; x, y). In this talk, I simplifying the previous 1.999-approximation algo- will outline our main results and techniques in this work. rithm of Assadi, Khanna, and Li (EC 2017). • Jin-Yi Cai An almost (3/2)-approximation algorithm for the University of Wisconsin, Madison fault-tolerant matching problem, implying the first [email protected] non-trivial algorithm for this problem. Our matching sparsifier is obtained by proving new prop- Tianyu Liu erties of the edge-degree constrained subgraph (EDCS) of University of WisconsinMadison Bernstein and Stein (ICALP 2015; SODA 2016)—designed [email protected] in the context of matchings in dynamic graphs—that iden- tifies EDCS as an excellent choice for a matching sparsifier. Pinyan Lu This leads to surprisingly simple and non-technical proofs Shanghai University of Finance and Economics of the above results in a unified way. Along the way, we [email protected] also provide a simpler proof of the fact that an EDCS is guaranteed to contain a large matching, which may be of independent interest. CP36 Zeros of Holant Problems: Locations and Algo- Sepehr Assadi rithms University of Pennsylvania [email protected] We present fully polynomial-time (deterministic or ran- domised) approximation schemes for Holant problems, de- Aaron Bernstein fined by a non-negative constraint function satisfying a Technical University of Berlin, Germany DA19 Abstracts 47

[email protected] mum number of disjoint pairs of adjacent edges of G whose removal results in a connected spanning subgraph of G.In this paper we describe a greedy 2-approximation algorithm CP37 for maximum genus by proving that removing pairs of adja- A New Application of Orthogonal Range Searching cent edges from G arbitrarily while retaining connectedness for Computing Giant Graph Diameters leads to at least γM (G)/2 pairs of edges removed. As a con- sequence of our approach we also obtain a 2-approximate A well-known problem for which it is difficult to improve counterpart of Xuong’s combinatorial characterisation of the textbook algorithm is computing the graph diame- maximum genus. ter. We present two versions of a simple algorithm (one being Monte Carlo and the other deterministic) that for Michal Kotrbcik every fixed h and graph G, either correctly concludes Comenius University, Department of Computer Science that diam(G) 0. We Smaller Approximate Kernel and Improved Ap- present a simplified and more intuitive primal-dual analy- proximation sis, for essentially the same algorithm, which also improves the space complexity to the optimal bound of O(n log n) In Maximum k-Vertex Cover (Max k-VC), the input is an bits — this is optimal as the output matching requires edge-weighted graph G andanintegerk, and the goal Ω(n log n)bits. is to find a subset S of k vertices that maximizes the total weight of edges covered by S.(Anedgeiscov-Mohsen Ghaffari ered by S iff at least one of its endpoints lies in S.) ETH Zurich We present a simple FPT approximation scheme (FPT- ghaff[email protected] AS) that runs in (1/)O(k)poly(n)timefortheproblem, which improves upon Gupta et al.’s (k/)O(k)poly(n)-time David Wajc FPT-AS [SODA’18, FOCS’18]. Our algorithm naturally Carnegie Mellon University yields an approximate kernelization scheme of O(k/)ver- [email protected] tices; previously, an O(k5/2)-vertex approximate kernel is only known for unweighted Max k-VC [Lokshtanov et al., STOC’17]. Moreover, using our approximate kernelization CP38 as a preprocessing step, we can directly apply Raghavendra and Tan’s algorithm for 2SAT with cardinality constraint Hierarchical Clustering Better than Average- [SODA’12] to give an 0.92-approximation algorithm for Linkage Max k-VC in polynomial time. This improves upon Feige and Langberg’s algorithm [J. Algorithms’01] which yields Hierarchical Clustering (HC) is a widely studied problem (0.75 + δ)-approximation for some δ>0. We also con- in exploratory data analysis, usually tackled by simple ag- sider the minimization version (called Min k-VC), where glomerative procedures like average-linkage, single-linkage the goal is to minimize the total weight of edges covered or complete-linkage. In this paper we focus on two objec- by S.WeprovideanFPT-ASforMink-VC with similar tives, introduced recently to give insight into the perfor- running time of (1/)O(k)poly(n). On the other hand, we mance of average-linkage clustering: a similarity based HC show that there is unlikely a polynomial size approximate objective proposed by [Moseley and Wang, 2017] and a dis- kernelization for Min k-VC for any factor less than two. similarity based HC objective proposed by [Cohen-Addad et al., 2018]. In both cases, we present tight counterex- Pasin Manurangsi amples showing that average-linkage cannot obtain bet- UC Berkeley ter than 1/3 and 2/3 approximations respectively (in the [email protected] worst-case), settling an open question raised in [Moseley and Wang, 2017]. This matches the approximation ratio of a random solution, raising a natural question: can we beat CP37 average-linkage for these objectives? We answer this in the Simple Greedy 2-Approximation Algorithm for the affirmative, giving two new algorithms based on semidefi- Maximum Genus of a Graph nite programming with provably better guarantees.

The maximum genus γM (G) of a graph G is the largest Moses Charikar, Vaggos Chatziafratis, Rad Niazadeh genus of an orientable surface into which G has a cellular Stanford University, California embedding. Combinatorially, it coincides with the maxi- [email protected], [email protected], 48 DA19 Abstracts

[email protected] called the LBFL with penalty (LBFL-P) and the trans- portation with configurable supplies and demands (TCSD) problems, which in turn can be reduced to the CFL prob- CP38 lem. Universal Trees Grow Inside Separating Automata: Quasi-Polynomial Lower Bounds for Parity Games Shi Li Toyota Technological Institute at Chicago Several distinct techniques have been proposed to design shil@buffalo.edu quasi-polynomial algorithms for solving parity games since the breakthrough result of Calude, Jain, Khoussainov, Li, CP38 and Stephan (2017): play summaries, progress measures and register games. We argue that all those techniques Exponential Lower Bounds on Spectrahedral Rep- can be viewed as instances of the separation approach to resentations of Hyperbolicity Cones solving parity games, a key technical component of which In an effort to better understand the relationship between is constructing (explicitly or implicitly) an automaton that semidefinite programming and hyperbolic programming, separates languages of words encoding plays that are (deci- we study dimension implications of certain representations. sively) won by either of the two players. Our main techni- The Generalized Lax Conjecture asks whether every hy- cal result is a quasi-polynomial lower bound on the size of perbolicity cone is a section of a semidefinite cone of suffi- such separating automata that nearly matches the current ciently high dimension. We prove that the space of hyper- best upper bounds. This forms a barrier that all exist- bolicity cones of hyperbolic polynomials contains pairwise ing approaches must overcome in the ongoing quest for a distant cones in the Hausdorff metric, and therefore pro- polynomial-time algorithm for solving parity games. The vide lower bounds on the size of representations of these key and fundamental concept that we introduce and study polynomials (even allowing a small approximation error). is a universal ordered tree. The technical highlights are a quasi-polynomial lower bound on the size of universal The cones are perturbations of the hyperbolicity cones of ordered trees and a proof that every separating safety au- elementary symmetric polynomials. tomaton has a universal tree hidden in its state space. Nick Ryder UC Berkeley Wojciech Czerwinski [email protected] University of Warsaw [email protected] Nikhil Srivastava University of California Berkeley Laure Daviaud [email protected] University of Warwick [email protected] Prasad Raghavendra U C Berkeley Nathanael Fijalkow [email protected] CNRS, University of Bordeaux nathanael.fi[email protected] Benjamin Weitz Pintrest Marcin Jurdzinski, Ranko Lazic [email protected] University of Warwick [email protected], [email protected] CP38 The Threshold for SDP-Refutation of Random Pawel Parys Regular NAE-3SAT University of Warsaw [email protected] Unlike its cousin 3SAT, the NAE-3SAT (not-all-equal- 3SAT) problem has the property that spectral/SDP algo- rithms can efficiently refute random instances when the CP38 constraint density is a large constant (with high probabil- On Facility Location with General Lower Bounds ity). But do these methods work immediately above the “satisfiability threshold”, or is there still a range of con- In this paper, we give the first constant approximation al- straint densities for which random NAE-3SAT instances gorithm for the lower bounded facility location (LBFL) are unsatisfiable but hard to refute? We show that the problem with general lower bounds. Prior to our work, latter situation prevails, at least in the context of random such algorithms were only known for the special case where regular instances and SDP-based refutation. More pre- all facilities have the same lower bound: Svitkina [Svi10] cisely, whereas a random d-regular instance of NAE-3SAT gave a 448-approximation for the special case, and subse- is easily shown to be unsatisfiable (whp) once d ≥ 8, we quently Ahmadian and Swamy [AS13] improved the ap- establish the following sharp threshold result regarding ef- proximation factor to 82.6. As in [Svi10] and [AS13], our ficient refutation: If d<13.5 then the basic SDP, even algorithm for LBFL with general lower bounds works by augmented with triangle inequalities, fails to refute satisfi- reducing the problem to the capacitated facility location ability (whp), if d>13.5 then even the most basic spectral (CFL) problem. To handle the challenges raised by the algorithm refutes satisfiability (whp). general lower bounds, it involves more reduction steps. One main complication is that after aggregating the clients Tselil Schramm and facilities at a few locations, each of these locations UC Berkeley may contain many facilities with different opening costs [email protected] and lower bounds. To address this issue, we introduce and reduce the LBFL problem to two intermediate problems Yash Deshpande DA19 Abstracts 49

