Final Program and Abstracts

The Symposium on Simplicity in Algorithms will take place Wednesday, January 10.

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

The SIAG 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. This activity group provides an opportunity to unify pure discrete mathematics and areas of applied research such as computer science, operations research, combinatorics, and the social sciences. It organizes the SIAM Conference on Discrete Mathematics; co-sponsors, with ACM SIGACT, the annual Symposium on Discrete Algorithms; and sponsors minisymposia at SIAM meetings and conferences. The activity group also publishes an electronic newsletter and maintains a member directory. Every two years, the activity group also awards the Dénes König Prize to a young researcher for outstanding research in the area of discrete mathematics.

Society for Industrial and Applied Mathematics 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: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (USA & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings/da18 www.siam.org/meetings/alenex18 www.siam.org/meetings/analco18 2 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Table of Contents Silvio Lattanzi Andreas Wiese Google Zurich, Switzerland Universidad de Chile, Santiago, Chile Paul Wollan Program-At-A-Glance… Yin Tat Lee University of Washington, USA University of Rome “La Sapienza”, Italy ...... See foldout Andrew McGregor David P. Woodruff General Information...... 2 University of Massachusetts, Amherst, USA Carnegie Mellon University, USA Get-togethers...... 5 Ulrich Meyer Yuichi Yoshida Symposium on Simplicity Goethe University, Frankfurt, Germany National Institute of Informatics, Tokyo, in Algorithms...... 7 Japan Benjamin Moseley Best Paper and Best Student Paper Washington University in St. Louis, USA Steering Committee Awards...... 8 Wolfgang Mulzer Pavol Hell Invited Plenary Presentations...... 9 Freie Universität Berlin, Germany Simon Fraser University, Canada Program Schedule...... 12 Huy Lê Nguyen Daniel Král Abstracts...... 30 Northeastern University, USA University of Warwick, United Kingdom Speaker Index...... 89 Krzysztof Onak Dana Randall Hotel Meeting Room Map.... Back Cover IBM Research, USA Georgia Institute of Technology, USA Gopal Pandurangan Cliff Stein University of Houston, USA Columbia University, USA (chair) SODA COMMITTEES Richard Peng Shang-Hua Teng Georgia Institute of Technology, USA University of Southern California, USA Program Committee Chair Marcin Pilipczuk Artur Czumaj University of Warsaw, Poland University of Warwick, United Kingdom ALENEX COMMITTEES Noga Ron-Zewi Program Committee Co-Chairs Program Committee Ben-Gurion University of the Negev, Israel Natan Rubin Rasmus Pagh Vladimir Braverman Ben Gurion University of the Negev, Israel Johns Hopkins University, USA IT University of Copenhagen, Denmark Aviad Rubinstein Niv Buchbinder University of California, Berkeley and Suresh Venkatasubramanian Tel-Aviv University, Israel Harvard University, USA University of Utah, USA Amin Coja-Oghlan Wojciech Samotij Goethe University, Frankfurt, Germany Tel Aviv University, Israel Program Committee Martin Dietzfelbinger Rahul Shah TU Ilmenau, Germany Louisiana State University, USA Gianlorenzo D’Angelo Ioana Dumitriu Rahul Savani Gran Sasso Science Institute, Italy University of Washington, USA University of Liverpool, United Kingdom Rolf Fagerberg Matthias Englert Asaf Shapira University of Southern Denmark, University of Warwick, United Kingdom Tel-Aviv University, Israel Denmark Kousha Etessami Anastasios Sidiropoulos Sorelle Friedler University of Edinburgh, United Kingdom University of Illinois at Chicago, USA Haverford College, USA Fedor V. Fomin Nike Sun Joachim Giesen University of Bergen, Norway University of California, Berkeley, USA University of Jena, Germany Mohsen Ghaffari Justin Thaler Aristides Gionis ETH Zürich, Switzerland Georgetown University, USA Aalto University, Finland Fabrizio Grandoni Jonathan Ullman Kunihiko Sadakane IDSIA, Switzerland Northeastern University, USA University of Tokyo, Japan Nicole Immorlica Erik Jan van Leeuwen Peter Sanders Microsoft Research New England, USA Utrecht University, The Netherlands Karlsruhe Institute of Technology, Germany Kasper Green Larsen Nisheeth Vishnoi Aarhus University, Denmark EPFL, Switzerland C. Seshadri University of California, Santa Cruz, USA ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 3

Nodari Sitchinava Paweł Hitczenko SIAM Registration Desk University of Hawaii at Manoa, USA Drexel University, USA The SIAM registration desk is located in Sabine Storandt Emma Yu Jin the Ballroom Foyer on the 2nd Floor. It University of Würzburg, Germany Technische Universität Wien, Austria is open during the following hours: Blair Sullivan Michael Mitzenmacher Saturday, January 6 North Carolina State University, USA Harvard University, USA 5:00 PM – 8:00 PM Sergei Vassilvitskii Daniel Panario Google, USA Carleton University, Canada Ke Yi Alfredo Viola Sunday, January 7 Hong Kong University of Science and Universidad de la República, Uruguay 8:00 AM – 5:00 PM Technology, Hong Kong Sebastian Wild University of Kaiserslautern, Germany Monday, January 8 Steering Committee Mark Wilson University of Auckland, New Zealand 8:00 AM – 5:00 PM Ulrik Brandes University of Konstanz, Germany Tuesday, January 9 Andrew V. Goldberg Steering Committee Amazon.com, USA (Chair) 8:00 AM – 5:00 PM Michael Drmota Michael Goodrich Technische Universität Wien, Austria University of California, Irvine, USA Wednesday, January 10 James Allen Fill (Jim Fill) Giuseppe F. Italiano Johns Hopkins University, USA 8:00 AM – 5:00 PM University of Rome “Tor Vergata”, Italy H.K. Hwang Vijaya Ramachandran Institute of Statistical Science, Academia University of Texas, Austin, USA Sinica, Taiwan Hotel Address Cliff Stein Conrado Martínez Astor Crowne Plaza - New Orleans Columbia University, USA Universitat Politècnica de Catalunya, Spain French Quarter Dorothea Wagner Markus Nebel 739 Canal Street at Bourbon Karlsruhe Institute of Technology, Germany Universität Bielefeld, Germany New Orleans, Louisiana 70130 USA Robert Sedgewick Phone Number: +1-504-962-0500 Princeton University, USA ANALCO COMMITTEES Toll Free Reservations (USA and Wojciech Szpankowski Canada): 877-408-9661 Program Committee Co-Chairs Purdue University, USA Reservation Fax: +1-504-962-0503 Mark Daniel Ward Hotel web address: http://www. Markus Nebel Purdue University, USA astorneworleans.com/ Universität Bielefeld, Germany Stephan Wagner Stellenbosch University, South Africa Hotel Telephone Number Program Committee To reach an attendee or leave a message, Child Care call +1-504-962-0500. If the attendee Frédérique Bassino is a hotel guest, the hotel operator can The New Orleans Convention Université Paris Nord, France connect you with the attendee’s room. and Visitors Bureau recommends Clara’s Sitting Service (http://www. Nicolas Broutin clarasittingservice.org/) or Dependable Inria Paris-Rocquencourt, France Hotel Check-in and Kid Care (http://dependablekidcare. Amalia Duch Check-out Times net/) for attendees interested in child Universitat Politècnica de Catalunya, care services. Attendees are responsible Spain Check-in time is 4:00 PM. for making their own child care Michael Fuchs Check-out time is 11:00 AM. arrangements. National Chiao Tung University, Taiwan Clemens Heuberger Alpen-Adria-Universität Klagenfurt, Austria 4 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Corporate Members Sandia National Laboratories SIAM Customer Service: and Affiliates Schlumberger-Doll Research Telephone: +1-215-382-9800 (worldwide); United States Department of Energy or 800-447-7426 (U.S. and Canada only) SIAM corporate members provide U.S. Army Corps of Engineers, Engineer Fax: +1-215-386-7999 their employees with knowledge about, Research and Development Center E-mail: [email protected] access to, and contacts in the applied US Naval Research Labs mathematics and computational sciences Postal mail: Society for Industrial and community through their membership Applied Mathematics, 3600 Market Street, benefits. Corporate membership is more List current November 2017. 6th floor, Philadelphia, PA than just a bundle of tangible products 19104-2688 USA and services; it is an expression of support for SIAM and its programs. Join SIAM and save! SIAM is pleased to acknowledge its Changes to the Printed corporate members and sponsors. Program In recognition of their support, non- Leading the applied The printed program and abstracts were member attendees who are employed by mathematics community . . . current at the time of printing, however, the following organizations are entitled SIAM members save up to $140 on please review the online program schedule to the SIAM member registration rate. full registration for the ACM-SIAM (http://meetings.siam.org/program. Symposium on Discrete Algorithms cfm?CONFCODE=DA18) Corporate/Institutional Members (SODA18) and its associated meetings. for the most up-to-date information. The Aerospace Corporation Join your peers in supporting the Air Force Office of Scientific Research premier professional society for applied Amazon mathematicians and computational Aramco Services Company scientists. SIAM members receive Standard Audio/Visual Bechtel Marine Propulsion Laboratory subscriptions to SIAM Review, SIAM Set-Up in Meeting Rooms The Boeing Company News and SIAM Unwrapped, and enjoy substantial discounts on SIAM books, SIAM does not provide computers for CEA/DAM any speaker. When giving an electronic Department of National Defence (DND/ journal subscriptions, and conference registrations. presentation, speakers must provide their CSEC) own computers. SIAM is not responsible DSTO- Defence Science and for the safety and security of speakers’ Technology Organisation If you are not a SIAM member and did computers. Hewlett-Packard not join SIAM before you registered Huawei FRC French R&D Center for the conference, you can apply the IBM Corporation difference between what you paid as A data (LCD) projector and screen will be IDA Center for Communications a Non-member attendee, and what provided in all technical session meeting Research, La Jolla a member would have paid ($140), rooms. The data projectors support both IDA Center for Communications towards a SIAM membership. Contact VGA and HDMI connections. Presenters Research, Princeton SIAM Customer Service for details or requiring an alternate connection must Institute for Defense Analyses, Center join at the conference registration desk. provide their own adaptor. for Computing Sciences Lawrence Berkeley National Laboratory Lawrence Livermore National Labs If you are a SIAM member, it only costs Internet Access Lockheed Martin $15 to join the SIAM Activity Group on Attendees booked within the SIAM Los Alamos National Laboratory Discrete Mathematics. room block will receive complimentary Max-Planck-Institute for Dynamics of Free Student Memberships are available wireless Internet access in their guest Complex Technical Systems to students who attend an institution that rooms and the public areas of the hotel. Mentor Graphics is an Academic Member of SIAM, are All conference attendees will have National Institute of Standards and members of Student Chapters of SIAM, complimentary wireless Internet access in Technology (NIST) or are nominated by a Regular Member the meeting space of the hotel. National Security Agency (DIRNSA) of SIAM. SIAM will provide a limited number Naval PostGrad of email stations for attendees during Oak Ridge National Laboratory, Join onsite at the registration desk, go to registration hours. managed by UT-Battelle for the www.siam.org/joinsiam to join online or Department of Energy download an application form, or contact ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 5

Registration Fee Includes Sponsors of gender, gender identity or expression, sexual orientation, race, color, national or • ALENEX, ANALCO, SODA, ethnic origin, religion or religious belief, and Symposium on Simplicity in age, marital status, disabilities, veteran Algorithms sessions status, field of expertise, or any other • Business meetings (ALENEX/ reason not related to scientific merit. ANALCO and SODA) This philosophy extends from SIAM • Coffee breaks daily conferences, to its publications, and to its governing structures and bodies. • Continental Breakfast daily We expect all members of SIAM and • Luncheon on Sunday, January 9 participants in SIAM activities to work towards this commitment. • Proceedings for ALENEX, ANALCO and SODA (posted online after meetings conclude) Please Note • Room set-ups and audio/visual SIAM is not responsible for the safety equipment and security of attendees’ computers. Do • Welcome Reception Get-togethers not leave your personal electronic devices Welcome Reception unattended. Please remember to turn off your cell phones and other devices during Job Postings Saturday, January 6 sessions. Please check with the SIAM registration 6:00 PM - 8:00 PM desk regarding the availability of job Astor Ballroom- 2nd Floor postings or visit http://jobs.siam.org. Recording of Presentations ALENEX and ANALCO Audio and video recording of presentations at Table Top Display Business Meeting SIAM meetings is prohibited without the writ- ten permission of the presenter and SIAM. Cambridge University Press Sunday, January 7 6:45 PM – 7:45 PM Social Media Name Badges Toulouse – Mezzanine SIAM is promoting the use of social A space for emergency contact media, such as Facebook and Twitter, information is provided on the back of SODA Business Meeting in order to enhance scientific discussion your name badge. Help us help you in the and Awards Presentation at its meetings and enable attendees event of an emergency! Monday, January 8 to connect with each other prior to, during and after conferences. If you 6:45 PM – 7:45 PM are tweeting about a conference, please Comments? Grand ABC - 2nd Floor use the designated hashtag to enable Comments about SIAM meetings are Complimentary beer and wine will be other attendees to keep up with the encouraged! Please send to: Cynthia served. Twitter conversation and to allow better Phillips, SIAM Vice President for archiving of our conference discussions. Programs ([email protected]). The hashtag for this meeting is The hashtag for SODA is #SIAMDA18. The Statement on Inclusiveness hashtags for ALENEX and ANALCO are As a professional society, SIAM is #ALENEX18 and #ANALCO18. committed to providing an inclusive climate that encourages the open expression and exchange of ideas, that SIAM’s Twitter handle is is free from all forms of discrimination, @TheSIAMNews. harassment, and retaliation, and that is welcoming and comfortable to all members and to those who participate in its activities. In pursuit of that commitment, SIAM is dedicated to the philosophy of equality of opportunity and treatment for all participants regardless 6 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 7

Symposium on Simplicity in Algorithms

Wednesday, January 10 Toulouse – Mezzanine

Visit https://simplicityalgorithms.wixsite.com/sosa for details and schedule. 8 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Best Paper and Best Student Paper Awards

Best Student Paper Award

Optimal Streaming and Tracking Distinct Elements with High Probability Jaroslaw Blasiok, Harvard University, USA

This paper will be presented on Wednesday, January 10 in session CP32 Session 11B. See page 27 for session details.

Best Paper Award

Awarded jointly to two papers

3 Approaching /2 for the s-t-path TSP Vera Traub and Jens Vygen, Universität Bonn, Germany

This paper will be presented on Tuesday, January 9 in session CP25 Session 9A. See page 25 for session details.

Online Bipartite Matching with Amortized O(log 2n) Replacements Aaron Bernstein, Technical University of Berlin, Germany; Jacob Holm, University of Copenhagen, Denmark; Eva Rotenberg, Technical University of Denmark, Denmark

This paper will be presented on Monday, January 8, in session CP13 Session 5A. See page 19 for session details. ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 9

Invited Plenary Speakers

** All Invited Plenary Presentations will take place in Grand ABC - 2nd Floor**

Sunday, January 7 11:30 AM - 12:30 PM IP1 Differential Privacy: A Gateway Concept Cynthia Dwork, Harvard University, USA

Monday, January 8 11:30 AM - 12:30 PM IP2 The Power of Theory in the Practice of Hashing with Focus on Similarity Estimation Mikkel Thorup, University of Copenhagen, Denmark

Tuesday, January 9 11:30 AM - 12:30 PM IP3 Approximation Algorithms for Uncertain Environments Anupam Gupta, Carnegie Mellon University, USA

Wednesday, January 10 11:30 AM - 12:30 PM IP4 Title Not Available at Time of Publication Virginia Vassilevska Williams, Massachusetts Institute of Technology, USA 10 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 11

SIAM Activity Group on Discrete Mathematics (SIAG/DM) www.siam.org/activity/dm A GREAT WAY TO GET INVOLVED! Collaborate and interact with mathematicians and applied scientists whose work involves discrete mathematics.

ACTIVITIES INCLUDE: • Special sessions at SIAM Annual Meetings • Biennial conference on Discrete Mathematics • Co-sponsors the annual ACM-SIAM Symposium on Discrete Algorithms • Dénes König Prize

BENEFITS OF SIAG/DM MEMBERSHIP: • Listing in the SIAG’s online membership directory • Additional $15 discount on registration at SIAM Conference on Discrete Mathematics (excludes student) • Electronic communications from your peers about recent developments in your specialty • Eligibility for candidacy for SIAG/DM office • Participation in the selection of SIAG/DM officers

ELIGIBILITY: • Be a current SIAM member.

COST: • $15 per year • Student members can join two activity groups for free!

2016-17 SIAG/DM OFFICERS • Chair: Sue Whitesides, University of Victoria • Vice-Chair: Dorit Hochbaum, University of California, Berkeley • Program Director: Jeannette Janssen, Dalhousie University • Secretary: Geir Agnarsson, George Mason University

SIAG/DM: my.siam.org/forms/join_siag.htm SIAM: www.siam.org/joinsiam 12 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO Program Schedule ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 13

Saturday, Sunday, January 7 Sunday, January 7 January 6 Registration CP1 8:00 AM-5:00 PM Session 1A Registration Room:Grand Ballroom Foyer - 2nd Floor 9:00 AM-11:05 AM 5:00 PM-8:00 PM Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom Foyer - 2nd Floor Chair: Fabrizio Grandoni, IDSIA, Switzerland Continental Breakfast 9:00-9:20 Dynamic Algorithms for 8:30 AM Graph Coloring Welcome Reception Room:Grand Gallery - 2nd Floor Sayan Bhattacharya, University of Warwick, 6:00 PM-8:00 PM United Kingdom; Deeparnab Chakrabarty, Dartmouth College, USA; Monika Room:Astor Ballroom - 2nd Floor Henzinger, University of Vienna, Austria; Danupon Nanongkai, KTH Royal Institute of Technology, Sweden ALENEX: Session 1 9:25-9:45 Incremental Topological Sort and Cycle Detection in Õ(m√n) 9:00 AM-10:40 AM Expected Total Time Room:Toulouse - Mezzanine Shiri Chechik, Tel Aviv University, Israel; Aaron Bernstein, Technical University Chair: Rasmus Pagh, IT University of Berlin, Germany Copenhagen, Denmark 9:50-10:10 Dynamic Bridge-Finding in 9:00-9:20 Hybrid Indexing Revisited Õ (log2n) Amortized Time Hector Ferrada, Dominik Kempa, and Jacob Holm, University of Copenhagen, Simon Puglisi, University of Helsinki, Denmark; Eva Rotenberg, Technical Finland University of Denmark, Denmark; Mikkel 9:25-9:45 Simple, Fast and Lightweight Thorup, University of Copenhagen, Parallel Wavelet Tree Construction Denmark Johannes Fischer, Florian Kurpicz, and 10:15-10:35 Incremental DFS Marvin Löbel, Technische Universität Algorithms: a Theoretical and Dortmund, Germany Experimental Study 9:50-10:10 Computing Top-k Surender Baswana and Ayush Goel, Indian Closeness Centrality in Fully-Dynamic Institute of Technology, Kanpur, India; Graphs Shahbaz Khan, University of Vienna, Patrick Bisenius, ; Elisabetta Bergamini, Austria Eugenio Angriman, and Henning 10:40-11:00 Decremental Transitive Meyerhenke, Karlsruhe Institute of Closure and Shortest Paths for Planar Technology, Germany Digraphs and Beyond 10:15-10:35 Adaptive Cuckoo Filters Adam Karczmarz, University of Warsaw, Michael Mitzenmacher, Harvard University, Poland USA; Salvatore Pontarelli, Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT), Italy; Pedro Reviriego, Universidad Antonio de Nebrija, Spain 14 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Sunday, January 7 Sunday, January 7 Sunday, January 7 CP2 CP3 IP1 Session 1B Session 1C Differential Privacy: A 9:00 AM-11:05 AM 9:00 AM-11:05 AM Gateway Concept Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor 11:30 AM-12:30 PM Chair: Rahul Shah, Louisiana State Chair: Richard Peng, Georgia Institute of Room:Grand Ballroom ABC - 2nd Floor University, USA Technology, USA Chair: Artur Czumaj, University of Warwick, 9:00-9:20 Polycubes with Small 9:00-9:20 Race Detection and United Kingdom Perimeter Defect Reachability in Nearly Series-Parallel Differential privacy is a definition of Gill Barequet, Technion Israel Institute of Dags privacy tailored to statistical analysis Technology, Israel; Andrei Asinowski, Jeremy Fineman, Georgetown University, Vienna University of Technology, Austria; USA; Kunal Agrawal, Washington of very large large datasets. Invented Yufei Zheng, Technion Israel Institute of University in St. Louis, USA; Joseph just over one decade ago, the notion has Technology, Israel Devietti, University of Pennsylvania, become widely (if not deeply) deployed, USA; I-Ting Angelina Lee, Robert and yet much remains to be done. The 9:25-9:45 A Grid-Based Approximation Utterback, and Changming Xu, Algorithm for the Minimum Weight theoretical investigation of privacy/ Triangulation Problem Washington University in St. Louis, USA accuracy tradeoffs that shaped the field Sharath Raghvendra and Mariette Wessels, 9:25-9:45 Planar Graphs As by delineating the boundary between Virginia Tech, USA L-Intersection Or L-Contact Graphs possible and impossible motivate the continued search for new algorithmic 9:50-10:10 Tightening Curves on Daniel Goncalves, Lucas Isenmann, Surfaces Via Local Moves and Claire Pennarun, Université de techniques, as well as still meaningful Hsien-Chih Chang and Jeff Erickson, Montpellier, France relaxations of the basic definition. Differential privacy has also led to new University of Illinois at Urbana- 9:50-10:10 The Complexity of approaches in other fields, most notably Champaign, USA; David Letscher, Independent Set Reconfiguration on Saint Louis University, USA; Arnaud Bipartite Graphs in algorithmic fairness and adaptive data de Mesmay, Université Grenoble Alpes, analysis, in which the questions being France; Saul Schleimer, University of Daniel Lokshtanov and Amer Mouawad, asked of the data depend on the data Warwick, United Kingdom; Eric Sedgwick, University of Bergen, Norway themselves. We will highlight some DePaul University, USA; Dylan Thurston, 10:15-10:35 Metric Violation Distance: recent algorithmic and definitional work, Indiana University, USA; Stephan Hardness and Approximation and focus on differential privacy as a Tillmann, University of Sydney, Australia Chenglin Fan, Benjamin A. Raichel, and gateway concept to these new areas of 10:15-10:35 A Near-Quadratic Lower Gregory Van Buskirk, University of Texas study. Bound for the Size of Quantum Circuits at Dallas, USA of Constant Treewidth 10:40-11:00 A Submodular Measure Cynthia Dwork Mateus De Oliveira Oliveira, University of and Approximate Gomory-Hu Harvard University, USA Bergen, Norway Theorem for Packing Odd Trails 10:40-11:00 The Classical Complexity Bojan Mohar, Simon Fraser University, of Boson Sampling Canada; Ross Churchley, Simon Fraser Raphael Clifford, University of Bristol, University, Canada United Kingdom; Peter Clifford, University Luncheon **Ticketed Event** of Oxford, United Kingdom Coffee Break 12:30 PM-2:00 PM 11:05 AM-11:30 AM Room:Astor Ballroom - 2nd Floor Room:Grand Gallery - 2nd Floor Please visit the SIAM Registration Desk if you did not receive a ticket with your registration materials. ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 15

Sunday, January 7 Sunday, January 7 Sunday, January 7 ALENEX: Session 2 CP4 CP5 2:00 PM-3:40 PM Session 2A Session 2B Room:Toulouse - Mezzanine 2:00 PM-4:05 PM 2:00 PM-4:05 PM Chair: Rolf Fagerberg, University of Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Southern Denmark, Denmark Chair: Erik Jan van Leeuwen, Utrecht Chair: Richard Peng, Georgia Institute of 2:00-2:20 Practical Minimum Cut University, The Netherlands Technology, USA Algorithms Monika Henzinger and Alexander Noe, 2:00-2:20 Minor-Matching Hypertree 2:00-2:20 Stochastic Packing Integer University of Vienna, Austria; Christian Width Programs with Few Queries Schulz, University of Vienna, Austria Nikola G. Yolov, University of Oxford, United Takanori Maehara, RIKEN Center for and Karlsruhe Institute of Technology, Kingdom Advanced Intelligence Project, Japan; Yutaro Yamaguchi, Osaka University, Japan Germany; Darren Strash, Colgate 2:25-2:45 A Polynomial Excluded- University, USA Minor Approximation of Treedepth 2:25-2:45 Algorithms to Approximate 2:25-2:45 Faster Approximation Ken-ichi Kawarabayashi, National Institute Column-Sparse Packing Problems Algorithm for the k-Regret Minimizing of Informatics, Japan; Benjamin Rossman, Brian Brubach and Karthik Abinav Set and Related Problems University of Toronto, Canada Sankararaman, University of Maryland, College Park, USA; Aravind Srinivasan, Nirman Kumar, University of Memphis, 2:50-3:10 Beating Brute Force for University of Maryland, USA; Pan Xu, USA; Stavros Sintos, Duke University, (Quantified) Satisfiability of Circuits of University of Maryland, College Park, USA Bounded Treewidth USA 2:50-3:10 A Practical Fpt Algorithm for Daniel Lokshtanov, University of Bergen, Flow Decomposition and Transcript Norway; Ivan Mikhailin and Ramamohan 2:50-3:10 Subquadratic Kernels Assembly Paturi, University of California, San for Implicit 3-Hitting Set and 3-Set Kyle Kloster, North Carolina State Diego, USA; Pavel Pudlak, Institute of Packing Problems University, USA; Philipp Kuinke, RWTH Mathematics of the Academy of Sciences of Tien-Nam Le, École Normale Supérieure Aachen University, Germany; Michael the Czech Republic, Czech Republic de Lyon, France; Daniel Lokshtanov, University of Bergen, Norway; Saket O’Brien and Felix J. Reidl, North Carolina 3:15-3:35 Cliquewidth III: The State University, USA; Fernando Sanchez Odd Case of Graph Coloring Saurabh, Institute of Mathematical Villaamil, RWTH Aachen University, Parameterized by Cliquewidth Sciences, India; Stéphan Thomassé, École Germany; Blair Sullivan and Andrew van Petr Golovach and Daniel Lokshtanov, Normale Supérieure de Lyon, France; Der Poel, North Carolina State University, University of Bergen, Norway; Saket Meirav Zehavi, University of Bergen, USA Saurabh, Institute of Mathematical Norway 3:15-3:35 Quadratic Time Algorithms Sciences, India; Meirav Zehavi, Ben- 3:15-3:35 Near Optimal Jointly Appear to Be Optimal for Sorting Gurion University, Israel Private Packing Algorithm Via Dual Evolving Data 3:40-4:00 Recognizing Weak Multiplicative Weight Update William Devanny, Juan Jose Besa Vial, Embeddings of Graphs Xue Zhu and Zhiyi Huang, University of David Eppstein, Michael Goodrich, and Hugo A. Akitaya, Tufts University, USA; Hong Kong, Hong Kong Timothy Johnson, University of California, Radoslav Fulek, Institute of Science 3:40-4:00 Randomized MWU for Irvine, USA and Technology Austria, Austria; Csaba Positive LPs D. Tóth, California State University, Chandra Chekuri and Kent Quanrud, Northridge, USA University of Illinois at Urbana- Champaign, USA 16 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Sunday, January 7 Sunday, January 7 Sunday, January 7 CP6 ALENEX: Session 3 CP7 Session 2C 4:30 PM-6:10 PM Session 3A 2:00 PM-4:05 PM Room:Toulouse - Mezzanine 4:30 PM-6:35 PM Room:St. Charles - 1st Floor Chair: Suresh Venkatasubramanian, Room:Grand Ballroom ABC - 2nd Floor University of Utah, USA Chair: Andreas Wiese, Universidad de Chile, Chair: Erik Jan van Leeuwen, Utrecht 4:30-4:50 Computing Floods Caused Chile University, The Netherlands by Non-Uniform Sea-Level Rise 2:00-2:20 Hierarchical Clustering: Lars Arge, Yujin Shin, and Constantinos 4:30-4:50 A Faster Algorithm for Objective Functions and Algorithms Tsirogiannis, Aarhus University, Denmark Minimum-Cost Bipartite Perfect Vincent Cohen-Addad, CNRS and Université Matching in Planar Graphs Pierre et Marie Curie, France; Varun 4:55-5:15 Grid Peeling and the Affine Mudabir Kabir Asathulla, Virginia Tech, Kanade, University of Oxford, United Curve-Shortening Flow USA; Sanjeev Khanna, University of David Eppstein, University of California, Kingdom; Claire Mathieu, CNRS - Ecole Pennsylvania, USA; Nathaniel Lahn and Irvine, USA; Sariel Har-Peled, University Normale Superieure, France; Frederik Sharath Raghvendra, Virginia Tech, USA of Illinois at Urbana-Champaign, USA; Mallmann-Trenn, Massachusetts Institute of Gabriel Nivasch, Ariel University, Israel 4:55-5:15 Minimum Cut of Directed Technology, USA Planar Graphs in Õ(nlog log n) Time 2:25-2:45 Approximation Schemes for 5:20-5:40 Area-Preserving Subdivision Shay Mozes, Interdisciplinary Center Clustering with Outliers Simplification With Topology Herzliya, Israel; Cyril Nikolaev, University Constraints: Exactly And In Practice of Haifa, Israel; Yahav Nussbaum, Tel Zachary Friggstad, Kamyar Khodamoradi, Thomas Mendel, Universität Stuttgart, Aviv University, Israel; Oren Weimann, Mohsen Rezapour, and Mohammad Germany University of Haifa, Israel Salavatipour, University of Alberta, Canada 5:45-6:05 A Geometric Heuristic for 5:20-5:40 Voronoi Diagrams on Planar 2:50-3:10 Adaptive Hierarchical Rectilinear Crossing Minimization Graphs, and Computing the Diameter Clustering Using Ordinal Queries Marcel Radermacher, Karlsruhe Institute of in Deterministic Õ(n5/3) Time Ehsan Emamjomeh-Zadeh and David Kempe, Technology, Germany; Klara Reichard, Pawel Gawrychowski, University of University of Southern California, USA University of Tuebingen, Germany; Wroclaw, Poland; Haim Kaplan, Tel 3:15-3:35 A Fast Approximation Ignaz Rutter, Technische Universiteit Aviv University, Israel; Shay Mozes, Scheme for Low-Dimensional k-Means Eindhoven, The Netherlands; Dorothea Interdisciplinary Center Herzliya, Israel; Vincent Cohen-Addad, CNRS and Université Wagner, Karlsruhe Institute of Technology, Micha Sharir, Tel Aviv University, Israel, Pierre et Marie Curie, France Germany and New York University, USA; Oren Weimann, University of Haifa, Israel 3:40-4:00 The Bane of Low- Dimensionality Clustering 5:45-6:05 Better Tradeoffs for Exact Vincent Cohen-Addad, CNRS and Université Distance Oracles in Planar Graphs Pierre et Marie Curie, France; Arnaud de Pawel Gawrychowski, University of Wroclaw, Mesmay, CNRS and Grenoble University, Poland; Shay Mozes, Interdisciplinary France; Eva Rotenberg, Technical Center Herzliya, Israel; Oren Weimann, University of Denmark, Denmark; Alan University of Haifa, Israel; Christian Roytman, University of Copenhagen, Wulff-Nilsen, University of Copenhagen, Denmark Denmark 6:10-6:30 Near-Optimal Compression for the Planar Graph Metric Coffee Break Amir Abboud, IBM Research, USA; Pawel Gawrychowski, University of Wroclaw, 4:05 PM-4:30 PM Poland; Shay Mozes, Interdisciplinary Center Herzliya, Israel; Oren Weimann, Room:Grand Gallery - 2nd Floor University of Haifa, Israel ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 17