MIT sized time intervals. Imagine mobile transmission sources [email protected] with broadcast ranges that interfere if they transmit on the same channel and their ranges intersect. Location uncer- Andrea Montanari tainty effectively expands their broadcast range to a po- Stanford University tential range. The chromatic number of the intersection [email protected] graph of these potential ranges gives the minimum num- ber of channels required to avoid interference. For fixed Ryan O’Donnell monitoring rate, our scheme provides an adaptive chan- Carnegie Mellon University, USA nel assignment that uses a number of channels competitive [email protected] with any other scheme. Daniel Busto Subhabrata Sen Ericsson MIT Montreal, Canada [email protected] [email protected]

CP39 William S. Evans University of British Columbia Theorems of Carathodory, Helly, and Tverberg [email protected] Without Dimension

Motivated by Barman, we initiate a systematic study of David Kirkpatrick the ‘no-dimensional’ analogues of some basic theorems in University of British Columbia, Canada combinatorial and convex geometry, including the colorful [email protected] Carath´eodory’s theorem, Tverberg’s theorem, Helly’s the- orem as well as their fractional and colorful extensions. We show that, besides optimally improving some of Barman’s CP39 theorems, they have several algorithmic and combinatorial On the Spanning and Routing Ratio of Theta-Four consequences. We present a routing algorithm for the Θ4-graph that com- Karim Adiprasito putes a path between any two vertices s and t having length Einstein Institute for Mathematics at most 17 times the Euclidean distance between s and t. Hebrew University of Jerusalem, Israel At each step the algorithm only uses knowledge of the loca- [email protected] tion of the current vertex, its (at most four) outgoing edges, the destination vertex, and one additional bit of informa- Imre B´ar´any tion in order to determine the next edge to follow. This Alfr´ed R´enyi Institute of Mathematics, Budapest provides the first known online, local, competitive routing University College London, UK algorithm with constant routing ratio for the Θ4-graph, [email protected] as well as improving the best known upper bound on the spanning ratio from 237 to 17. NabilH.Mustafa Darryl R. Hill, Prosenjit Bose Laboratoire d’Informatique Gaspard-Monge Carleton University ESIEE Paris, France [email protected], [email protected] [email protected] Jean-Lou De Carufel Monika Csikos University of Ottawa Universite Paris-Est, Laboratoire d’Informatique [email protected] Gaspard-Mon [email protected] Michiel Smid Carleton University CP39 [email protected] Minimizing Interference Potential Among Moving Entities CP39 We consider the problem of monitoring the interference Greedy Spanners Are Optimal in Doubling Metrics among a collection of entities moving with bounded speed in d. Uncertainty in entity locations due to unmonitored We show that the greedy spanner algorithm constructs a − and unpredictable motion gives rise to a space of possible (1 + )-spanner of weight  O(d)w(MST) for a point set in entity configurations at each time, with possibly very dif- metrics of doubling dimension d, resolving an open prob- ferent interference properties. We define measures of the lem posed by Gottlieb. Our result generalizes the result by interference potential of such spaces to describe the inter- Narasimhan and Smid who showed that a point set in d- ference that might actually occur. We study how limited dimension Euclidean space has a (1 + )-spanner of weight monitoring rate impacts interference potential by study- at most −O(d)w(MST). Our proof only uses the pack- ing a clairvoyant scheme (one that knows the trajectories ing property of doubling metrics and greatly simplifies the of all entities) subject to the same monitoring restriction. proof of the same result in Euclidean space. This forms a benchmark for the analysis of uninformed schemes. We describe and analyse an adaptive monitoring Glencora Borradaile, Hung Le scheme for minimizing interference potential over time that Oregon State University is competitive (to within a constant factor) with any other [email protected], scheme (in particular, a clairvoyant scheme) over modest [email protected] 50 DA19 Abstracts

Christian Wulff-Nilsen Jaroslaw Blasiok Department of Computer Science Harvard University University of Copenhagen [email protected] [email protected] Mark Bun Princeton University CP39 [email protected] Viewing the Rings of a Tree: Minimum Distortion Embeddings into Trees Thomas Steinke IBM Research We describe a (1 + ε) approximation algorithm for finding [email protected] the minimum distortion embedding of an n-point metric space, (X, Xd), into a tree with vertex set X. The run- 2λ+1 ning time is n2 · (Δ/ε)(O(δopt/ε)) parameterized with CP40 respect to the spread of X, denoted by Δ, the minimum Lower Bounds for Oblivious Data Structures possible distortion for embedding X into any tree, denoted by δopt, and the doubling dimension of X, denoted by λ. An oblivious data structure is a data structure where the Hence we obtain a PTAS, provided δopt is constant and X memory access patterns reveals no information about the is a finite doubling metric space with polynomial spread, operations performed on it. Such data structures were in- for example, a point set with polynomial spread in con- troduced by Wang et al. [ACM SIGSAC’14] and are in- stant dimensional Euclidean space. Our algorithm implies tended for situations where one wishes to store the data a constant factor approximation with the same running structure at an untrusted server. One way to obtain an time when Steiner vertices are allowed. Moreover, we de- oblivious data structure is simply to run a classic data scribe a (1 + ε) approximation algorithm with a similar structure on an oblivious RAM (ORAM). With the cur- running time for finding a tree spanner of (X, Xd)that rent best ORAM implementations, this results in an over- minimizes the maximum stretch. Finally, we generalize head of ω(lg n) for the most natural setting of parameters. our tree spanner algorithm to a (1 + ε) approximation al- Moreover, a recent lower bound for ORAMs by Larsen and gorithm for computing a minimum stretch tree spanner of Nielsen [CRYPTO’18] show that they always incur an over- a weighted graph, where the running time is also param- head of at least Ω(lg n) if used in a black box manner. To eterized with respect to maximum degree. In particular, circumvent the current ω(lg n) overhead, researchers have we obtain a PTAS for computing minimum stretch tree instead studied classic data structure problems more di- spanners of weighted graphs, with polynomially bounded rectly and have obtained efficient solutions for many such spread, constant doubling dimension, and constant max- problems such as stacks, queues, deques, priority queues imum degree, when a tree spanner with constant stretch and search trees. However, none of these data structures exists. process operations faster than Θ(lg n), leaving open the question of whether even faster solutions exist. In this pa- Benjamin A. Raichel per, we rule out this possibility by proving Ω(lg n)lower University of Texas at Dallas bounds for oblivious stacks, queues, deques, priority queues [email protected] and search trees.