Sunday, January 7 Sunday, January 7 Monday, CP8 CP9 January 8 Session 3B Session 3C 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Registration Chair: Martin Dietzfelbinger, Technische Chair: Vladimir Braverman, Johns Hopkins 8:00 AM-5:00 PM Universität Ilmenau, Germany University, USA Room:Grand Ballroom Foyer - 2nd Floor 4:30-4:50 Time and Space Efficient 4:30-4:50 Coding Against Deletions in Representations of Distributive Lattices Oblivious and Online Models Corwin Sinnamon, University of Waterloo, Venkatesan Guruswami, Carnegie Mellon Canada University, USA; Ray Li, Stanford Continental Breakfast University, USA 4:55-5:15 A Hamilton Path for the 8:30 AM Sigma-Tau Problem 4:55-5:15 Average-Radius List- Room:Grand Gallery - 2nd Floor Joe Sawada, University of Guelph, Canada; Recoverability of Random Linear Aaron Williams, Bard College at Simon’s Codes Rock, USA Atri Rudra, University of Buffalo, SUNY, USA; Mary Wootters, Stanford University, 5:20-5:40 Discrete Choice, USA Permutations, and Reconstruction ALENEX: Session 4 Flavio Chierichetti, Universita di Roma “La 5:20-5:40 Approximate Local 9:00 AM-10:40 AM Sapienza,” Italy; Ravi Kumar and Andrew Decoding of Cubic Reed-Muller Tomkins, Google, Inc., USA Codes Beyond the List Decoding Room:Toulouse - Mezzanine Radius 5:45-6:05 Consistent Hashing with Chair: Blair D. Sullivan, Oak Ridge National Pooya Hatami, University of Texas at Bounded Loads Laboratory, USA Austin, USA; Madhur Tulsiani, Toyota Vahab Mirrokni, Google, Inc., USA; Mikkel Technological Institute at Chicago, USA 9:00-9:20 A Generic Framework for Thorup, University of Copenhagen, Engineering Graph Canonization 5:45-6:05 Syndrome Decoding of Algorithms Denmark; Morteza Zadimoghaddam, Reed-Muller Codes and Tensor Google, Inc., USA Jakob L. Andersen, University of Vienna, Decomposition over Finite Fields Austria; Daniel Merkle, University of 6:10-6:30 Nearly Tight Bounds for Aditya Potukuchi and Swastik Kopparty, Southern Denmark, Denmark Sandpile Transience on the Grid Rutgers University, USA David Durfee, Matthew Fahrbach, and Yu 9:25-9:45 Linear Time Canonicalization 6:10-6:30 The Gotsman-Linial and Enumeration of Non-Isomorphic Gao, Georgia Institute of Technology, Conjecture is False USA; Tao Xiao, Shanghai Jiao Tong 1-Face Embeddings Brynmor Chapman, Massachusetts Institute Marc Hellmuth, University of Greifswald, University, China of Technology, USA Germany; Anders S. Knudsen, University of Southern Denmark, Denmark; Michal Kotrbcik, University of Queensland, Australia; Daniel Merkle and Nikolai Nøjgaard, University of Southern ALENEX and ANALCO Denmark, Denmark Business Meeting 9:50-10:10 Computing 2-Connected 6:45 PM-7:45 PM Components and Maximal 2-Connected Subgraphs in Directed Room:Toulouse - Mezzanine Graphs: An Experimental Study Aikaterini Karanasiou, Universita di Roma “Tor Vergata”, Italy; Loukas Georgiadis, University of Ioannina, Greece; Giuseppe Italiano, Nikos Parotsidis, and Nilakantha Paudel, Universita di Roma “Tor Vergata”, Italy 10:15-10:35 Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs Petteri Kaski, Aalto University, Finland 18 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Monday, January 8 Monday, January 8 Monday, January 8 CP10 CP11 CP12 Session 4A Session 4B Session 4C 9:00 AM-11:05 AM 9:00 AM-11:05 AM 9:00 AM-11:05 AM Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Silvio Lattanzi, Google Zurich, Chair: Vladimir Braverman, Johns Hopkins Chair: Martin Dietzfelbinger, Technische Switzerland University, USA Universität Ilmenau, Germany 9:00-9:20 Prophet Secretary for 9:00-9:20 Lifting Linear Extension 9:00-9:20 The Entropy of Backwards Combinatorial Auctions and Matroids Complexity Bounds to the Mixed- Analysis Soheil Ehsani, University of Maryland, Integer Setting Mathias Knudsen and Mikkel Thorup, College Park, USA; MohammadTaghi Alfonso Cevallos, Stefan Weltge, and Rico University of Copenhagen, Denmark Hajiaghayi, University of Maryland, Zenklusen, ETH Zürich, Switzerland 9:25-9:45 More Logarithmic-Factor USA; Thomas Kesselheim, Technische 9:25-9:45 Proximity Results and Faster Speedups for 3SUM, (median,+)- Universität Dortmund, Germany; Sahil Algorithms for Integer Programming Convolution, and Some Geometric Singla, Carnegie Mellon University, USA Using the Steinitz Lemma 3SUM-Hard Problems 9:25-9:45 Strong Algorithms for the Friedrich Eisenbrand, École Polytechnique Timothy M. Chan, University of Illinois at Ordinal Matroid Secretary Problem Fédérale de Lausanne, Switzerland; Robert Urbana-Champaign, USA Jose A. Soto and Abner Turkieltaub, Weismantel, ETH Zürich, Switzerland 9:50-10:10 On the Complexity of Range Universidad de Chile, Chile; Victor 9:50-10:10 Approximating Weighted Searching Among Curves Verdugo, Universidad de Chile, Chile and Tree Augmentation Via Chvátal- Peyman Afshani, Aarhus University, Denmark; École Normale Supérieure, France Gomory Cuts Anne Driemel, Technische Universiteit 9:50-10:10 A Framework for the Martin Groß, University of Waterloo, Eindhoven, The Netherlands Secretary Problem on the Intersection Canada; Samuel Fiorini, Université Libre 10:15-10:35 On Separating Points by of Matroids de Bruxelles, Belgium; Jochen Könemann Lines Moran Feldman, The Open University and Laura Sanità, University of Waterloo, of Israel, Israel; Ola Svensson, École Canada Sariel Har-Peled and Mitchell F. Jones, Polytechnique Fédérale de Lausanne, University of Illinois at Urbana-Champaign, 10:15-10:35 Geometric Rescaling Switzerland; Rico Zenklusen, ETH Zürich, USA Algorithms for Submodular Function Switzerland Minimization 10:40-11:00 Voronoi Tessellations in the 10:15-10:35 Truthful Multi-Parameter Daniel Dadush, Centrum Wiskunde & Crt and Continuum Random Maps of Auctions with Online Supply: An Informatica, Netherlands; Laszlo A. Vegh Finite Excess Impossible Combination and Giacomo Zambelli, London School of Louigi Addario-Berry, McGill University, Vasilis Syrgkanis and Nikhil R. Economics, United Kingdom Canada; Omer Angel, University of British Devanur, Microsoft Research, USA; Columbia, Canada; Guillaume Chapuy, 10:40-11:00 Submodular Minimization Université Paris-Diderot, France; Christina Balasubramanian Sivan, Google Research, Under Congruency Constraints USA Goldschmidt, University of Oxford, United Martin Nägele, Benny Sudakov, and Rico Kingdom; Éric Fusy, Ecole Polytechnique, 10:40-11:00 Variance Reduced Value Zenklusen, ETH Zürich, Switzerland France Iteration and Faster Algorithms for Solving Markov Decision Processes Xian Wu and Aaron Sidford, Stanford University, USA; Mengdi Wang, Princeton Coffee Break University, USA; Yinyu Ye, Stanford University, USA 11:05 AM-11:30 AM Room:Grand Gallery - 2nd Floor ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 19

Monday, January 8 Monday, January 8 Monday, January 8 IP2 Lunch Break CP13 The Power of Theory in the 12:30 PM-2:00 PM Session 5A Practice of Hashing with Attendees on their own 2:00 PM-4:05 PM Focus on Similarity Estimation Room:Grand Ballroom ABC - 2nd Floor 11:30 AM-12:30 PM Chair: Andreas Wiese, Universidad de Chile, Room:Grand Ballroom ABC - 2nd Floor ALENEX: Session 5 Chile Chair: Martin Dietzfelbinger, Technische 2:00 PM-3:15 PM 2:00-2:20 Online Bipartite Matching 2 Universität Ilmenau, Germany Room:Toulouse - Mezzanine with Amortized O(log N) Replacements Hash functions have become ubiquitous Chair: Petteri Kaski, Aalto University, Aaron Bernstein, Technical University Berlin, tools in modern data analysis, e.g., Finland Germany; Jacob Holm, University of the construction of small randomized 2:00-2:20 Hyperbolic Embeddings for Copenhagen, Denmark; Eva Rotenberg, sketches of large data streams. We like Near-Optimal Greedy Routing Technical University of Denmark, Denmark to think of abstract hash functions, Thomas Blaesius, Tobias Friedrich, 2:25-2:45 Randomized Online assigning independent uniformly random Maximilian Katzmann, and Anton Krohmer, Matching in Regular Graphs hash values to keys, but in practice, we Hasso Plattner Institute, Germnay David Wajc, Carnegie Mellon University, have to choose a hash function that only 2:25-2:45 Scaling Up Group Closeness USA; Ilan R. Cohen, Hebrew University of has an element of randomness, e.g., Maximization Jerusalem, Israel 2-independence. While this works for Elisabetta Bergamini and Tanya Gonser, 2:50-3:10 Randomized Algorithms for sufficiently random input, the real world Karlsruhe Institute of Technology, Online Vector Load Balancing has structured data where such simple Germany; Henning Meyerhenke, University Yossi Azar, Tel Aviv University, Israel; Ilan hash functions fail, calling for the need of Cologne, Germany R. Cohen, Hebrew University of Jerusalem, of more powerful hash functions. In this 2:50-3:10 Scalable Kernelization for Israel; Debmalya Panigrahi, Duke talk, we focus hashing for set similarity, Maximum Independent Sets University, USA which is an integral component in the Darren Strash, Colgate University, USA; analysis of Big Data. The basic idea 3:15-3:35 Competitive Algorithms Demian Hespe and Christian Schulz, is to use the same hash function to do for Generalized k-Server in Uniform Karlsruhe Institute of Technology, Germany Metrics coordinated sampling from different Nikhil Bansal, Eindhoven University of sets. Depending on the context, we want Technology, Netherlands; Marek Elias, subsets sampled without replacement, or Grigorios Koumoutsos, and Jesper Nederlof, fixed-length vectors of samples that may Technische Universiteit Eindhoven, The be with replacement. The latter is used as Netherlands input to support vector machines (SVMs) 3:40-4:00 Online Facility Location and locality sensitive hashing (LSH). Against a t-Bounded Adversary The most efficient constructions require Harry Lang, Johns Hopkins University, USA very powerful hash functions that are also needed for efficient size estimation. We discuss the interplay between the hash functions and the algorithms using them. Finally, we present experiments on both real and synthetic data where standard 2-independent hashing yield systematically poor similarity estimates, while the right theoretical choice is sharply concentrated, and faster than standard cryptographic hash functions with no proven guarantees. Mikkel Thorup University of Copenhagen, Denmark 20 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Monday, January 8 Monday, January 8 Monday, January 8 CP14 CP15 ANALCO: Session 1 Session 5B Session 5C 4:30 PM-6:35 PM 2:00 PM-4:05 PM 2:00 PM-4:05 PM Room:Toulouse - Mezzanine Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Markus Nebel, Universität Bielefeld, Germany Chair: Richard Peng, Georgia Institute of Chair: Artur Czumaj, University of Warwick, Technology, USA United Kingdom 4:30-4:50 Probabilistic Analysis of the Dual-Pivot Quicksort “Count” 2:00-2:20 Approximating the Largest 2:00-2:20 Frechet-Stable Signatures Ralph Neininger and Jasmin Straub, J.W. Root and Applications to Interlacing Using Persistence Homology Goethe-Universität, Germany Families Donald Sheehy, University of Connecticut, Nima Anari, Stanford University, USA; USA 4:55-5:15 Quicksort Is Optimal For Shayan Oveis Gharan, University of Many Equal Keys 2:25-2:45 On the Decidability of the Washington, USA; Amin Saberi, Stanford Sebastian Wild, University of Waterloo, Frechet Distance Between Surfaces University, USA; Nikhil Srivastava, Canada Amir Nayyeri, Oregon State University, USA University of California, Berkeley, USA 5:20-5:40 On Deletions in Open 2:50-3:10 On the Complexity of 2:25-2:45 Improved Rectangular Addressing Hashing Optimal Homotopies Matrix Multiplication Using Powers of Conrado Martínez, Universidad Politecnica Erin Chambers, Saint Louis University, USA; the Coppersmith-Winograd Tensor de Catalunya, Spain; Rosa Jiménez, Arnaud de Mesmay, CNRS and Grenoble François Le Gall, Kyoto University, Japan; Universitat Politècnica de Catalunya, University, France; Tim Ophelders, Spain Florent Urrutia, Université Paris-Diderot, Technische Universiteit Eindhoven, The France Netherlands 5:45-6:05 Parameterizing the 2:50-3:10 A Fast Generalized DFT for Hardness of Binary Search Tree 3:15-3:35 Computing Simplicial Finite Groups of Lie Type Access Sequences by Inversion Representatives of Homotopy Group Chris Umans, California Institute of Counts Elements Meng He, Dalhousie University, Canada; Technology, USA; Chloe Hsu, California Peter Franek, Institute of Science and Institute of Technology, USA Richard Peng, Georgia Institute Technology Austria, Austria; Marek of Technology, USA; Yinzhan Xu, 3:15-3:35 A Two-Pronged Progress Filakovsky, Masaryk University, Czech Massachusetts Institute of Technology, in Structured Dense Matrix Vector Republic; Uli Wagner and Stephan USA Multiplication Zhechev, Institute of Science and Christopher De Sa, Cornell University, Technology Austria, Austria 6:10-6:30 The Complexity of the USA; Albert Gu, Stanford University, Multiple Pattern Matching Problem for 3:40-4:00 Persistent Path Homology of USA; Rohan Puttagunta, Instagram, USA; Random Strings Directed Networks Christopher Re, Stanford University, USA; Andrea Sportiello, Université de Paris Nord, Samir Chowdhury and Facundo Memoli, Ohio France; Frederique Bassino and Tsinjo Atri Rudra, University of Buffalo, SUNY, State University, USA USA Rakotoarimalala, Universite Paris-Nord, France 3:40-4:00 A Tight Lower Bound for Counting Hamiltonian Cycles Via Matrix Rank Coffee Break Radu Curticapean, Hungarian Academy 4:05 PM-4:30 PM of Sciences, Hungary; Nathan Lindzey, University of Waterloo, Canada; Jesper Room:Grand Gallery - 2nd Floor Nederlof, Technische Universiteit Eindhoven, The Netherlands ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 21

Monday, January 8 Monday, January 8 Monday, January 8 CP16 CP17 CP18 Session 6A Session 6B Session 6C 4:30 PM-6:35 PM 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Fabrizio Grandoni, IDSIA, Chair: Benjamin Moseley, Washington Chair: Gopal Pandurangan, University of Switzerland University in St. Louis, USA Houston, USA 4:30-4:50 Approximating Edit 4:30-4:50 Nested Convex Bodies Are 4:30-4:50 Embeddability in R3 is Distance in Truly Subquadratic Time: Chaseable NP-hard Quantum and MapReduce Nikhil Bansal, Eindhoven University of Arnaud de Mesmay, CNRS and Grenoble Mahdi Boroujeni, Sharif University Technology, Netherlands; Martin Bohm, University, France; Yo’av Rieck, University of Technology, Iran; Soheil Ehsani, Charles University, Czech Republic; Marek of Arkansas, USA; Eric Sedgwick, DePaul University of Maryland, USA; Mohammad Elias, Grigorios Koumoutsos, and Seeun W. University, USA; Martin Tancer, Charles Ghodsi, Sharif University of Technology, Umboh, Technische Universiteit Eindhoven, University in Prague, Czech Republic Iran; MohammadTaghi Hajiaghayi and The Netherlands 4:55-5:15 Fast, Deterministic and Sparse Saeed Seddighin, University of Maryland, 4:55-5:15 Scheduling When You Don’t Dimensionality Reduction College Park, USA Know the Number of Machines Daniel Dadush, Centrum Wiskunde & 4:55-5:15 Tree Edit Distance Cannot Clifford Stein and Mingxian Zhong, Columbia Informatica, Netherlands Be Computed in Strongly Subcubic University, USA 5:20-5:40 Impossibility of Dimension Time (unless Apsp Can) 5:20-5:40 Stochastic Load Balancing Reduction in the Nuclear Norm Karl Bringmann, Max Planck Institute on Unrelated Machines Assaf Naor, Princeton University, USA; Gilles for Informatics, Germany; Pawel Xiangkun Shen, University of Michigan, Pisier, Texas A&M University, USA; Gideon Gawrychowski, University of Wroclaw, USA; Anupam Gupta, Carnegie Mellon Schechtman, Weizmann Institute of Science, Poland; Shay Mozes, Interdisciplinary University, USA; Amit Kumar, Indian Israel Center Herzliya, Israel; Oren Weimann, Institute of Technology, Delhi, India; University of Haifa, Israel 5:45-6:05 Steiner Point Removal --- Viswanath Nagarajan, University of Distant Terminals Don’t (Really) Bother 5:20-5:40 On the Difference Michigan, USA Yun Kuen Cheung, Max Planck Institute for Between Closest, Furthest, and 5:45-6:05 Boolean Function Analysis Informatics, Germany Orthogonal Pairs: Nearly-Linear Vs Meets Stochastic Optimization: An Barely-Subquadratic Complexity in 6:10-6:30 Steiner Point Removal with Approximation Scheme for Stochastic Computational Geometry Distortion O(log K) Knapsack Ryan Williams, Massachusetts Institute of Arnold Filtser, Ben Gurion University Negev, Anindya De, Northwestern University, USA Technology, USA Israel 6:10-6:30 An Alon-Boppana 5:45-6:05 Multivariate Fine-Grained Type Bound for Weighted Graphs Complexity of Longest Common and Lowerbounds for Spectral Subsequence Sparsification SODA Business Meeting and Karl Bringmann and Marvin Künnemann, Luca Trevisan and Nikhil Srivastava, Max Planck Institute for Informatics, Awards Presentation University of California, Berkeley, USA Germany 6:45 PM-7:45 PM 6:10-6:30 Tight Hardness for Shortest Cycles and Paths in Sparse Graphs Room:Grand Ballroom ABC- 2nd Floor Andrea Lincoln, Virginia Vassilevska Williams, and Ryan Williams, Complimentary beer and wine will be served. Massachusetts Institute of Technology, USA 22 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Tuesday, January 9 Tuesday, January 9 Tuesday, January 9 ANALCO: Session 2 CP19 9:00 AM-11:05 AM Session 7A Registration Room:Toulouse - Mezzanine 9:00 AM-11:05 AM 8:00 AM-5:00 PM Chair: Sebastian Wild, University of Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom Foyer - 2nd Floor Waterloo, Canada Chair: Andreas Wiese, Universidad de Chile, 9:00-9:20 Trace Reconstruction with Chile Varying Deletion Probabilities Nina Holden, Massachusetts Institute of 9:00-9:20 Approximating Cycles in Continental Breakfast Technology, USA; Lisa Hartung, Courant Directed Graphs 8:30 AM Institute of Mathematical Sciences, New Jakub Pachocki, OpenAI, USA; Liam York University, USA; Yuval Peres, Roditty, Bar-Ilan University, Israel; Aaron Room:Grand Gallery - 2nd Floor Microsoft Research, USA Sidford, Stanford University, USA; Roe Tov, Bar-Ilan University, Israel; Virginia 9:25-9:45 Theoretical Analysis of Vassilevska Williams, Massachusetts Beaconless Geocast Protocols in 1D Institute of Technology, USA Joachim Gudmundsson, University of Sydney, Australia; Irina Kostitsyna, 9:25-9:45 A Tight √2-Approximation for Technische Universiteit Eindhoven, The Linear 3-Cut Netherlands; Maarten Löffler, Utrecht Vivek Madan, University of Illinois at University, The Netherlands; Tobias Urbana-Champaign, USA; Kristof Berczi, Müller, University of Groningen, The Eötvös Loránd University, Hungary; Netherlands; Vera Sacristán and Rodrigo Karthekeyan Chandrasekaran, University of Silveira, Universitat Politecnica de Illinois at Urbana-Champaign, USA; Tamas Catalunya, Spain Kiraly, Eötvös Loránd University, Hungary 9:50-10:10 Efficiently Inferring 9:50-10:10 Near-Optimal Pairwise Subtree Prune-and-Regraft Approximation Algorithm for Adjacencies Between Phylogenetic Simultaneous Max-Cut Trees Amey Bhangale, Weizmann Institute of Chris Whidden and Frederick Matsen, Fred Science, Israel; Subhash Khot, New York Hutchinson Cancer Research Center, USA University, USA; Swastik Kopparty, Rutgers University, USA; Sushant 10:15-10:35 Polynomial Tuning of Sachdeva, Google, Inc., USA; Devanathan Multiparametric Combinatorial Thiruvenkatachari, New York University, Samplers USA Maciej Bendkowski, Jagiellonian University, Krakow, Poland; Olivier Bodini, Université 10:15-10:35 Hypergraph k-Cut in Paris 13, France; Sergey Dovgal, Randomized Polynomial Time Université Paris 7, France and Moscow Karthekeyan Chandrasekaran, Chao Xu, and Institute of Physics and Technology, Russia Xilin Yu, University of Illinois at Urbana- Champaign, USA 10:40-11:00 Analyzing Boltzmann Samplers for Bose-Einstein 10:40-11:00 A Near-Linear Condensates with Dirichlet Approximation Scheme for Multicuts Generating Functions of Embedded Graphs with a Fixed Matthew Fahrbach, Megan Bernstein, Number of Terminals and Dana Randall, Georgia Institute of Vincent Cohen-Addad, CNRS and Université Technology, USA Pierre et Marie Curie, France; Éric Colin De Verdière, Université Paris-Est Marne- la-Vallée, France; Arnaud de Mesmay, CNRS and Grenoble University, France ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 23

Tuesday, January 9 Tuesday, January 9 Tuesday, January 9 CP20 CP21 IP3 Session 7B Session 7C Approximation Algorithms for 9:00 AM-11:05 AM 9:00 AM-11:05 AM Uncertain Environments Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor 11:30 AM-12:30 PM Chair: Rahul Shah, Louisiana State Chair: Gopal Pandurangan, University of Room:Grand Ballroom ABC - 2nd Floor University, USA Houston, USA Chair: Gopal Pandurangan, University of 9:00-9:20 Optimal-Time Text Indexing 9:00-9:20 Probabilistic Existence of Houston, USA in BWT-runs Bounded Space Large Sets of Designs The past decade has seen considerable Nicola Prezza, Technical University of Sankeerth Rao Karingula, Shachar Lovett, and work on algorithms in models with Denmark, Denmark; Gonzalo Navarro, Alexander Vardy, University of California, uncertainty: where either the inputs to the University of Chile, Chile; Travis Gagie, San Diego, USA Diego Portales University, Chile algorithm or the algorithm’s actions have 9:25-9:45 Computing the some degree of uncertainty. Designing 9:25-9:45 Lempel-Ziv: A “One-Bit Independence Polynomial: from the algorithms for these settings give rise Catastrophe” But Not a Tragedy Tree Threshold Down to the Roots to new problems and techniques. I will Guillaume Lagarde and Sylvain Perifel, Nicholas Harvey, University of British survey some algorithmic models that try Université Paris-Diderot, France Columbia, Canada; Piyush Srivastava, Tata to capture uncertainty in optimization 9:50-10:10 In-Place Sparse Suffix Institute of Fundamental Research, India; Jan Vondrak, Stanford University, USA problems, talk about some example Sorting problems, and indicate some of the Nicola Prezza, Technical University of 9:50-10:10 Localization of Electrical Denmark, Denmark techniques and ideas used to tackle the Flows uncertainty in these problems and get Nikhil Srivastava, Microsoft Research, India; 10:15-10:35 Optimal Dynamic Strings provable guarantees on the performance Aaron Schild and Satish Rao, University of Pawel Gawrychowski, University of of these algorithms. Wroclaw, Poland; Adam Karczmarz and California, Berkeley, USA Tomasz Kociumaka, University of Warsaw, 10:15-10:35 Lower Bounds for Anupam Gupta Poland; Jakub Łácki, Google Research, Approximating the Matching Polytope Carnegie Mellon University, USA USA; Piotr Sankowski, University of Makrand Sinha, University of Washington, Warsaw, Poland Seattle, USA 10:40-11:00 Improved Bounds for 10:40-11:00 Stability of the Lanczos Testing Dyck Languages Method for Matrix Function Tatiana Starikovskaya, École Normale Approximation Lunch Break Supérieure Paris, France; Eldar Fischer, Christopher Musco, Massachusetts Institute of 12:30 PM-2:00 PM Technion Israel Institute of Technology, Technology, USA; Aaron Sidford, Stanford Israel; Frédéric Magniez, Université Paris- University, USA Attendees on their own Diderot, France