Amir Nayyeri Riko Jacob School of Electrical Eng and Computer Science IT University Copenhagen Oregon State University [email protected] [email protected] Kasper G. Larsen MADALGO, Aarhus University CP40 [email protected] Towards Instance-optimal Private Query Release Jesper B. Nielsen We study efficient mechanisms for the query release prob- Aarhus University lem in differential privacy: given a workload of m statis- [email protected] tical queries, output approximate answers to the queries while satisfying the constraints of differential privacy. In particular, we are interested in mechanisms that optimally CP40 adapt to the given workload. Building on the projec- Foundations of Differentially Oblivious Algorithms tion mechanism of Nikolov, Talwar, and Zhang, and using the ideas behind Dudley’s chaining inequality, we propose It is well-known that a program’s memory access pattern new efficient algorithms for the query release problem, and can leak information about its input. To thwart such leak- prove that they achieve optimal sample complexity for the age, most existing works adopt the technique of obliv- given workload (up to constant factors, in certain param- ious RAM (ORAM) simulation. Such an obliviousness eter regimes) with respect to the class of mechanisms that notion has stimulated much debate. Although ORAM satisfy concentrated differential privacy. We also give vari- techniques have significantly improved over the past few ants of our algorithms that satisfy local differential privacy, years, the concrete overheads are arguably still undesir- and prove that they also achieve optimal sample complex- able for real-world systems — part of this overhead is in ity among all local sequentially interactive private mecha- fact inherent due to a well-known logarithmic ORAM lower nisms. bound by Goldreich and Ostrovsky. Inspired by the el- egant notion of differential privacy, we initiate the study Aleksandar Nikolov of a new notion of access pattern privacy, which we call University of Toronto “(, δ)-differential obliviousness’. We separate the notion [email protected] of (, δ)-differential obliviousness from classical oblivious- DA19 Abstracts 51

ness by considering several fundamental algorithmic ab- Sorting? stractions including sorting small-length keys, merging two sorted lists, and range query data structures. We show It is well-known that non-comparison-based techniques can that by adopting differential obliviousness with reasonable allow us to sort n elements in o(n log n) time on a Random- choices of  and δ, not only can one circumvent several im- Access Machine (RAM). On the other hand, it is a long- possibilities pertaining to full obliviousness, one can also, standing open question whether (non-comparison-based) in several cases, obtain meaningful privacy with little over- circuits can sort n elements from the domain [1..2k ]with head relative to the non-private baselines. o(kn log n) boolean gates. We consider weakened forms of this question: first, we consider a restricted class of sorting T-H. Hubert Chan where the number of distinct keys is much smaller than The University of Hong Kong the input length; and second, we explore Oblivious RAMs [email protected] and probabilistic circuit families, i.e., computational mod- els that are somewhat more powerful than circuits but Kai-Min Chung much weaker than RAM. We show that Oblivious RAMs Academia Sinica and probabilistic circuit families can sort o(log n)-bit keys [email protected] in o(n log n)timeoro(kn log n) circuit complexity. Our algorithms work in the balls-and-bins model, i.e., not only Bruce M. Maggs can they sort an array of numerical keys — if each key ad- Duke University and Akamai Technologies ditionally carries an opaque ball, our algorithms can also [email protected] move the balls into the correct order. We further show that in such a balls-and-bins model, it is impossible to sort Ω(log n)-bit keys in o(n log n)time,andthustheo(log n)- Elaine Shi bit-key assumption is necessary for overcoming the n log n Cornell University barrier. Finally, after optimizing the IO efficiency, we show [email protected] that even the 1-bit special case can solve open questions: our oblivious algorithms solve tight compaction and selec- tion with optimal IO efficiency for the first time. CP40 Amplification by Shuffling: From Local to Central Wei-Kai Lin, Elaine Shi Differential Privacy via Anonymity Cornell University [email protected], [email protected] Sensitive statistics are often collected across sets of users, with repeated collection of reports done over time. For Tiancheng Xie example, trends in users’ private preferences or software Shanghai Jiao Tong University usage may be monitored via such reports. Building on re- [email protected] cent work, we study the collection of such statistics in the local differential privacy (LDP) model, and describe an al- gorithm whose privacy cost is polylogarithmic in the num- CP41 ber of changes to a user’s value. This algorithm is of par- A Simple Near-Linear Pseudopolynomial Time ticular practical benefit in applications where each user’s Randomized Algorithm for Subset Sum value may change only a small number of times. More fundamentally—by building on anonymity of the users’ Given a multiset of n positive integers and a target inte- reports—we also demonstrate how the privacy cost of our ger t,theSubset Sum problem asks to determine whether LDP algorithm can actually be much lower when viewed there exists a subset of S that sums up to t.Thecur- in the central model of differential privacy, We show, via a rent best deterministic√ algorithm, by Koiliaris and Xu new and general technique, that any permutation-invariant [SODA’17], runs in O˜( nt) time, where O˜ hides poly- algorithm satisfying√ ε-local differential privacy will satisfy logarithm factors. Bringmann [SODA’17] later gave a ran- O(εlog(1/δ)/ n, δ)-central differential√ privacy. By this, we domized O˜(n + t) time algorithm using two-stage color- clarify how the high noise and n overhead of LDP pro- ˜ tocols is a consequence of them being significantly more coding. The O(n + t) running time is believed to be near- private in the central model. As a final, practical corol- optimal. In this paper, we present a simple and elegant ran- Subset Sum ˜ lary, our results also imply that industrial deployments of domized algorithm for in O(n + t)time.Our LDP mechanism may have much lower privacy cost than new algorithm actually solves its counting version modulo their advertised ε would indicate—at least if reports are prime p>t, by manipulating generating functions using FFT anonymized. . Ce Jin, Hongxun Wu Ulfar Erlingsson, Vitaly Feldman, Ilya Mironov, Ananth Institute for Interdisciplinary Information Sciences Raghunathan, Kunal Talwar Tsinghua University Google [email protected], [email protected], [email protected], [email protected] [email protected], [email protected], [email protected] CP41 Abhradeep Thakurta Compressed Sensing with Adversarial Sparse Noise UC Santa Cruz and Google via L1 Regression [email protected] We present a simple and effective algorithm for the prob- lem of sparse robust linear regression. In this problem, one CP40 would like to estimate a sparse vector w∗ ∈n from linear CanweOvercomethen log n Barrier for Oblivious measurements corrupted by sparse noise that can arbitrar- 52 DA19 Abstracts

ily change an adversarially chosen η fraction of measured J time slots, then this scheme will achieve channel utiliza- responses y, as well as introduce bounded norm noise to tion 1/e − , excluding O(J) wasted slots. Results similar the responses. For Gaussian measurements, we show that to these (Bender et al. 2016) were already achieved, but a simple algorithm based on L1 regression can successfully with much lower efficiency and a more complex algorithm. ∗ estimate w for any η<η0 ≈ 0.239, and that this threshold is tight for the algorithm. The number of measurements n required by the algorithm is O(k log k )fork-sparse esti- Yi-Jun Chang, Wenyu Jin, Seth Pettie mation, which is within constant factors of the number University of Michigan needed without any sparse noise. Of the three properties [email protected], [email protected], [email protected] we show—the ability to estimate sparse, as well as dense, w∗; the tolerance of a large constant fraction of outliers; and tolerance of adversarial rather than distributional (e.g., CP41 Gaussian) dense noise—to the best of our knowledge, no Approximating Maximin Share Allocations previous polynomial time algorithm was known to achieve more than two. We study the problem of fair allocation of M indivisible items among N agents using the popular notion of max- Sushrut Karmalkar imin share as our measure of fairness. The maximin share The University of Texas at Austin of an agent is the largest value she can guarantee herself [email protected] if she is allowed to choose a partition of the items into N bundles (one for each agent), on the condition that she Eric Price receives her least preferred bundle. A maximin share al- The Unviersity of Texas at Austin location provides each agent a bundle worth at least their [email protected] maximin share. While it is known that such an alloca- tion need not exist [Procaccia and Wang, 2014, Kurokawa et al., 2016], a series of work [Procaccia and Wang, 2014, CP41 Kurokawa et al., 2018, Amanatidis et al., 2017, Barman Submodular Optimization in the MapReduce and Murthy, 2017] provided 2/3 approximation algorithms Model in which each agent receives a bundle worth at least 2/3 times their maximin share. Recently, [Ghodsi et al., 2018] Submodular optimization has received significant attention improved the approximation guarantee to 3/4. Prior works in both practice and theory, as a wide array of problems utilize intricate algorithms, with an exception of [Barman in machine learning, auction theory, and combinatorial op- and Murthy, 2017] which is a simple greedy solution but re- timization have submodular structure. In practice, these lies on sophisticated analysis techniques. In this paper, we problems often involve large amounts of data, and must propose an alternative 2/3 maximin share approximation be solved in a distributed way. One popular framework which offers both a simple algorithm and straightforward for running such distributed algorithms is MapReduce. In analysis. In contrast to other algorithms, our approach this paper, we present two simple algorithms for cardinal- allows for a simple and intuitive understanding of why it ity constrained submodular optimization in the MapRe- works. duce model: the first is a (1/2 − o(1))-approximation in 2 MapReduce rounds, and the second is a (1 − 1/e − )- 1+o(1) Jugal Garg, Peter McGlaughlin approximation in  MapReduce rounds. University of Illinois at Urbana-Champaign [email protected], [email protected] Paul Liu, Jan Vondrak Stanford University [email protected], [email protected] Setareh Taki University of Illinois at Urbana Champaign [email protected] CP41 Simple Contention Resolution via Multiplicative Weight Updates CP42 Non-Empty Bins with Simple Tabulation Hashing We consider the classic contention resolution problem, in which devices conspire to share some common resource, We consider the hashing of a set X ⊆ U with |X| = m for which they each need temporary and exclusive access. using a simple tabulation hash function h : U → [n]= To ground the discussion, suppose identical devices wake {0,...,n− 1} and analyze the number of non-empty bins, up at various times, and must send a single packet over that is, the size of h(X). We show that the expected size a shared multiple-access channel. In each time step they of h(X) matches that with fully random hashing to within may attempt to send their packet; they receive ternary low-order terms. We also provide concentration bounds. feedback {0, 1, 2+} from the channel. We prove that a sim- The number of non-empty bins is a fundamental measure ple strategy suffices to achieve a channel utilization rate in the balls and bins paradigm, and it is critical in applica- of 1/e − O(), for any >0. In each step, device i at- tions such as Bloom filters and Filter hashing. For exam- tempts to send its packet with probability pi, then applies ple, normally Bloom filters are proportioned for a desired a rudimentary multiplicative weight-type update to pi. low false-positive probability assuming fully random hash- ⎧ ing (see en.wikipedia.org/wiki/Bloom filter). Our results ·  ⎨ pi e upon hearing silence (0) imply that if we implement the hashing with simple tab- pi ← pi upon hearing success (1) ulation, we obtain the same low false-positive probability ⎩ −/(e−2) + pi · e upon hearing noise (2 ) for any possible input.

This scheme works well even if the introduction of de- Anders Aamand vices/packets is adversarial, and even if the adversary can University of Copenhagen, BARC jam time slots (make noise) at will. If the adversary jams [email protected] DA19 Abstracts 53

Mikkel Thorup VMWare Research Group University of Copenhagen [email protected] [email protected] Meng-Tsung Tsai National Chiao Tung University CP42 [email protected] Derandomized Balanced Allocation

In this paper, we study the maximum loads of explicit hash CP42 families in the d-choice schemes when allocating sequen- A Fourier-Analytic Approach for the Discrepancy tially n balls into n bins. We consider the Uniform-Greedy of Random Set Systems scheme, which provides d independent bins for each ball and places the ball into the bin with the least load, and One of the prominent open problems in combinatorics is its non-uniform variant — the Always-Go-Left scheme in- the discrepancy of set systems where each element lies troduced by V¨ocking. We construct a hash family with in at most t sets. The Beck-Fiala√ conjecture suggests O(log n log log n) random bits based on the previous work that the right bound is O( t), but for three decades the of Celis et al. and show the following results. only known bound not depending on the size of set sys- 1. With high probability, this hash family has a maxi- tem has been O(t). Arguably we currently lack techniques log log n for breaking that barrier. In this paper we introduce dis- mum load of log d + O(1) in the Uniform-Greedy scheme. crepancy bounds based on Fourier analysis. We demon- strate our method on random set systems. Suppose one 2. With high probability, it has a maximum load of has n elements and m sets containing each element inde- log log n + O(1) in the Always-Go-Left scheme for a d log φd pendently with probability p. We prove that in the regime 2 constant φd > 1.61. of n ≥ Θ(m log(m)), the discrepancy is at most 1 with high probability. Previously, a result of Ezra and Lovett The maximum loads of our hash family match the max- gave a bound of O(1) under the stricter assumption that imum loads of a perfectly random hash function in the n  mt. Uniform-Greedy and Always-Go-Left scheme separately, up to the low order term of constants. Previously, the best Rebecca Hoberg, Thomas Rothvoss known hash families matching the same maximum loads of University of Washington a perfectly random hash function in d-choice schemes were [email protected], [email protected] O(log n)-wise independent functions by V¨ocking, which needs Θ(log2 n) random bits. CP42 Xue Chen Department of Computer Science On the Discrepancy of Random Low Degree Set University of Texas at Austin Systems [email protected] Motivated by the celebrated Beck-Fiala conjecture, we con- sider the random setting where there are n elements and CP42 m sets and each element lies in t randomly chosen sets. 1/2 Optimal Ball Recycling In this setting, Ezra and Lovett showed an O((t log t) ) discrepancy bound in the regime when n ≤ m and an O√(1) Balls-and-bins games have been a wildly successful tool for bound when n  mt. Inthispaper,wegiveatightO( t) modeling load balancing problems. In this paper, we study bound for the entire range of n and m, under a mild as- a new scenario, which we call the ball recycling game,de- sumption that t =Ω(loglogm)2. The result is based on fined as follows: Throw m balls into n bins i.i.d. according two steps. First, applying the partial coloring method to to a given probability distribution p. Then, at each time the case when n = m logO(1) m and using the properties of step, pick a non-empty bin and recycle its balls: take the the random set system we show√ that the overall discrep- balls from the selected bin and re-throw them according ancy incurred is at most O( t). Second, we reduce the to p. This balls-and-bins game closely models memory- general case to that of n ≤ m logO(1) m using LP duality access heuristics in databases. The goal is to have a bin- and a careful counting argument. picking method that maximizes the recycling rate, defined to be the expected number of balls recycled per step in the Nikhil Bansal stationary distribution. We study two natural strategies CWI and TU Eindhoven for ball recycling: FB, which greedily picks the bin with [email protected] the maximum number of balls, and RB, which picks a ball at random and recycles its bin. We show that for general Raghu Meka p,RBisO(1)-optimal, whereas FB can be pessimal. How- UCLA ever, when p = u, the uniform distribution, FB is optimal [email protected] to within an additive constant.

Michael A. Bender, Jake Christensen CP43 Stony Brook University Optimal Lower Bounds for Sketching Graph Cuts [email protected], [email protected] We study the space complexity of sketching cuts and Lapla- Alexander Conway, Martin Farach-Colton cian quadratic forms of graphs. We show that any data Rutgers University structure which approximately stores the sizes of all cuts [email protected], [email protected] in an undirected graph on n vertices up to a 1 +  error must use Ω(n log n/2) bits of space in the worst case, im- Rob Johnson proving the Ω(n/2) bound of [Andoni et al., ITCS 2016] 54 DA19 Abstracts

and matching the best known upper bound achieved by ities of algorithms for solving problems that involve the spectral sparsifiers [Batson et al., STOC 2009]. Our proof quadratic form, such as computing the eigenvalues of LG, is based on a rigidity phenomenon for cut (and spectral) computing the effective resistance between a pair of ver- approximation which may be of independent interest: any tices in G, semi-supervised learning based on LG,andcut two d−regular graphs which approximate each other’s cuts problems on G. In addition, our sparsification result im- significantly better than a random graph approximates the plies that any nonnegative submodular function f with complete graph must overlap in a constant fraction of their f(∅)=f(V ) = 0 can be concisely represented by a di- edges. rected hypergraph. Accordingly, we show that, for any distribution, we can properly and agnostically learn sub- Charles A. Carlson, Alexandra Kolla modular functions f :2V → [0, 1] with f(∅)=f(V )=0, University of Colorado Boulder with O(n4 log(n/)/4)samples. [email protected], [email protected] Tasuku Soma Nikhil Srivastava university of Tokyo University of California Berkeley tasuku [email protected] [email protected] Yuichi Yoshida Luca Trevisan National Institute of Informatics UC Berkeley Preferred Infrastructure [email protected] [email protected]