Coffee Break 11:05 AM-11:30 AM Room:Grand Gallery - 2nd Floor 24 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Tuesday, January 9 Tuesday, January 9 Tuesday, January 9 ANALCO: Session 3 CP22 CP23 2:00 PM-4:05 PM Session 8A Session 8B Room:Toulouse - Mezzanine 2:00 PM-4:05 PM 2:00 PM-4:05 PM Chair: Stephan Wagner, Stellenbosch Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor University, South Africa Chair: Benjamin Moseley, Washington Chair: Silvio Lattanzi, Google Zurich, 2:00-2:20 Exponential~Bounds on University in St. Louis, USA Switzerland Graph~Enumerations From~Vertex~Inc remental~Characterizations 2:00-2:20 Quasi-Regular Sequences 2:00-2:20 Estimating Graph Parameters Jeremie O. Lumbroso and Jessica Shi, and Optimal Schedules for Security Via Random Walks with Restarts Princeton University, USA Games Anna Ben-Hamou, Université Pierre et Marie David Kempe, University of Southern Curie, France; Roberto I. Oliveira, Instituto 2:25-2:45 Asymptotic Enumeration of California, USA; Leonard Schulman Nacional de Matematica Pura e Aplicada, Graph Classes with Many Components and Omer Tamuz, California Institute of Brazil; Yuval Peres, Microsoft Research, Konstantinos Panagiotou and Leon Ramzews, Technology, USA USA University of Munich, Germany 2:25-2:45 A Hamiltonian Cycle in the 2:25-2:45 Tight Bounds for Coalescing- 2:50-3:10 Split-Decomposition Trees Square of a 2-Connected Graph in Branching Random Walks on Regular with Prime Nodes: Enumeration and Linear Time Graphs Random Generation of Cactus Graphs Stephen Alstrup, University of Copenhagen, Petra Berenbrink, University of Hamburg, Maryam Bahrani and Jérémie Lumbroso, Denmark; Agelos Georgakopoulos, Germany; George Giakkoupis, Inria Princeton University, USA University of Warwick, United Kingdom; Rennes, France; Peter Kling, University of 3:15-3:35 The Cover Time of a Biased Eva Rotenberg and Carsten Thomassen, Hamburg, Germany Random Walk on Gn,p Technical University of Denmark, 2:50-3:10 Comparing Mixing Times on Denmark Samantha N. Petti, Georgia Institute of Sparse Random Graphs Technology, USA; Colin Copper, King’s 2:50-3:10 Ramsey Spanning Trees and Anna Ben-Hamou, Université Pierre et Marie College London, United Kingdom; Alan Their Applications Curie, France; Eyal Lubetzky, Courant Frieze, Carnegie Mellon University, USA Ittai Abraham, Vmware Research, USA; Institute of Mathematical Sciences, New 3:40-4:00 On Induced Paths, Holes and Shiri Chechik, Tel Aviv University, Israel; York University, USA; Yuval Peres, Trees in Random Graphs Michael Elkin, Ben-Gurion University, Microsoft Research, USA Israel; Arnold Filtser and Ofer Neiman, C R. Subramanian, Institute of Mathematical 3:15-3:35 Uniform Generation of Ben Gurion University Negev, Israel Sciences, Chennai, India; Kunal Dutta, Inria Random Graphs with Power-Law Sophia Antipolis, France 3:15-3:35 Erdös-Pósa Property of Degree Sequences Chordless Cycles and Its Applications Pu Gao and Nick Wormald, Monash O-Joung Kwon, Technische Universität University, Australia Berlin, Germany; Eun Jung Kim, 3:40-4:00 Sampling Random Colorings Universite Paris Dauphine and CNRS, of Sparse Random Graphs France Charilaos Efthymiou, Goethe Universität 3:40-4:00 Thin Graph Classes and Frankfurt, Germany; Thomas Hayes, Polynomial-Time Approximation University of New Mexico, USA; Daniel Schemes Stefankovic, University of Rochester, Zdenek Dvorak, Charles University, Czech USA; Eric Vigoda, Georgia Institute of Republic Technology, USA ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 25

Tuesday, January 9 Tuesday, January 9 Tuesday, January 9 CP24 CP25 CP26 Session 8C Session 9A Session 9B 2:00 PM-4:05 PM 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room:St. Charles - 1st Floor Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Chair: Artur Czumaj, University of Warwick, Chair: Fabrizio Grandoni, IDSIA, Chair: Silvio Lattanzi, Google Zurich, United Kingdom Switzerland Switzerland 2:00-2:20 The Complexity of Counting 4:30-4:50 Approaching 3/2 for the s-t- 4:30-4:50 The Diameter of Dense Surjective Homomorphisms and path TSP Random Regular Graphs Compactions Vera Traub and Jens Vygen, Universitat Nobutaka Shimizu, University of Tokyo, Japan Jacob Focke, Leslie Ann Goldberg, and Bonn, Germany Standa Živný, University of Oxford, United 4:55-5:15 Consensus of Interacting 4:55-5:15 Reachability Preservers: New Particle Systems on Erdös-Rényi Kingdom Extremal Bounds and Approximation Graphs 2:25-2:45 Promise Constraint Algorithms Grant Schoenebeck and Fang-Yi Yu, Satisfaction: Structure Theory and a Amir Abboud, IBM Research, USA; Greg University of Michigan, USA Symmetric Boolean Dichotomy Bodwin, Massachusetts Institute of 5:20-5:40 Spatial Mixing and Non- Joshua Brakensiek and Venkatesan Technology, USA Local Markov Chains Guruswami, Carnegie Mellon University, 5:20-5:40 Optimal Vertex Fault Tolerant Antonio Blanca, Georgia Institute of USA Spanners (for fixed stretch) Technology, USA; Pietro Caputo, 2:50-3:10 Dichotomy for Real Holantc Greg Bodwin, Massachusetts Institute Università degli Studi Roma Tre, Italy; Problems of Technology, USA; Michael Dinitz, Alistair Sinclair, University of California, Pinyan Lu, Shanghai University of Finance Johns Hopkins University, USA; Merav Berkeley, USA; Eric Vigoda, Georgia and Economics, China; Jin-Yi Cai, Parter, Weizmann Institute of Science, Institute of Technology, USA University of Wisconsin, Madison, USA; Israel; Virginia Vassilevska Williams, 5:45-6:05 Exponentially Slow Mixing Mingji Xia, Chinese Academy of Sciences, Massachusetts Institute of Technology, in the Mean-Field Swendsen-Wang China USA Dynamics 3:15-3:35 The Robust Sensitivity of 5:45-6:05 Approximate Single Source Reza Gheissari and Eyal Lubetzky, Courant Boolean Functions Fault Tolerant Shortest Path Institute of Mathematical Sciences, New Shachar Lovett, University of California, Keerti Choudhary and Surender Baswana, York University, USA; Yuval Peres, San Diego, USA; Avishay Tal, Stanford Indian Institute of Technology, Kanpur, Microsoft Research, USA India; Moazzam Hussain, WorldQuant University, USA; Jiapeng Zhang, University 6:10-6:30 Testing Ising Models of California, San Diego, USA Research, India; Liam Roditty, Bar-Ilan Constantinos Daskalakis, Nishanth Dikkala, University, Israel 3:40-4:00 Resource-Efficient Common and Gautam Kamath, Massachusetts Randomness and Secret-Key Schemes 6:10-6:30 When Recursion Is Better Institute of Technology, USA Badih Ghazi, Massachusetts Institute of Than Iteration: A Linear-Time Technology, USA; T.S. Jayram, IBM Algorithm for Acyclicity with Few Error Research, USA Vertices Ramanujan M. Sridharan, University of Warwick, United Kingdom; Daniel Lokshtanov, University of Bergen, Coffee Break Norway; Saket Saurabh, Institute of 4:05 PM-4:30 PM Mathematical Sciences, India Room:Grand Gallery - 2nd Floor 26 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Tuesday, January 9 Wednesday, CP28 CP27 January 10 Session 10A Session 9C 9:00 AM-11:05 AM 4:30 PM-6:35 PM Room:Grand Ballroom ABC - 2nd Floor Room:St. Charles - 1st Floor Registration Chair: Krzysztof Onak, IBM Research, USA Chair: Rahul Shah, Louisiana State 8:00 AM-5:00 PM 9:00-9:20 Testing Bounded Arboricity University, USA Reut Levi, Weizmann Institute of Science, Room:Grand Ballroom Foyer - 2nd Floor Israel; Talya Eden and Dana Ron, Tel Aviv 4:30-4:50 On the Competition University, Israel Complexity of Dynamic Mechanism Design 9:25-9:45 Improved Bounds for Testing Siqi Liu, University of California, Berkeley, Continental Breakfast Forbidden Order Patterns Omri Ben-Eliezer, Tel Aviv University, Israel; USA; Alexandros Psomas, Carnegie Mellon 8:30 AM University, USA Clément Canonne, Columbia University, Room:Grand Gallery - 2nd Floor USA 4:55-5:15 The Menu Complexity of ‘One-and-a-Half-Dimensional’ 9:50-10:10 Tolerant Junta Testing Mechanism Design and the Connection to Submodular Raghuvansh R. Saxena, Ariel Schvartzman, Symposium on Simplicity Optimization and Function and Matt Weinberg, Princeton University, Isomorphism USA in Algorithms Eric Blais, University of Waterloo, Canada; Clément Cannone, Columbia University, 5:20-5:40 On the Complexity of See https://simplicityalgorithms.wixsite. USA; Talya Eden, Tel Aviv University, Simple and Optimal Deterministic com/sosa for details Israel; Amit Levi, University of Waterloo, Mechanisms for An Additive Buyer 9:00 AM-6:35 PM Canada; Dana Ron, Tel Aviv University, Dimitris Paparas, University of Wisconsin, Israel Madison, USA; Xi Chen, Mihalis Room:Toulouse - Mezzanine Yannakakis, and George Matikas, Columbia 10:15-10:35 Cache-Oblivious University, USA and Data-Oblivious Sorting and Applications 5:45-6:05 Revenue Maximization with T-H. Hubert Chan, University of Hong Kong, an Uncertainty-Averse Buyer Hong Kong; Yue Guo, Wei-Kai Lin, and Shuchi Chawla, University of Wisconsin, Elaine Shi, Cornell University, USA Madison, USA; Kira Goldner, University of Washington, USA; J. Benjamin Miller, 10:40-11:00 A o(d)·polylog n University of Wisconsin, Madison, USA; Monotonicity Tester for Boolean Functions over the Hypergrid [n]d Emmanouil Pountourakis, University of Texas at Austin, USA Hadley Black, University of California, Santa Cruz, USA; Deeparnab Chakrabarty, 6:10-6:30 Separation in Correlation- Dartmouth College, USA; C. Seshadhri, Robust Monopolist Problem with University of California, Santa Cruz, USA Budget Pinyan Lu and Nick Gravin, Shanghai University of Finance and Economics, China ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 27

Wednesday, January 10 Wednesday, January 10 Wednesday, January 10 CP29 CP30 Coffee Break Session 10B Session 10C 11:05 AM-11:30 AM 9:00 AM-11:05 AM 9:00 AM-11:05 AM Room:Grand Gallery - 2nd Floor Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Silvio Lattanzi, Google Zurich, Chair: Benjamin Moseley, Washington Switzerland University in St. Louis, USA 9:00-9:20 Tight Analysis of Parallel 9:00-9:20 On Simultaneous Two-Player IP4 Randomized Greedy Mis Combinatorial Auctions Title Not Available at Time of Manuela Fischer and Andreas Noever, ETH Mark Braverman, Jieming Mao, and S. Zürich, Switzerland Matthew Weinberg, Princeton University, Publication 9:25-9:45 Derandomized USA Concentration Bounds for Polynomials, 9:25-9:45 Nash Social Welfare for and Hypergraph Maximal Indivisible Items under Separable, 11:30 AM-12:30 PM Independent Set Piecewise-Linear Concave Utilities Room:Grand Ballroom ABC - 2nd Floor David G. Harris, University of Maryland, Tung Mai, Georgia Institute of Technology, USA USA; Nima Anari, Stanford University, Chair: Fabrizio Grandoni, IDSIA, Switzerland 9:50-10:10 Community Detection on USA; Shayan Oveis Gharan, University Abstract not available. Euclidean Random Graphs of Washington, USA; Vijay Vazirani, Abishek Sankararaman and François Baccelli, University of California, Irvine, USA Virginia Vassilevska Williams University of Texas at Austin, USA 9:50-10:10 From Battlefields to Massachusetts Institute of Technology, USA 10:15-10:35 Space-Optimal Majority in Elections: Winning Strategies of Blotto Population Protocols and Auditing Games Rati Gelashvili, University of Toronto, Soheil Behnezhad, University of Maryland, USA; Avrim Blum, Carnegie Mellon Canada; Dan Alistarh, ETH Zürich, Lunch Break Switzerland; James Aspnes, Yale University, University, USA; Mahsa Derakhshan, USA University of Maryland, USA; 12:30 PM-2:00 PM MohammadTaghi Hajiaghayi, University of 10:40-11:00 Approximate Positive Maryland, College Park, USA; Mohammad Attendees on their own Correlated Distributions and Mahdian, Google Research, USA; Christos Approximation Algorithms for H. Papadimitriou, University of California, D-Optimal Design Berkeley, USA; Ronald L. Rivest, Weijun Xie, Virginia Tech, USA; Mohit Singh, Massachusetts Institute of Technology, Georgia Institute of Technology, USA USA; Saeed Seddighin, University of Maryland, College Park, USA; Philip B. Stark, University of California, Berkeley, USA 10:15-10:35 A New Class of Combinatorial Markets with Covering Constraints: Algorithms and Applications Sadra Yazdanbod, Georgia Institute of Technology, USA; Nikhil R. Devanur, Microsoft Research, USA; Jugal Garg and Ruta Mehta, University of Illinois at Urbana-Champaign, USA; Vijay V. Vazirani, Georgia Institute of Technology, USA 10:40-11:00 Approximating the Nash Social Welfare with Budget-Additive Valuations Jugal Garg, University of Illinois at Urbana- Champaign, USA; Martin Hoefer, Goethe Universität Frankfurt, Germany; Kurt Mehlhorn, Max Planck Institute for Informatics, Germany 28 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Wednesday, January 10 Wednesday, January 10 Wednesday, January 10 CP31 CP32 CP33 Session 11A Session 11B Session 11C 2:00 PM-4:05 PM 2:00 PM-4:05 PM 2:00 PM-4:05 PM Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Richard Peng, Georgia Institute of Chair: Krzysztof Onak, IBM Research, USA Chair: Vladimir Braverman, Johns Hopkins University, USA Technology, USA 2:00-2:20 Optimal Streaming and 2:00-2:20 Lower Bounds for Symbolic Tracking Distinct Elements with High 2:00-2:20 The Price of Information in Computation on Graphs: Strongly Probability Combinatorial Optimization Connected Components, Liveness, Jaroslaw Blasiok, Harvard University, USA Sahil Singla, Carnegie Mellon University, Safety, and Diameter USA 2:25-2:45 Estimating Graph Veronika Loitzenbauer, University of Parameters from Random Order 2:25-2:45 The Value of Information Vienna, Austria; Krishnendu Chatterjee, Streams Concealment Institute of Science and Technology Pan Peng, University of Vienna, Austria; Zhihao Gavin Tang, University of Hong Austria, Austria; Wolfgang Dvorák, Christian Sohler, Technische Universität Kong, Hong Kong; Hu Fu and Chris Liaw, Universität Wien, Austria; Monika Dortmund, Germany University of British Columbia, Canada; Henzinger, University of Vienna, Austria Pinyan Lu, Shanghai University of Finance 2:50-3:10 Set Cover in Sub-Linear 2:25-2:45 Algorithms Based on and Economics, China Time Algebras, and Their Applications Piotr Indyk and Sepideh Mahabadi, 2:50-3:10 Targeting and Signaling in to Isomorphism of Polynomials with Massachusetts Institute of Technology, Ad Auctions One Secret, Group Isomorphism, and USA; Ronitt Rubinfeld, Massachusetts Ashwinkumar Badanidiyuru and Kshipra Polynomial Identity Testing Institute of Technology, USA and Tel Bhawalkar, Google Research, USA; Youming Qiao, University of Technology, Aviv University, Israel; Ali Vakilian Haifeng Xu, University of Southern Sydney, Australia; Gábor Ivanyos, and Anak Yodpinyanee, Massachusetts California, USA Hungarian Academy of Sciences, Hungary Institute of Technology, USA 3:15-3:35 Envy-Free Chore Division for 2:50-3:10 Kirchhoff Index As a 3:15-3:35 Efficient Õ(n/ε) Spectral An Arbitrary Number of Agents Measure of Edge Centrality in Sketches for the Laplacian and Its Hadi Yami, Sina Dehghani, Alireza Farhadi, Weighted Networks: Nearly Linear Pseudoinverse and MohammadTaghi Hajiaghayi, Time Algorithms Arun Jambulapati and Aaron Sidford, University of Maryland, USA Huan Li and Zhongzhi Zhang, Fudan Stanford University, USA University, China 3:40-4:00 Almost Envy-Freeness with 3:40-4:00 A Nearly Instance Optimal General Valuations 3:15-3:35 Conflict-Free Coloring of Algorithm for Top-K Ranking under Benjamin Plaut and Tim Roughgarden, Intersection Graphs of Geometric the Multinomial Logit Model Stanford University, USA Objects Xi Chen, New York University, USA; Chaya Keller and Shakhar Smorodinsky, Yuanzhi Li and Jieming Mao, Princeton Ben-Gurion University, Israel University, USA 3:40-4:00 Tight Bounds on the Coffee Break Round Complexity of the Distributed Maximum Coverage Problem 4:05 PM-4:30 PM Sepehr Assadi and Sanjeev Khanna, Room:Grand Gallery - 2nd Floor University of Pennsylvania, USA ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 29