CP43 CP43 Short Cycles via Low-diameter Decompositions Expander Decomposition and Pruning: Faster, Stronger, and Simpler We present improved algorithms for short cycle decompo- sition of a graph. Short cycle decompositions were intro- Expander decomposition is a useful method for graph duced in the recent work of Chu [?],andwereusedto clustering introduced by [Kannan, Vempala, and Vetta, make progress on several questions in graph sparsification. FOCS’00] with wide applications in theory and in prac- For all constants δ ∈ (0, 1], we give an O(mnδ ) time al- tice. In this paper, we study the parametrized version gorithm that, given a graph G, partitions its edges into of expander decomposition, where given a graph G of m 1 cycles of length O(log n) δ ,withO(n) extra edges not in edges and a parameter φ, we find a partition of the vertices any cycle. This gives the first subquadratic, in fact al- into clusters such that each cluster induces a subgraph of ˜ most linear time, algorithm achieving√ polylogarithmic cycle conductance at least φ (i.e. an expander) and only O(φ)- lengths. We also give an m·exp(O( log n)) time algorithm fraction of edges have endpoints in different clusters. Our that partitions the edges of a graph into cycles of length algorithm runs in O˜(m/φ) time and is the first near-linear √ − exp(O( log n log log n)), with O(n) extra edges not in any time algorithm when φ is at least (polylog m) 1,whichis cycle. This improves on the short cycle decomposition al- the case in most practical settings and theoretical applica- gorithms given in Chu [?] in terms of all parameters, and tions. This affirmatively answers the open question noted is significantly simpler. As a result, we obtain faster al- in [Spielman and Teng, STOC’04] and also in [Koutis and gorithms and improved guarantees for several problems in Miller, SPAA’08; Orecchia and Vishnoi, SODA’11; Orec- graph sparsification – construction of resistance sparsifiers, chia, Sachdeva, and Vishnoi, STOC’12]. Previous algo- graphical spectral sketches, degree preserving sparsifiers, rithms either take Ω(m1+o(1)) time or only guarantee that and approximating the effective resistances of all edges. each cluster is contained in some unspecified expander. Our decomposition algorithm is developed from first princi- Yang Liu ples based on local flow techniques and is relatively simple. Stanford University The techniques can be extended to obtain a significant im- [email protected] provement in an expander pruning algorithm, which is the key tool for maintaining the expander decomposition on Sushant Sachdeva, Zejun Yu dynamic graphs. University of Toronto [email protected], [email protected] Thatchaphol Saranurak Toyota Technological Institute at Chicago [email protected] CP43 Spectral Sparsification of Hypergraphs Di Wang Georgia Institute of Technology For an undirected/directed hypergraph G =(V,E), its [email protected] Laplacian LG is defined such that its “quadratic form’  x LG(x) captures the cut information of G.Inpartic-  ⊆ ular, 1S LG(1S ) coincides with the cut size of S V , CP43 where 1S is the characteristic vector of S.Aweighted Cheeger Inequalities for Submodular Transforma- subgraph H of a hypergraph G on a vertex set V is said  tions to be an -spectral sparsifier of G if (1 − )x LH (x) ≤   x LG(x) ≤ (1 + )x LH (x)holdsforeveryx.Inthispa- The Cheeger inequality for undirected graphs, which re- per, we present a polynomial-time algorithm that, given lates the conductance of an undirected graph and the sec- an undirected/directed hypergraph G on n vertices, con- ond smallest eigenvalue of its normalized Laplacian, is a structs an -spectral sparsifier of G with O(n3 log n/2) cornerstone of spectral graph theory. The Cheeger inequal- hyperedges/hyperarcs. The proposed spectral sparsifica- ity has been extended to directed graphs and hypergraphs tioncanbeusedtoimprovethetimeandspacecomplex- using normalized Laplacians for those, that are no longer DA19 Abstracts 55

linear but piecewise linear transformations. In this paper, for complexes embedded in R4 and beyond in less than we introduce the notion of a submodular transformation quadratic or even near-quadratic time. But, what about F : {0, 1}n → Rm, which applies m submodular functions dimension three? The question for general simplicial com- to the n-dimensional input vector, and then introduce the plexes K linearly embedded in R3 is not completely settled. notions of its Laplacian and normalized Laplacian. With No algorithm with a complexity better than that of the ma- these notions, we unify and generalize the existing Cheeger trix multiplication is known for this important case. We inequalities by showing a Cheeger inequality for submod- show that the persistence for height functions on such com- ular transformations, which relates the conductance of a plexes, hence called height persistence, can be computed in submodular transformation and the smallest non-trivial O(n log n) time. This allows us to compute a basis (gen- eigenvalue of its normalized Laplacian. This result recov- erators) of Hi(K), i =1, 2, in O(n log n + k)timewherek ers the Cheeger inequalities for undirected graphs, directed is the size of the output. This improves significantly the graphs, and hypergraphs, and derives novel Cheeger in- current best bound of O(nω ), ω being the matrix multi- equalities for mutual information and directed information. plication exponent. We achieve these improved bounds by Computing the smallest non-trivial eigenvalue of a nor- leveraging recent results on zigzag persistence in computa- malized Laplacian of a submodular transformation is NP- tional topology, new observations about Reeb graphs, and hard under the small set expansion hypothesis. In this pa- some efficient geometric data structures. per, we present a polynomial-time O(log n)-approximation algorithm for the symmetric case, which is tight, and a TamalK.Dey polynomial-time O(log2 n+logn·log m)-approximation al- Ohio State University gorithm for the general case. Columbus, Ohio 43210 [email protected] Yuichi Yoshida National Institute of Informatics Preferred Infrastructure CP44 [email protected] Constructive Polynomial Partitioning for Algebraic Curves In 3 with Applications

CP44 In 2015, Guth proved that for any set of k-dimensional va- rieties in d and for any positive integer D,thereexistsa Improved Topological Approximations by Digitiza- d tion polynomial of degree at most D whose zero-set divides R into open connected “cells,’ so that only a small fraction of Cechˇ complexes are useful simplicial complexes for com- the given varieties intersect each cell. Guth’s result gener- puting and analyzing topological features of data that lies alized an earlier result of Guth and Katz for points. Guth’s in Euclidean space. Unfortunately, computing these com- proof relies on a variant of the Borsuk-Ulam theorem, and plexes becomes prohibitively expensive for large-sized data for k>0, it is unknown how to obtain an explicit rep- sets even for medium-to-low dimensional data. We present resentation of such a partitioning polynomial and how to an approximation scheme for (1 + )-approximating the construct it efficiently. In particular, it is unknown how to ˇ effectively construct such a polynomial for curves (or even topological information of the Cech complexes for n points 3 in Rd,for ∈ (0, 1]. Our approximation has a total size of lines) in R . We present an efficient algorithmic construc- tion for this setting. Given a set of n input curves and a n 1 O(d) for constant dimension d, improving all the cur-  positive integer D, we efficiently construct a decomposition rently available (1+)-approximation schemes of simplicial of space into O(D3 log3 D)opencells,eachofwhichmeets filtrations in Euclidean space. Perhaps counter-intuitively, at most O(n/D2) curves from the input. As an application, 1 O(d) we arrive at our result by adding additional n  sam- we revisit the problem of eliminating depth cycles among ple points to the input. We achieve a bound that is inde- non-vertical pairwise disjoint triangles in 3-space, recently pendent of the spread of the point set by pre-identifying the studied by Aronov (2017) and de Berg (2017). scales at which the Cechˇ complexes changes and sampling accordingly. Esther Ezra Georgia Tech Aruni Choudhary [email protected] Freie Universit¨at Berlin [email protected] Boris Aronov New York University Michael Kerber [email protected] University of Technology, Graz, Austria [email protected] Joshua Zahl University of British Columbia Sharath Raghvendra [email protected] Virginia Tech [email protected] CP44 Full Tilt: Universal Constructors for General CP44 Shapes with Uniform External Forces Computing Height Persistence and Homology Gen- erators in R3 Efficiently We investigate the problem of assembling general shapes and patterns in a model in which particles move based on Recently it has been shown that computing the dimension uniform external forces until they encounter an obstacle. of the first homology group H1(K) of a simplicial 2-complex In this model, corresponding particles may bond when ad- K embedded linearly in R4 is as hard as computing the rank jacent with one another. Succinctly, this model considers a of a sparse 0 − 1 matrix. This puts a major roadblock to 2D grid of “open” and “blocked” spaces, along with a set of computing persistence and a homology basis (generators) slidable polyominoes placed at open locations on the board. 56 DA19 Abstracts

The board may be tilted in any of the 4 cardinal directions, Nearly-linear Time causing all slidable polyominoes to move maximally in the specified direction until blocked. By successively applying We study the fundamental problem of high-dimensional a sequence of such tilts, tilt sequences provide a method to mean estimation in a robust model where a constant frac- reconfigure an initial board configuration so as to assemble tion of the samples are adversarially corrupted. Recent a collection of previous separate polyominoes into a larger work gave the first polynomial time algorithms for this shape. While previous work within this model of assem- problem with dimension-independent error guarantees for bly has focused on designing a specific board configuration several families of structured distributions. In this work, for the assembly of a specific given shape, we propose the we give the first nearly-linear time algorithms for high- problem of designing universal configurations that are ca- dimensional robust mean estimation. We focus on distri- pable of constructing a large class of shapes and patterns. butions with (i) known covariance and sub-gaussian tails, We also include a study of the complexity of deciding if and (ii) unknown bounded covariance. Given N samples a particle within a configuration may be relocated to an- on Rd,an-fraction of which may be arbitrarily corrupted, other position, and deciding if a given configuration may our algorithms run in time O˜(Nd)/poly() and approxi- be transformed into a second given configuration. In both mate the true mean within the information-theoretically cases, we show this problem to be PSPACE-complete, even optimal error, up to constant factors. Previous robust al- when movable particles are restricted to 1 × 1and2× 2 gorithms with comparable error guarantees have running polyominoes that do not stick to one another. times Ω(˜ Nd2). Our algorithms rely on a natural family of SDPs parameterized by our current guess ν for the un- Jose Balanza-Martinez, David Caballero, Angel Cantu, known mean μ . We give a win-win analysis as follows: Luis Garcia, Austin Luchsinger, Rene Reyes either the primal SDP yields a good estimate for μ ,orthe University of Texas - Rio Grande Valley dual SDP yields a better guess ν closer to μ . We exploit [email protected], [email protected], the special structure of the corresponding SDPs to show [email protected], [email protected], that they are approximately solvable in nearly-linear time. [email protected], [email protected] Our approach is quite general, and we believe it can also be applied to obtain nearly-linear time algorithms for other Robert T. Schweller high-dimensional robust learning problems. University of Texas - Pan American [email protected] Yu Cheng Duke University Tim Wylie [email protected] University of Texas - Rio Grande Valley [email protected] Ilias Diakonikolas University of Southern California [email protected] CP44 Hardness of Approximation for Morse Matching Rong Ge Duke University Discrete Morse theory has emerged as a powerful tool for [email protected] a wide range of computational problems in topology. In this context, discrete Morse theory is used to reduce the problem of computing a topological invariant of an input CP45 simplicial complex to computing the same topological in- Adaptive Sparse Recovery with Limited Adaptivity variant of a (significantly smaller) collapsed cell or chain complex. Consequently, devising methods for obtaining The goal of adaptive sparse recovery is to estimate an ap- gradient vector fields on complexes to reduce the size of the proximately sparse vector x from a series of linear mea- problem instance has become an emerging theme over the surements A1x, A2x,...,ARx,whereeachmatrixAi may last decade. While computing the optimal gradient vector depend on the previous observations. With an unlimited field on a simplicial complex is NP-hard, several heuristics number of rounds R,itisknownthatO(k log log n)mea- have been observed to compute near-optimal gradient vec- surements suffice for O(1)-approximate k-sparse recovery tor fields on a wide variety of datasets. Understanding the in Rn,andthatΩ(k +loglogn) measurements are nec- theoretical limits of these strategies is therefore a funda- essary. We initiate the study of what happens with a mental problem in computational topology. In this paper, small, constant number amount of adaptivity. Previous we establish hardness of approximation results for maxi- techniques could not give nontrivial bounds using less than mization and minimization variants of the Morse match- 5 rounds of adaptivity, and were inefficient for any constant ing problem. In particular, we show that, for a simplicial R. We give nearly matching upper and lower bounds for ≥ complex of dimension d 3withn simplices, it is NP- any constant number of rounds R. Our lower bound shows hard to approximate Min-Morse matching within a factor n 1/R 1− that Ω(k(log k ) ) measurements are necessary for any of O(n ), for any >0. Moreover, we establish hardness n 1/R of approximation results for Max-Morse matching for sim- k<2(log k ) ; significantly, this is the first lower bound plicial complexes of dimension d ≥ 2, using an L-reduction that combines k and n in an adaptive setting. Our up- ∗ from Degree 3 Max-Acyclic Subgraph to Max-Morse match- per bound shows that O(k(log n )1/R ·log k)measurements ∗ k ing. suffice. The O(log k) gap between the two bounds comes from a similar gap for nonadaptive sparse recovery in the Abhishek J. Rathod, Ulrich Bauer high-SNR regime, and would be reduced to constant fac- Technische Universit¨at M¨unchen tors with improvements to nonadaptive high-SNR sparse [email protected], [email protected] recovery.

Akshay Kamath CP45 The University of Texas at Austin High-Dimensional Robust Mean Estimation in [email protected] DA19 Abstracts 57

Eric Price time domain and O(k log N)runtimeperfrequency,inany The Unviersity of Texas at Austin dimension d. We also investigate natural average case mod- [email protected] els of the input signal: (1) worst-case support in Fourier domain with randomized coefficients and (2) random loca- tions in Fourier domain with worst case coefficients. Our CP45 techniques lead to an O(k2) time algorithm for the former Efficient Algorithms and Lower Bounds for Robust and an O(k) time algorithm for the latter. Linear Regression Michael Kapralov We study the prototypical problem of high-dimensional lin- IBMT.J.WatsonResearchCenter, ear regression in a robust model where an -fraction of michael.kapralov@epfl.ch the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the un- Ameya Velingker corrupted samples are drawn from a Gaussian distribution Google AI N d (0, Σ) on R . We give nearly tight upper bounds and ameya.velingker@epfl.ch computational lower bounds for this problem as follows: • For the case that the covariance matrix is known Amir Zandieh to be the identity, we give a computationally effi- EPFL cient algorithm that draws O˜(d/2) labeled exam- amir.zandieh@epfl.ch ples and approximates the unknown regression vector within 2-norm O( log(1/)σ). An error of Ω(σ)is information-theoretically necessary. Hence, the error CP45 guarantee of our algorithm is optimal, up to a loga- Relative Error Tensor Low Rank Approximation rithmic factor in 1/. We consider relative error low rank approximation of ten- • q For the case of unknown covariance Σ, we show that sors: given an order-q tensor A ∈ R i=1 ni , output a rank- we can efficiently achieve the same error guarantee − 2 ≤ k tensor B for which A B F (1 + )OPT, where  2 as in the known covariance case, using an additional OPT= inf  A − A . One structural issue for ˜ 2 2 rank-kA F O(d / ) unlabeled examples. On the other hand, obtaining relative error low rank approximation is that an error of O(σ) can be information-theoretically at- there may be no rank-k tensor A achieving the above in- 2 k tained with O(d/ ) samples. We prove a Statistical finum. Another, computational issue, is that an efficient Query (SQ) lowerbound showing that any polynomial relative error low rank approximation for tensors would al- time SQ algorithm (in Huber’s contamination model) low one to compute the rank of a tensor, which is NP-hard. 1.99 with estimation√ complexity O(d ), must incur an We bypass these issues via (1) bicriteria and (2) param- error of Ω( σ). eterized complexity solutions: (1) We give an algorithm which outputs a rank k = O((k/)q−1)tensorB for which − 2 ≤ · Weihao Kong A B F (1+)OPT in nnz(A)+n poly(k/)timeinthe Stanford University real RAM model. Here nnz(A) is the number of non-zero [email protected] entries in A. (2) We give an algorithm for any δ>0which − 2 ≤ outputs a rank k tensor B for which A B F (1+)OPT 2 δ Ilias Diakonikolas and runs in (nnz(A)+n·poly(k/)+exp(k /))·n time in USC the unit cost RAM model. For outputting a rank-k tensor, 1−o(1) [email protected] orevenabicriteriasolution,weshowa2Ω(k ) time lower bound under the Exponential Time Hypothesis. We Alistair Stewart also obtain new results for matrices, such as nnz(A)-time Stanford CUR decompositions, which may be of independent inter- [email protected] est. Zhao Song CP45 UT-Austin Dimension-independent Sparse Fourier Transform [email protected]