Wednesday, January 10 Wednesday, January 10 Wednesday, January 10 CP34 CP35 CP36 Session 12A Session 12B Session 12C 4:30 PM-6:35 PM 4:30 PM-6:35 PM 4:30 PM-6:35 PM Room:Grand Ballroom ABC - 2nd Floor Room:Grand Ballroom D - 2nd Floor Room:St. Charles - 1st Floor Chair: Benjamin Moseley, Washington Chair: Krzysztof Onak, IBM Research, USA Chair: Erik Jan van Leeuwen, Utrecht University in St. Louis, USA 4:30-4:50 Robustly Learning a University, The Netherlands 4:30-4:50 Labeling Schemes for Gaussian: Getting Optimal Error, 4:30-4:50 Fully Polynomial Fpt Nearest Common Ancestors Through Efficiently Algorithms for Some Classes of Minor-Universal Trees Ilias Diakonikolas, University of Southern Bounded Clique-Width Graphs Pawel Gawrychowski, University of Wroclaw, California, USA; Gautam Kamath, David Coudert, Université Côte d’Azur, Poland; Fabian Kuhn, Universität Freiburg, Massachusetts Institute of Technology, INRIA, CNRS, France; Guillaume Ducoffe Germany; Jakub Lopuszanski, University of USA; Daniel Kane, University of and Alexandru Popa, ICI – National Institute Wroclaw, Poland; Konstantinos Panagiotou, California, San Diego, USA; Jerry Li and for Research and Development informatics, University of Munich, Germany; Pascal Su, Ankur Moitra, Massachusetts Institute Romania ETH Zürich, Switzerland of Technology, USA; Alistair Stewart, 4:55-5:15 Covering Small Independent University of Southern California, USA 4:55-5:15 Mst in O(1) Rounds of Sets and Separators with Applications Congested Clique 4:55-5:15 Cycles in Adversarial to Parameterized Algorithms Tomasz Jurdzinski and Krzysztof Nowicki, Regularized Learning Daniel Lokshtanov and Fahad Panolan, University of Wroclaw, Poland Panayotis Mertikopoulos, CNRS and University of Bergen, Norway; Saket Grenoble University, France; Christos 5:20-5:40 The Complexity of Distributed Saurabh, Institute of Mathematical Sciences, Papadimitriou, Columbia University, USA; Edge Coloring with Small Palettes India; Roohani Sharma, Institute of Georgios Piliouras, Singapore University Yi-Jun Chang, University of Michigan, Ann Mathematical Sciences, Chennai, India; of Technology & Design, Singapore Arbor, USA; Qizheng He and Wenzheng Meirav Zehavi, Ben-Gurion University, Li, Tsinghua University, China; Seth Pettie, 5:20-5:40 Improved Coresets for Israel University of Michigan, Ann Arbor, USA; Kernel Density Estimates 5:20-5:40 Covering a Tree with Rooted Jara Uitto, ETH Zürich, Switzerland Wai Ming Tai and Jeff Phillips, University of Subtrees -- Parameterized and Utah, USA 5:45-6:05 Fast Space Optimal Leader Approximation Algorithms Election in Population Protocols 5:45-6:05 Non Interactive Simulation of Lin Chen, Zhejiang University, China; Dániel Leszek A. Gasieniec, University of Liverpool, Correlated Distributions Is Decidable Marx, Hungarian Academy of Sciences, United Kingdom; Grzegorz Stachowiak, Anindya De, Northwestern University, Hungary Uniwersytet Wroclawski, Poland USA; Elchanan Mossel, Massachusetts 5:45-6:05 An Fpt Algorithm Beating Institute of Technology, USA; Joe Neeman, 6:10-6:30 Ergodic Effects in Token 2-Approximation for K-Cut University of Texas, Austin, USA Circulation Jason M. Li, Anupam Gupta, and Euiwoong Adrian Kosowski, INRIA Paris, France; 6:10-6:30 Which Distribution Distances Lee, Carnegie Mellon University, USA Przemyslaw Uznanski, ETH Zürich, Are Sublinearly Testable? 6:10-6:30 Parameterized Algorithms Switzerland Constantinos Daskalakis, Gautam Kamath, for Survivable Network Design with and John Wright, Massachusetts Institute of Uniform Demands Technology, USA Joergen Bang-Jensen, University of Southern Denmark, Denmark; Manu Basavaraju, NIT Surathkal, India; Kristine Vittin Klinkby and Pranabendu Misra, University of Bergen, Norway; Ramanujan M. S., University of Warwick, United Kingdom; Saket Saurabh, Institute of Mathematical Sciences, India; Meirav Zehavi, Ben-Gurion University, Israel 30 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

Abstracts

Abstracts are printed as submitted by the authors.

Abtracts for ALENEX and ANALCO appear in the beginning of the Section under CP0, and are alphabetized by speaker last name. DA18 Abstracts 31

IP1 and indicate some of the techniques and ideas used to tackle Differential Privacy: A Gateway Concept the uncertainty in these problems and get provable guar- antees on the performance of these algorithms. Differential privacy is a definition of privacy tailored to statistical analysis of very large large datasets. Invented Anupam Gupta just over one decade ago, the notion has become widely (if Carnegie Mellon University not deeply) deployed, and yet much remains to be done. [email protected] The theoretical investigation of privacy/accuracy tradeoffs that shaped the field by delineating the boundary between possible and impossible motivate the continued search for IP4 new algorithmic techniques, as well as still meaningful re- Title To Be Determined - Vassilevska Williams laxations of the basic definition. Differential privacy has also led to new approaches in other fields, most notably in Not available. algorithmic fairness and adaptive data analysis, in which the questions being asked of the data depend on the data Virginia Vassilevska Williams themselves. We will highlight some recent algorithmic and MIT definitional work, and focus on differential privacy as a [email protected] gateway concept to these new areas of study.

Cynthia Dwork CP0 Harvard University, USA A Generic Framework for Engineering Graph Can- [email protected] onization Algorithms The state-of-the-art tools for practical graph canonization IP2 are all based on the individualization-refinement paradigm, ThePowerofTheoryinthePracticeofHashing and their difference is primarily in the choice of heuristics with Focus on Similarity Estimation they include and in the actual tool implementation. It is thus not possible to make a direct comparison of how Hash functions have become ubiquitous tools in modern individual algorithmic ideas affect the performance on dif- data analysis, e.g., the construction of small randomized ferent graph classes. We present an algorithmic software sketches of large data streams. We like to think of abstract framework that facilitates implementation of heuristics as hash functions, assigning independent uniformly random independent extensions to a common core algorithm. It hash values to keys, but in practice, we have to choose a therefore becomes easy to perform a detailed comparison hash function that only has an element of randomness, e.g., of the performance and behaviour of different algorithmic 2-independence. While this works for sufficiently random ideas. Implementations are provided of a range of algo- input, the real world has structured data where such simple rithms for tree traversal, target cell selection, and node hash functions fail, calling for the need of more powerful invariant, including choices from the literature and new hash functions. In this talk, we focus hashing for set sim- variations. The framework readily supports extraction and ilarity, which is an integral component in the analysis of visualization of detailed data from separate algorithm ex- Big Data. The basic idea is to use the same hash function ecutions for subsequent analysis and development of new to do coordinated sampling from different sets. Depending heuristics. Using collections of different graph classes we on the context, we want subsets sampled without replace- investigate the effect of varying the selections of heuristics, ment, or fixed-length vectors of samples that may be with often revealing exactly which individual algorithmic choice replacement. The latter is used as input to support vec- is responsible for particularly good or bad performance. On tor machines (SVMs) and locality sensitive hashing (LSH). several benchmark collections, including a newly proposed The most efficient constructions require very powerful hash class of difficult instances, we additionally find that our functions that are also needed for efficient size estimation. implementation performs better than the current state-of- We discuss the interplay between the hash functions and the-art tools. the algorithms using them. Finally, we present experi- ments on both real and synthetic data where standard Jakob L. Andersen 2-independent hashing yield systematically poor similar- Research group Bioinformatics and Computational ity estimates, while the right theoretical choice is sharply Biology concentrated, and faster than standard cryptographic hash Faculty of Computer Science, University of Vienna functions with no proven guarantees. [email protected]

Mikkel Thorup Daniel Merkle University of Copenhagen Department of Mathematics and Computer Science [email protected] University of Southern Denmark [email protected]

IP3 Approximation Algorithms for Uncertain Environ- CP0 ments Computing Top-k Closeness Centrality in Fully- Dynamic Graphs The past decade has seen considerable work on algorithms in models with uncertainty: where either the inputs to the Closeness is a widely-studied centrality measure. Since it algorithm or the algorithm’s actions have some degree of requires all pairwise distances, computing closeness for all uncertainty. Designing algorithms for these settings give nodes is infeasible for large real-world networks. However, rise to new problems and techniques. I will survey some for many applications, it is only necessary to find the k algorithmic models that try to capture uncertainty in op- most central nodes and not all closeness values. Prior work timization problems, talk about some example problems, has shown that computing the top-k nodes with highest 32 DA18 Abstracts

closeness can be done much faster than computing close- [email protected] ness for all nodes in real-world networks. However, for networks that evolve over time, no dynamic top-k closeness Sergey Dovgal algorithm exists that improves on static recomputation. In Institut Galil´ee, Universit´e Paris 13 this paper, we present several techniques that allow us to L’IRIF Universit´e Paris 7; Moscow Inst. of Physics and efficiently compute the k nodes with highest (harmonic) Tech closeness after an edge insertion or an edge deletion. Our [email protected] algorithms use information obtained during earlier compu- tations to omit unnecessary work. However, they do not require asymptotically more memory than the static algo- CP0 rithms (i. e., linear in the number of nodes). We propose Scaling Up Group Closeness Maximization separate algorithms for complex networks (which exhibit the small-world property) and networks with large diame- Closeness is a widely-used centrality measure in social net- ter such as street networks, and we compare them against work analysis. While the identification of the k nodes with static recomputation on a variety of real-world networks. highest closeness received significant attention, many ap- On many instances, our dynamic algorithms are two or- plications are actually interested in finding a group of nodes ders of magnitude faster than recomputation; on some large that is central as a whole. For this problem, only recently graphs, we even reach average speedups between 103 and − 4 a greedy algorithm with approximation ratio (1 1/e)has 10 . been proposed [Chen et al., ADC 2016]. Since this algo- rithm’s running time is still expensive for large networks, Patrick Bisenius a heuristic without approximation guarantee has also been n/a proposed in the same paper. In the present paper we de- n/a velop techniques to speed up the greedy algorithm without losing its guarantee. Compared to a straightforward im- Elisabetta Bergamini, Elisabetta Bergamini plementation, our approach is orders of magnitude faster Institute of Theoretical Informatics and, compared to the heuristic proposed by Chen et al., we Karlsruhe Institute of Technology (KIT) always find a solution with better quality in a comparable [email protected], running time in our experiments. Our method Greedy++ [email protected] allows us to approximate the group with maximum close- ness on networks with up to hundreds of millions of edges Eugenio Angriman in at most a few hours. To have the same theoretical guar- Karlsruhe Institute of Technology antee, the greedy approach by [Chen et al., ADC 2016] [email protected] would take several days already on networks with hun- dreds of thousands of edges. In a comparison with the Henning Meyerhenke optimum, our experiments show that the solution found Karlsruhe Institute of Technology (KIT) by Greedy++ is much better than the theoretical guaran- [email protected] tee. Over all tested networks, the empirical approximation ratio is never lower than 0.97.