The Discrete Fourier Transform (DFT) is a fundamental David Woodruff computational primitive, and the fastest known algorithm Carnegie Mellon University for computing the DFT is the FFT (Fast Fourier Trans- [email protected] form) algorithm. One remarkable feature of FFT is the fact that its runtime depends only on the size N of the Peilin Zhong input vector, but not on d, the dimensionality of the input Columbia University d domain: FFT runs in time O(N log N), where N = n . [email protected] The state of the art for Sparse FFT, i.e. the problem of computing the DFT of a signal with at most k nonzeros in Fourier domain, is very different: all current techniques CP46 for sublinear Sparse FFT incur an exponential dependence Stochastic Matching with Few Queries: New Algo- on the dimension d. In this paper, we give the first algo- rithms and Tools rithm that computes the DFT of a k-sparse signal in time (k, log N) in any dimension d, avoiding the curse of di- We consider the stochastic matching problem: A graph mensionality inherent in all previously known techniques. G =(V,E) along with a parameter p ∈ (0, 1) is given in Our main tool is a new class of filters that we refer to the input. Each edge of G is realized independently with as adaptive aliasing filters: these filters allow isolating fre- probability p. The goal is to select a degree bounded sub- quencies of a k-Fourier sparse signal using O(k)samplesin graph H of G such that the expected maximum match- 58 DA19 Abstracts

ing size/weight of H is close to that of G.Thismodel Tata Institute of Fundamental Research of stochastic matching has attracted significant attention [email protected] over the recent years. The fundamental open question is the best approximation factor achievable for such algo- Vladlena Powers, Xingyu Zhang rithms. Prior work has identified breaking (near) half- Columbia University approximation as a barrier for both weighted and un- [email protected], [email protected] weighted graphs. We give an algorithm that for unweighted graphs, finds a 0.6568 approximation by querying O˜(1/p) edges per vertex. This is a significant improvement over CP46 the known close-to half approximations of the literature. Beating Greedy for Stochastic Bipartite Matching In particular, it improves the state-of-the-art 0.5001 ap- proximation of Assadi et al. [EC’17]. We also show that We consider the maximum bipartite matching problem in the the same algorithm achieves a 0.501 approximation stochastic settings, namely the query-commit and price-of- for weighted graphs by querying O˜(1/p) edges per vertex. information models. In the query-commit model, an edge This improves both, the approximation factor and the per- e independently exists with probability pe.Wecanquery vertex queries of the algorithms by Yamaguchi and Mae- whether an edge exists or not, but if it does exist, then hara [SODA’18] and Behnezhad and Reyhani [EC’18]. Our we have to take it into our solution. In the unweighted algorithms are fundamentally different from those consid- case, one can query edges in the order given by the clas- ered in the literature, yet are very simple and natural. We sical online algorithm of Karp, Vazirani, and Vazirani to consider the new algorithms and our analytical tools to be get a (1 − 1/e)-approximation. In contrast, the previously the main contributions of this paper. best known algorithm in the weighted case is the (1/2)- approximation achieved by the greedy algorithm that sorts Soheil Behnezhad, Alireza Farhadi the edges according to their weights and queries in that or- University of Maryland der. Improving upon the basic greedy, we give a (1 − 1/e)- [email protected], [email protected] approximation algorithm in the weighted query-commit model. We use a linear program (LP) to upper bound MohammadTaghi Hajiaghayi the optimum achieved by any strategy. The proposed LP University of Maryland, College Park admits several structural properties that play a crucial role [email protected] in the design and analysis of our algorithm. We also ex- tend these techniques to get a (1 − 1/e)-approximation al- Nima Reyhani gorithm for maximum bipartite matching in the price-of- University of Maryland information model introduced by Singla, who also used the [email protected] basic greedy algorithm to give a (1/2)-approximation. Buddhima Gamlath, Sagar Kale ´ CP46 Ecole polytechnique f´ed´erale de Lausanne buddhima.gamlath@epfl.ch, sagar.kale@epfl.ch Popular Matchings and Limits to Tractability

We consider popular matching problems in both bipartite Ola Svensson and non-bipartite graphs with strict preference lists. It EPFL is known that every stable matching is a min-size popu- ola.svensson@epfl.ch lar matching. A subclass of max-size popular matchings called dominant matchings has been well-studied in bipar- tite graphs: they always exist and there is a simple linear CP46 time algorithm to find one. We show that stable and dom- A (1+1/e)-Approximation Algorithm for Maxi- inant matchings are the only two tractable subclasses of mum Stable Matching with One-sided Ties and In- popular matchings in bipartite graphs; more precisely, we complete Lists show that it is NP-complete to decide if G admits a popu- lar matching that is neither stable nor dominant. We also We study the problem of finding large weakly stable match- show a number of related hardness results, such as (tight) ings when preference lists are incomplete and contain one- inapproximability of the maximum weight popular match- sided ties. Computing maximum weakly stable matchings ing problem. In non-bipartite graphs, we show a strong is known to be NP-hard. We present a polynomial-time negative result: it is NP-hard to decide whether a popu- algorithm that achieves an improved approximation ratio lar matching exists or not, and the same result holds if we of 1+1/e. Building on existing approximation algorithms replace popular with dominant. On the positive side, we for this problem, our algorithm is motivated by a proposal show the following results in any graph: process in which numerical priorities are adjusted accord- ing to the solution of a linear program, and are used for • we identify a subclass of dominant matchings called tie-breaking purposes. Our main idea is to use an in- strongly dominant matchings and show a linear time finitesimally small step size for incrementing the priori- algorithm to decide if a strongly dominant matching ties. Our analysis involves solving an infinite-dimensional exists or not; factor-revealing linear program. We also show that the ra- • we show an efficient algorithm to compute a popular tio 1+1/e is an upper bound for the integrality gap, which matching of minimum cost in a graph with edge costs matches the known lower bound. and bounded treewidth. Chi-Kit Lam, C. Gregory Plaxton University of Texas at Austin Yuri Faenza [email protected], [email protected] Ecole Polytechnique Federale de Lausanne [email protected] CP46 Telikepalli Kavitha Tight Competitive Ratios of Classic Matching Al- DA19 Abstracts 59

gorithms in the Fully Online Model [email protected]