CP0 Elisabetta Bergamini, Elisabetta Bergamini Institute of Theoretical Informatics Polynomial Tuning of Multiparametric Combinato- Karlsruhe Institute of Technology (KIT) rial Samplers [email protected], Boltzmann samplers and the recursive method are promi- [email protected] nent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial struc- Tanya Gonser tures, such as maps, tilings, RNA sequences or various tree- Karlsruhe Institute of Technology like structures. In their multiparametric variants, these [email protected] samplers allow to control the profile of expected values cor- responding to multiple combinatorial parameters. One can Henning Meyerhenke control, for instance, the number of leaves, profile of node University of Cologne degrees in trees or the number of certain subpatterns in [email protected] strings. However, such a flexible control requires an ad- ditional non-trivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the CP0 number of tuned parameters, tuning algorithm based on Quadratic Time Algorithms Appear to Be Optimal convex optimisation techniques. Finally, we illustrate the for Sorting Evolving Data efficiency of our approach using several applications of ra- tional, algebraic and P´olya structures including polyomino We empirically study sorting in the evolving data model. tilings with prescribed tile frequencies, planar trees with a In this model, a sorting algorithm maintains an approx- given specific node degree distribution, and weighted par- imation to the sorted order of a list of data items while titions. simultaneously, with each comparison made by the algo- rithm, an adversary randomly swaps the order of adjacent Maciej Bendkowski items in the true sorted order. Previous work studies only Theoretical Computer Science Department two versions of quicksort, and has a gap between the lower Jagiellonian University, Krak´ow, Poland bound of Ω(n) and the best upper bound of O(n log log n). [email protected] The experiments we perform in this paper provide empir- ical evidence that some quadratic-time algorithms such as Olivier Bodini insertion sort and bubble sort are asymptotically optimal LIPN, Universit´e Paris 13 for any constant rate of random swaps. In fact, these algo- DA18 Abstracts 33

rithms perform as well as or better than algorithms such [email protected].fi as quicksort that are more efficient in the traditional algo- rithm analysis model. CP0 William Devanny, Juan Jose Besa Vial, David Eppstein, Trace Reconstruction with Varying Deletion Prob- Michael Goodrich, Timothy Johnson abilities University of California, Irvine Department of Computer Science In the trace reconstruction problem an unknown string n [email protected], [email protected], [email protected], x =(x0,...,xn−1) ∈{0, 1, ..., m − 1} is observed through [email protected], [email protected] the deletion channel, which deletes each xk with a certain probability, yielding a contracted string X . Earlier works have proved that if each xk is deleted with the same prob- CP0 ability q ∈ [0, 1), then exp(O(n1/3)) independent copies of  Analyzing Boltzmann Samplers for Bose-Einstein the contracted string X suffice to reconstruct x with high Condensates with Dirichlet Generating Functions probability. We extend this upper bound to the setting where the deletion probabilities vary, assuming certain reg- Boltzmann sampling is commonly used to uniformly sam- ularity conditions. First we consider the case where xk is deleted with some known probability qk. Then we consider ple objects of a particular size from large combinatorial ∈{ − } sets. For this technique to be effective, one needs to prove the case where each letter ζ 0, 1, ..., m 1 is associated that (1) the sampling procedure is efficient and (2) ob- with some possibly unknown deletion probability qζ . jects of the desired size are generated with sufficiently high probability. We use this approach to give a provably ef- Nina Holden ficient sampling algorithm for a class of weighted integer Massachusetts Institute of Technology partitions related to Bose–Einstein condensation from sta- [email protected] tistical physics. Our sampling algorithm is a probabilistic interpretation of the ordinary generating function for these Lisa Hartung objects, derived from the symbolic method of analytic com- Courant, New York University binatorics. Using the Khintchine–Meinardus probabilis- [email protected] tic method to bound the rejection rate of our Boltzmann sampler through singularity analysis of Dirichlet generat- Yuval Peres ing functions, we offer an alternative approach to analyze Microsoft Research, Redmond Boltzmann samplers for objects with multiplicative struc- [email protected] ture.

Matthew Fahrbach, Megan Bernstein, Dana Randall CP0 Georgia Institute of Technology Scalable Kernelization for Maximum Independent [email protected], bern- Sets [email protected], [email protected] The most efficient algorithms for finding maximum inde- pendent sets use reduction rules to obtain a much smaller CP0 problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms or by re- Hybrid Indexing Revisited peatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms Hybrid indexing is a recent approach to text indexing that that kernelization is fast and returns a small kernel. Cur- allows the space-usage of conventional text indexes (e.g., rent algorithms are either slow but produce a small kernel, suffix trees, suffix arrays, FM-indexes) to scale well with or fast and give a large kernel. We attempt to accomplish the text size, n,whenz, the size of the Lempel-Ziv pars- both of these goals simultaneously, by giving an efficient ing of the text, is small relative to n. The price for this parallel kernelization algorithm based on graph partition- improved scalability is that an upper bound M on the pat- ing and parallel bipartite maximum matching. We com- tern length that can be searched for must be declared at bine our parallelization techniques with two techniques to index construction time. Because the size of the resulting accelerate kernelization further: dependency checking that index contains an O(Mz)term,M must be kept reason- prunes reductions that cannot be applied, and reduction ably small, though it has been shown that M ≈ 100 leads tracking that allows us to stop kernelization when reduc- to acceptable performance in some genomic applications. tions become less fruitful. Our algorithm produces kernels However, despite its promise, the practical performance that are orders of magnitude smaller than the fastest ker- of hybrid indexing relative to other compressed index data nelization methods, while having a similar execution time. structures is poorly understood. This paper addresses that Furthermore, our algorithm is able to compute kernels with need, detailing experiments that show hybrid indexing — size comparable to the smallest known kernels, but up to when carefully implemented — to be significantly smaller two orders of magnitude faster than previously possible. and faster than alternative approaches on a broad range of Finally, we show that our kernelization algorithm can be data of different levels of compressibility. We also describe used to accelerate existing state-of-the-art heuristic algo- practical extensions to hybrid indexing that obviate the re- rithms, allowing us to find larger independent sets faster striction on M, supporting search for patterns of arbitrary on large real-world networks and synthetic instances. length. Darren Strash Hector Ferrada, Dominik Kempa, Simon Puglisi Department of Computer Science University of Helsinki Colgate University [email protected].fi, [email protected].fi, si- [email protected] 34 DA18 Abstracts

Demian Hespe petteri.kaski@aalto.fi Karlsruhe Institute of Technology [email protected] CP0 Christian Schulz Institute of Theoretical Informatics Hyperbolic Embeddings for Near-Optimal Greedy Karlsruhe Institute of Technology Routing [email protected] Greedy routing computes paths between nodes in a net- work by successively moving to the neighbor closest to the CP0 target with respect to coordinates given by an embedding into some metric space. Its advantage is that only local Computing 2-Connected Components and Maxi- information is used for routing decisions. We present dif- mal 2-Connected Subgraphs in Directed Graphs: ferent algorithms for generating graph embeddings into the An Experimental Study hyperbolic plane that are well suited for greedy routing. In particular our embeddings guarantee that greedy routing Motivated by very recent work on 2-connectivity in di- always succeeds in reaching the target and we try to mini- rected graphs, we revisit the problem of computing the mize the lengths of the resulting greedy paths. We evaluate 2-edge- and 2-vertex-connected components, and the maxi- our algorithm on multiple generated and real wold net- mal 2-edge- and 2-vertex-connected subgraphs of a directed works. For networks that are generally assumed to have a graph G. We explore the design space for efficient algo- hidden underlying hyperbolic geometry, such as the Inter- rithms in practice, based on recently proposed techniques, net graph, we achieve near-optimal results, i.e., the result- and conduct a thorough empirical study to highlight the ing greedy paths are only slightly longer than the corre- merits and weaknesses of each technique. sponding shortest paths. In the case of the Internet graph, they are only 6% longer when using our best algorithm, which greatly improves upon the previous best known em- Aikaterini Karanasiou bedding, whose creation required substantial manual inter- University of Rome Tor Vergata vention. [email protected] Thomas Blaesius, Tobias Friedrich, Loukas Georgiadis Maximilian Katzmann, Anton Krohmer University of Ioannina, Greece Hasso Plattner Institute [email protected] [email protected], [email protected], maximil- [email protected], [email protected] Giuseppe Italiano Universita di Roma “Tor Vergata’ [email protected] CP0 Nikos Parotsidis, Nilakantha Paudel Faster Approximation Algorithm for the k-Regret University of Rome Tor Vergata Minimizing Set and Related Problems [email protected], nilakan- [email protected] Efficient multi-criteria decision making often requires look- ing at a small set of representative objects from a large collection. A recently proposed method for finding rep- CP0 resentative objects is the k-regret minimizing set (k-RMS problem). Intuitively, given a large set of objects (points) Engineering a Delegatable and Error-Tolerant Al- in d dimensions, the goal is to choose a small representa- gorithm for Counting Small Subgraphs tive subset, such that for every user preference, there is always an object in the subset whose preference score is We study the problem of counting the number of occur- not much worse than the score of the k-th most preferred rences of a given six-vertex pattern graph S in an n-vertex object in the original set. We propose two new efficient host graph H. We engineer an open-source GPU imple- approximation algorithms for the k-regret minimizing set mentation of a distributed algorithm design of Bj¨orklund problem with provable theoretical guarantees. Our algo- and Kaski [PODC 2016] where (i) the execution of the algo- rithms improve on the space and time complexities of pre- rithm can be delegated [Goldwasser, Kalai, and Rothblum, vious approximation algorithms for the k-RMS problem. J. ACM 2015] to produce a noninteractive probabilistically In addition, we run extensive experiments on real and syn- checkable proof of correctness, and (ii) the execution of the thetic data sets showing that simple modifications of our algorithm when preparing the proof tolerates a controllable theoretical algorithms run significantly faster than the pre- number of adversarial errors. Experiments with NVIDIA vious implementations of the k-RMS problem. Finally, we Tesla K80 and Tesla P100 Accelerators demonstrate that present an efficient approximation algorithm with theoret- the framework is practical for inputs of up to 512 vertices, ical guarantees for an extension of the k-RMS problem, with proof checking being several orders of magnitude more which is called the Top-k regret minimizing set problem. efficient than preparing the proof; however, proof prepara- tion still carries at least one order of magnitude overhead Nirman Kumar compared with just solving the problem. University of Memphis [email protected] Petteri Kaski Aalto University Stavros Sintos Department of Computer Science Duke University DA18 Abstracts 35

[email protected] node uses local decision rules based on the message source and destination, and its own location. In this paper we analyze six different beaconless geocast protocols, focusing CP0 on two relevant 1D scenarios. The selection of protocols re- Simple, Fast and Lightweight Parallel Wavelet Tree flects the most relevant types of protocols proposed in the Construction literature, including those evaluated in previous computer simulations. We present a formal and structured analysis The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet of the maximum number of messages that a node can re- matrix (Claude et al. [Inf. Syst., 47:15–32, 2015]) are com- ceive, for each protocol, in each of the two scenarios. This pact indices for texts over an alphabet [0,σ) that support is a measure of the network load incurred by each proto- rank, select and access queries in O(lg σ)time.Wefirst col. Our analysis, that for some of the protocols requires present new practical sequential and parallel algorithms an involved probabilistic analysis, confirms behaviors that for wavelet tree construction. Their unifying characteris- had been observed only through simulations before. tics is that they construct the wavelet tree bottom-up,i.e., they compute the last level first. We also show that this Joachim Gudmundsson bottom-up construction can easily be adapted to wavelet University of Sydney matrices. In practice, our best sequential algorithm is up [email protected] to twice as fast as the currently fastest sequential wavelet tree construction algorithm (Shun [DCC, 2015]), simulta- Irina Kostitsyna neously saving a factor of 2 in space. This scales up to Technical University Eindhoven 32 cores, where we are about equally fast as the currently [email protected] fastest parallel wavelet tree construction algorithm (Labeit et al. [DCC, 2016]), but still use only about 75 % of the Maarten L¨offler space. An additional theoretical result shows how to adapt Utrecht University any wavelet tree construction algorithm to the wavelet ma- m.loffl[email protected] trix in the same (asymptotic) time, using only little extra space. Tobias M¨uller Johannes Fischer, Florian Kurpicz,MarvinL¨obel Groningen University TU Dortmund [email protected] johannes.fi[email protected], florian.kurpicz@tu- dortmund.de, [email protected] Vera Sacrist´an Universitat Politecnica de Catalunya [email protected] CP0 Split-Decomposition Trees with Prime Nodes: Rodrigo Silveira Enumeration and Random Generation of Cactus Universitat Polit`ecnica de Catalunya Graphs [email protected]

In this paper, we build on recent results by Chauve et al. and Bahrani and Lumbroso, which combined the split- CP0 decomposition, as exposed by Gioan and Paul, with ana- lytic combinatorics, to produce new enumerative results on On Deletions in Open Addressing Hashing graphs—in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptole- Deletions in open addressing tables have often been seen maic). Our goal was to study a simple family of graphs, as problematic. The usual solution is to use a special mark of which the split-decomposition trees have prime nodes ’deleted’ so that probe sequences continue past deleted drawn from a enumerable (and manageable!) set of graphs. slots, as if there was an element still sitting there. Such a The cactus graphs, which we describe in more detail further solution, notwithstanding is wide applicability, may involve down in this paper, can be thought of as trees with their performance degradation. In the first part of this paper we vertices replaced by cycles (or arbitrary lengths). Their review a practical implementation of the often overlooked split-decomposition trees contain prime nodes that are cy- deletion algorithm for linear probing hash tables, analyze cles, making them ideal for study. We derive a character- its properties and performance, and provide several strong ization of the split-decomposition trees of cactus graphs, arguments in favor of the Robin Hood variant. In partic- we produce a general template of symbolic grammar for ular, we show how a small variation can yield substantial cactus graphs, and then we implement random generation improvements for unsuccessful search. In the second part for these graphs, building on work by Iriza. weproposeanalgorithmfortruedeletioninopenaddress- ing hashing with secondary clustering, like quadratic hash- Maryam Bahrani, J´er´emie Lumbroso ing. As far as we know, this is the first time that such an Princeton University algorithm appears in the literature. Moreover, for tables [email protected], [email protected] built using the Robin Hood variant the deletion algorithm strongly preserves randomness (the resulting table is iden- tical to the table that would result if the item were not CP0 inserted at all). Although it involves some extra memory Theoretical Analysis of Beaconless Geocast Proto- for bookkeeping, the algorithm is comparatively easy and cols in 1D efficient, and it might be of some practical value, besides its theoretical interest. Beaconless geocast protocols are routing protocols used to send messages in mobile ad-hoc wireless networks, in which Conrado Mart´ınez,RosaJim´enez the only information available to each node is its own lo- Department of Computer Science cation. Messages get routed in a distributed manner: each Univ. Polit`ecnica de Catalunya 36 DA18 Abstracts

[email protected], [email protected] baum (1993). We present empirical evidence that, in a certain well-defined sense, grid peeling behaves at the limit like ACSF on convex curves. We offer some theoretical ar- CP0 guments in favor of this conjecture. We also pay closer Area-Preserving Subdivision Simplification With attention to the simple case where G = N 2 is a quarter- Topology Constraints: Exactly And In Practice infinite grid. This case corresponds to ACSF starting with an infinite L-shaped curve, which when transformed using Given a planar subdivision and a set of points, we want the ACSF becomes a hyperbola for all times t>0. We to simplify the subdivision by removing vertices of degree prove that, in the grid peeling of N 2,(1)thenumberof 2. The vertices should be removed in such a way that all grid points removed up to iteration n is Θ(n3/2 log n); and points remain in their respective faces, the area of any face (2) the boundary at iteration n is sandwiched between two changes by a factor of at most δ and the distance of the hyperbolas that are separated from each other by a con- resulting lines to the original ones is at most ε. While stant factor. inapproximability carries over from less general problems, we present an heuristic approach which solves continental David Eppstein sized instances in seconds. For city-sized instances we can University of California, Irvine compute optimal results via Integer-Linear-Programming Department of Computer Science and show, that our algorithm provides close-to-optimal re- [email protected] sults. Sariel Har-Peled Thomas Mendel Department of Computer Science University of Stuttgart University of Illinois, Urbana Champaign [email protected] [email protected]