Huang et al. (STOC 2018) introduced the fully online Saket Saurabh matching problem, a generalization of the classic online IMSc +UiB bipartite matching problem in that it allows all vertices to [email protected] arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al. (STOC 1990) is strictly better than 0.5-competitive and the problem is Meirav Zehavi strictly harder than the online bipartite matching problem Ben-Gurion University in that no algorithms can be (1 − 1/e)-competitive. This [email protected] paper pins down two tight competitive ratios of classic algo- rithms for the fully online matching problem. For the frac- CP47 tional version of the problem, we show that a√ natural in- stantiation of the water-filling algorithm is 2− 2 ≈ 0.585- Approximating (k,l)-Center Clustering for Curves competitive, together with a matching hardness result. In- terestingly, our hardness result applies to arbitrary algo- The Euclidean k-center problem is a classical problem that rithms in the edge-arrival models of the online matching has been extensively studied in computer science. Given G problem, improving the state-of-art 1 ≈ 0.5906 upper aset of n points in Euclidean space, the problem is to 1+ln 2 C G bound. For integral algorithms, we show a tight competi- determine a set of k centers (not necessarily part of ) ≈ such that the maximum distance between a point in G and tive ratio of 0.567 for the ranking algorithm on bipartite C graphs, matching a hardness result by Huang et al. (STOC its nearest neighbor in is minimized. In this paper we 2018). study the corresponding (k, )-center problem for polyg- onal curves under the Fr´echet distance, that is, given a G Zhiyi Huang set of n polygonal curves, each of complexity m,de- C The University of Hong Kong termine a set of k polygonal curves, each of complexity [email protected] , such that the maximum Fr´echet distance of a curve in G to its closest curve in C is minimized. In their 2016 paper, Driemel, Krivoˇsija, and Sohler give a near-linear Binghui Peng time (1 + ε)-approximation algorithm for one-dimensional Tsinghua University curves, assuming that k and  are constants. In this paper, [email protected] we substantially extend and improve the known approxi- mation bounds for curves in dimension 2 and higher. Our Zhihao Gavin Tang approximation bounds are close to being tight. The University of Hong Kong [email protected] Kevin Buchin TU Eindhoven Runzhou Tao [email protected] Tsinghua University [email protected] Anne Driemel University of Bonn Xiaowei Wu [email protected] City University of Hong Kong [email protected] Joachim Gudmundsson University of Sydney Yuhao Zhang [email protected] The University of Hong Kong [email protected] Michael Horton New York University University of Sydney CP46 [email protected] Popular Matching in Roommates Setting is Np- Hard Irina Kostitsyna Technical University Eindhoven An input to the Popular Matching problem, in the room- [email protected] mates setting, consists of a graph G and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether Maarten Loffler there exists a matching M such that there is no matching Utrecht University M where more people are happier with M than with M . m.loffl[email protected] In this paper we settle the computational complexity of the Popular Matching problem in the roommates setting Martijn Struijs by showing that the problem is NP-complete. Thus, we re- TU Eindhoven solve an open question that has been repeatedly, explicitly [email protected] asked over the last decade.

Pranabendu Misra CP47 UiB Exact Algorithms and Lower Bounds for Stable In- [email protected] stances of Euclidean K-Means

Sushmita Gupta We investigate the complexity of solving stable or University of Bergen perturbation-resilient instances of k-means and k-median 60 DA19 Abstracts

clustering in fixed dimension Euclidean metrics (or more [email protected] generally doubling metrics). The notion of stable or per- turbation resilient instances was introduced by Bilu and Andr´e Nusser Linial [2010] and Awasthi, Blum, and Sheffet [2012]. In our Max Planck Institute for Informatics context, we say a k-means instance is α-stable if there is a Saarland Informatics Campus unique optimum solution which remains unchanged if dis- [email protected] tances are (non-uniformly) stretched by a factor of at most α. Stable clustering instances have been studied to explain why heuristics such as Lloyd’s algorithm perform well in CP47 practice. In this work we show that for any fixed >0, Seth Says: Weak Fr´echet Distance is Faster, But (1 + )-stable instances of k-means in doubling metrics, Only if it is Continuous and in One Dimension which include fixed-dimensional Euclidean metrics, can be solved in polynomial time. We complement this result by We show by reduction from the Orthogonal Vectors prob- showing that under a plausible PCP hypothesis, this is es- lem that algorithms with strongly subquadratic running sentially tight: that when the dimension d is part of the time cannot approximate the Fr´echet distance between input, there is a fixed 0 > 0 such there is not even a PTAS curves better than a factor 3 unless SETH fails. We show d for (1+0)-stable k-means in R unless NP=RP. Given this that similar reductions cannot achieve a lower bound with a hypothesis, we consider “stability-preserving” reductions factor better than 3. Our lower bound holds for the contin- to prove our hardness for stable k-means. Such reductions uous, the discrete, and the weak discrete Fr´echet distance seem to be more fragile and intricate than standard L- even for curves in one dimension. Interestingly, the contin- reductions and may be of further use to demonstrate other uous weak Fr´echet distance behaves differently. Our lower stable optimization problems are hard to solve. bound still holds for curves in two dimensions and higher. However, for curves in one dimension, we provide an exact Zachary Friggstad algorithm to compute the weak Fr´echet distance in linear University of Alberta, Canada time. [email protected] Tim Ophelders Kamyar Khodamoradi, Mohammad Salavatipour Department of Mathematics and Computer Science University of Alberta TU Eindhoven [email protected], [email protected] [email protected]

Kevin Buchin CP47 TU Eindhoven Frchet Distance under Translation: Conditional [email protected] Hardness and an Algorithm via Offline Dynamic Grid Reachability Bettina Speckmann Dept. of Mathematics and Computer Science The discrete Fr´echet distance is a popular measure for TU Eindhoven comparing polygonal curves. An important variant is the [email protected] discrete Fr´echet distance under translation, which enables detection of similar movement patterns in different spa- tial domains. For polygonal curves of length n in the CP47 plane, the fastest known algorithm runs in time O˜(n5) Analysis of Ward’s Method [Ben Avraham, Kaplan, Sharir ’15]. This is achieved by constructing an arrangement of disks of size O(n4), and We study Ward’s method for the hierarchical k-means then traversing its faces while updating reachability in a problem in Rd. This popular greedy heuristic is based 2 directed grid√ graph of size N := O(n ), which can be done on the complete linkage paradigm: Starting with all data in time O˜( N) per update [Diks, Sankowski ’07]. The points as singleton clusters, it successively merges two clus- contribution of this paper is two-fold. First, although it is ters to form a clustering with one cluster less. The pair of an open problem to solve dynamic√ reachability in directed clusters is chosen to (locally) minimize the k-means cost grid graphs faster than O˜( N), we improve this part of of the clustering in the next step. Complete linkage algo- the algorithm: We observe that an offline variant of dy- rithms are very popular for hierarchical clustering prob- namic s-t-reachability in directed grid graphs suffices, and lems, yet their theoretical properties have been studied very little. For the k-center problem, the k-clustering in the we solve this variant in amortized time O˜(N 1/3) per up- O˜ 4.66.. hierarchy computed by complete linkage has a worst-case date, resulting in an improved running time of (n ) approximation ratio of Ω(log k) in general metric spaces, for the discrete Fr´echet distance under translation. Second, and the best known upper bound is O(d) for inputs in R we provide evidence that constructing the arrangement of O 4 with constant d. Complete linkage for k-median/k-means size (n ) is necessary in the worst case, by proving a con- has not been analyzed so far. We show that Ward’s method 4−o(1) ditional lower bound of n on the running time for the computes a 2-approximation if the optimal k-clustering is discrete Fr´echet distance under translation, assuming the well separated. If the optimal clustering additionally satis- Strong Exponential Time Hypothesis. fies a balance condition, then Ward’s method fully recovers the optimum solution. These results hold in arbitrary di- Karl Bringmann mension. We accompany our positive results with a lower Max Planck Institute for Informatics, bound of Ω((3/2)d) for data sets in Rd that holds if no Saarland Informatics Campus, Germany separation is guaranteed, and with lower bounds when the [email protected] guaranteed separation is not sufficiently strong. Finally, we show that Ward produces an O(1)-approximative clus- Marvin K¨unnemann tering when d =1. Max-Planck-Institut f¨ur Informatik, Saarbr¨ucken, Germany Anna Großwendt, Heiko R¨oglin DA19 Abstracts 61

University of Bonn [email protected], [email protected]

Melanie Schmidt TU Dortmund [email protected]

Clemens R¨osner University of Bonn [email protected]