CP0 Gabriel Nivasch Adaptive Cuckoo Filters Ariel University [email protected] We introduce the adaptive cuckoo filter (ACF), a data structure for approximate set membership that extends cuckoo filters by reacting to false positives, removing them CP0 for future queries. As an example application, in packet Practical Minimum Cut Algorithms processing queries may correspond to flow identifiers, so a search for an element is likely to be followed by re- The minimum cut problem for an undirected edge-weighted peated searches for that element. Removing false posi- graph asks us to divide its set of nodes into two blocks while tives can therefore significantly lower the false positive rate. minimizing the weight sum of the cut edges. Here, we in- The ACF, like the cuckoo filter, uses a cuckoo hash table troduce a linear-time algorithm to compute near-minimum to store fingerprints. We allow fingerprint entries to be cuts. Our algorithm is based on cluster contraction using changed in response to a false positive in a manner de- label propagation and Padberg and Rinaldi’s contraction signed to minimize the effect on the performance of the heuristics [SIAM Review, 1991]. We give both sequen- filter. We show that the ACF is able to significantly re- tial and shared-memory parallel implementations of our duce the false positive rate by presenting both a theoreti- algorithm. Extensive experiments on both real-world and cal model for the false positive rate and simulations using generated instances show that our algorithm finds the op- both synthetic data sets and real packet traces. timal cut on nearly all instances significantly faster than other state-of-the-art exact algorithms, and our error rate Michael Mitzenmacher is lower than that of other heuristic algorithms. In addi- Harvard University tion, our parallel algorithm shows good scalability. [email protected] Monika Henzinger Univeristy of Vienna, Austria Salvatore Pontarelli [email protected] Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT) [email protected] Alexander Noe University of Vienna [email protected] Pedro Reviriego Universidad Antonio de Nebrija [email protected] Christian Schulz University of Vienna Karlsruhe Institute of Technology CP0 [email protected] Grid Peeling and the Affine Curve-Shortening Flow Darren Strash In this paper we study an experimentally-observed con- Colgate University nection between two seemingly unrelated processes, one [email protected] from computational geometry and the other from differen- tial geometry. The first one (which we call ”grid peeling”) is the convex-layer decomposition of subsets G ⊂ Z2 of CP0 the integer grid, previously studied for the particular case Linear Time Canonicalization and Enumeration of G = {1, ..., m}2 by Har-Peled and Lidicky (2013). The sec- Non-Isomorphic 1-Face Embeddings ond one is the affine curve-shortening flow (ACSF), first studied by Alvarez et al. (1993) and Sapiro and Tannen- Antiparallel strong traces (ASTs) are a type of walks in DA18 Abstracts 37

graphs which use every edge exactly twice. They corre- While there is a lot of work on heuristics for topological spond to 1-face embeddings in orientable surfaces and can drawings, these techniques are typically not transferable be used to design self-assembling protein or DNA strands. to the rectilinear (i.e., straight-line) setting. We introduce Based on a novel canonical form invariant for ASTs, gap and evaluate three heuristics for rectilinear crossing mini- vector, we provide a linear-time isomorphism test for ASTs mization. The approaches are based on the primitive op- and thus, also for orientable 1-face embeddings of graphs. eration of moving a single vertex to its crossing-minimal Using the canonical form, we develop an algorithm for enu- position in the current drawing Γ, for which we give an merating all pairwise non-isomorphic 1-face embeddings of O (kn + m)2 log (kn + m) -time algorithm, where k is the graphs. We compare our algorithm with an independent degree of the vertex and n and m are the numbers of ver- implementation of a recent algebraic approach (Baic et al., tices and edges of the graph, respectively. In an exper- MATCH Commun. Math. Comput. Chem. 78 (3), 2017) imental evaluation, we demonstrate that our algorithms on large data sets. Our results yield the first large-scale compute straight-line drawings with fewer crossings than enumeration of non-isomorphic embeddings and investiga- energy-based algorithms implemented in the Open Graph tion of their properties. Drawing Framework on a varied set of benchmark in- stances. All experiments are evaluated with a statistical Marc Hellmuth significance level of α =0.05. University of Greifswald [email protected] Marcel Radermacher Karlsruhe Institute of Technology Anders S. Knudsen [email protected] University of Southern Denmark [email protected] Klara Reichard Universitaet Tuebingen Michal Kotrbcik [email protected] The University of Queensland, Department of Mathematics Ignaz Rutter Brisbane St Lucia, QLD 4072 TU Eindhoven [email protected] [email protected]

Daniel Merkle Dorothea Wagner Department of Mathematics and Computer Science Karlsruhe Institute of Technology University of Southern Denmark Institute of Theoretical Informatics [email protected] [email protected]

Nikolai Nøjgaard CP0 University of Southern Denmark [email protected] Asymptotic Enumeration of Graph Classes with Many Components G CP0 We consider graph classes in which every graph has com- ponents in a class C of connected graphs. We provide a The Cover Time of a Biased Random Walk on Gn,p framework for the asymptotic study of |Gn,N |,thenumber G   We analyse the cover time of a biased random walk on the of graphs in with n vertices and N := λn components, where λ ∈ (0, 1). Assuming that the number of graphs random graph Gn,p. The walk is biased towards visiting C vertices of low degree and this makes the cover time less with n vertices in satisfies −(1+α) −n than in the unbiased case. |Cn|∼bn ρ n!,n→∞, Samantha N. Petti for some b, ρ > 0andα>1 – a property commonly en- Georgia Tech countered in graph enumeration – we show that Georgia Tech − n! |G |∼c(λ)nf(λ)(log n)g(λ)ρ nh(λ)N ,n→∞, [email protected] n,N N! for explicitly given c(λ),f(λ),g(λ)andh(λ). These func- Colin Copper tions are piecewise continuous with a discontinuity at a King’s College London critical value λ∗, which we also determine. The central [email protected] idea in our approach is to sample objects of G randomly by so-called Boltzmann generators in order to translate Alan Frieze enumerative problems to the analysis of iid random vari- Carnegie Mellon University ables. By that we are able to exploit local limit theo- Department of Mathematical Sciences rems and large deviation results well-known from proba- [email protected] bility theory to prove our claims. The main results are formulated for generic combinatorial classes satisfying the SET-construction. CP0 A Geometric Heuristic for Rectilinear Crossing Konstantinos Panagiotou, Leon Ramzews Minimization University of Munich [email protected], [email protected] In this paper we consider the rectilinear crossing mini- mization problem, i.e., we seek a straight-line drawing Γ of a graph G =(V,E) with a small number of edge cross- CP0 ings. Crossing minimization is an active field of research. Exponential Bounds on Graph Enumerations 38 DA18 Abstracts

From Vertex Incremental Characterizations [email protected]

In this paper, building on previous work by Nakano et al., Yujin Shin 2009, we develop an alternate technique which almost au- MADALGO, Department of Computer Science tomatically translates (existing) vertex incremental charac- Aarhus University terizations of graph classes into asymptotics of that class. [email protected] Specifically, we construct trees corresponding to the se- quences of vertex incremental operations which character- ize a graph class, and then use analytic combinatorics to Constantinos Tsirogiannis enumerate the trees, giving an upper bound on the graph MADALGO, Aarhus University class. This technique is applicable to a wider set of graph [email protected] classes compared to the tree decompositions, and we show that this technique produces accurate upper bounds. We CP0 first validate our method by applying it to the case of distance-hereditary graphs, and comparing the bound ob- The Complexity of the Multiple Pattern Matching tained by our method with that obtained by Nakano et Problem for Random Strings al., 2009, and the exact enumeration obtained by Chauve We generalise a multiple string pattern matching algo- et al., 2014. We then illustrate its use by applying it to rithm, proposed by Fredriksson and Grabowski [J. Discr. switch cographs, for which there are few known results: Alg. 7, 2009], to deal with arbitrary dictionaries on an al- our method provide a bound of 6.301n,tobecompared phabet of size s.Ifr is the number of words of length m with the precise exponential growth, 6.159n ,whichwe m in the dictionary, and φ(r)=max ln(smr )/m,thecom- obtained independently through the relationship between m m plexityrateforthestringcharacterstobereadbythisal- switch cographs and bicolored cographs, first introduced gorithm is at most K φ(r)forsomeconstantK . Then, by Hertz, 1999. We believe the popularity of vertex in- ub ub we generalise the classical lower bound of Yao [SIAM J. cremental characterizations might mean this may prove a Comput. 8, 1979], for the problem with a single pattern, fairly convenient to tool for future exploration of graph to deal with arbitrary dictionaries, and determine it to be classes. at least Klbφ(r). This proves the optimality of the algo- Jeremie O. Lumbroso rithm, improving and correcting previous claims. Further- more, we establish a tightness result for dictionaries with Princeton University { } Department of Computer Science the same set rm : the worst-case, average-case, and best- [email protected] case complexities (the latter, up to a finite fraction of the dictionaries) are all equal, up to a finite multiplicative con- stant. Jessica Shi Princeton University Andrea Sportiello, Frederique Bassino, Tsinjo [email protected] Rakotoarimalala LIPN, Universit´eParisNord Villetaneuse, FRANCE CP0 [email protected], Computing Floods Caused by Non-Uniform Sea- [email protected], tsin- Level Rise [email protected] Predicting floods caused by the rise of the sea level is a critical task for preventing large scale catastrophes. Such CP0 predictions can potentially be made using a forecast of the Probabilistic Analysis of the Dual-Pivot Quicksort sea level and a detailed model of the terrain. However, ”Count” since available terrain datasets can easily exceed the size of the main memory of a standard computer, I/O (rather Recently, Aum¨uller and Dietzfelbinger proposed a version than internal computation time) can often be the bottle- of a dual-pivot quicksort, called “Count”, which is opti- neck when computing such predictions. Thus to perform mal among dual-pivot versions with respect to the average predictions efficiently we need an I/O-efficient approach, number of key comparisons required. In this note we pro- which minimizes the transfer of data blocks between main vide further probabilistic analysis of “Count”. We derive memory and disk. Given a terrain raster T and a sea-level an exact formula for the average number of swaps needed forecast raster S of N cells each, we examine the prob- by “Count” as well as an asymptotic formula for the vari- lem of computing the water level of the induced flood for ance of the number of swaps and a limit law. Also for the each cell in T . We introduce an I/O-efficient algorithm for number of key comparisons the asymptotic variance and a this problem that uses O((N/B)logM/B(X/B)) I/Os after limit law are identified. We also consider both complexity O((N/B)logM/B(N/B)) I/Os of preprocessing, where X measures jointly and find their asymptotic correlation. is the number of local minima in T ,andM and B are the size of main memory and data block, respectively. When Ralph Neininger, Jasmin Straub X

Lars Arge The concentration of the sizes of largest induced paths Madalgo, Aarhus University and cycles (holes) are studied in the random graph model DA18 Abstracts 39

G(n, p). A 2-point concentration is proved for the size of [email protected] the largest induced path and cycle, for all p = p(n)satis- fying p ≥ n−1/2(ln n)2 and p ≤ 1 − where >0isany constant. No such tight concentration (within two con- CP0 secutive values) was known before for induced paths and Efficiently Inferring Pairwise Subtree Prune-and- cycles. As a corollary, a significant additive improvement Regraft Adjacencies Between Phylogenetic Trees is obtained over a 25-year old result of Erd˝os and Palka 2 [?]concerning the size of the largest induced tree in a dense We develop a time-optimal O(mn )-time algorithm to con- random graph. The proofs are based on second moment struct the subtree prune-regraft (SPR) graph on a collec- tion of m phylogenetic trees with n leaves. This improves calculations and an explanation as to why more powerful 3 concentration tools cannot be employed is also provided. on the previous bound of O(mn ). Such graphs are used to better understand the behaviour of phylogenetic meth- C R. Subramanian ods and recommend parameter choices and diagnostic cri- The Institute of Mathematical Sciences, Chennai, INDIA. teria. The limiting factor in these analyses has been the [email protected] difficulty in constructing such graphs for large numbers of trees. We also develop the first efficient algorithms for con- structing the nearest-neighbor interchange (NNI) and tree Kunal Dutta bisection-and-reconnection (TBR) graphs. These new al- DataShape, INRIA Sophia Antipolis-Mediterranee, gorithms are enabled by a change of perspective: rather [email protected] than focusing on the trees and checking for pairs of adja- cencies, we enumerate the potential adjacencies themselves in the form of structures called “agreement forests.’ To CP0 turn this observation into an efficient algorithm, we de- A Practical Fpt Algorithm for Flow Decomposition velop two tools: SDLNewick, the first unique string rep- and Transcript Assembly resentation for agreement forests, and a new AFContainer data structure which efficiently stores tree adjacencies us- The Flow Decomposition problem, which asks for the ing such strings. smallest set of weighted paths that covers a flow on a DAG, has recently been used as an important computa- Chris Whidden, Frederick Matsen tional step in transcript assembly. We prove the problem Fred Hutchinson Cancer Research Center is in FPT when parameterized by the number of paths by [email protected], [email protected] giving a practical linear fpt algorithm. Further, we im- plement and engineer a Flow Decomposition solver based on this algorithm, and evaluate its performance on RNA- CP0 sequence data. Crucially, our solver finds exact solutions Quicksort Is Optimal For Many Equal Keys while achieving runtimes competitive with a state-of-the- art heuristic. Finally, we contextualize our design choices I prove that the average number of comparisons for median- with two hardness results related to preprocessing and of-k Quicksort (with fat-pivot a.k.a. three-way partition- weight recovery. Specifically, k-Flow Decomposition does ing) is asymptotically only a constant αk times worse than not admit polynomial kernels under standard complexity the lower bound for sorting random multisets of n elements ε assumptions, and the related problem of assigning (known) with Ω(n ) duplicates of each value (for any ε>0). The − weights to a given set of paths is NP-hard. constant is αk =ln(2)/ Hk+1 H(k+1)/2 ,whichconverges to1ask →∞, so Quicksort is asymptotically optimal Kyle Kloster for inputs with many duplicates. This partially resolves NCSU a conjecture by Sedgewick and Bentley (1999, 2002) and Computer Science constitutes the first progress on the analysis of Quicksort [email protected] with equal elements since Sedgewick’s 1977 article. Sebastian Wild Philipp Kuinke David R. Cheriton School of Computer Science RWTH Aachen University University of Waterloo [email protected] [email protected] Michael O’Brien NC State University CP0 [email protected] Parameterizing the Hardness of Binary Search Tree Access Sequences by Inversion Counts Felix J. Reidl North Carolina State University We study a new way of measuring the expected perfor- [email protected] mance of various binary search tree algorithms that is be- tween the worst and the average case. Our starting point is Fernando Sanchez Villaamil the correspondence between binary search trees and inser- RWTH Aachen University tion sequences, and we will measure the difficulty of such [email protected] sequences based on inversion counts. This measure nat- urally interpolates between random and sequential inser- tion orders. We show that if the tree is randomly picked Blair Sullivan from all trees built upon insertion length n permutations North Carolina State University with t inversions, the  height of the tree can be bounded by [email protected] 2 { n − } O(n log n/ min t, 2 t ). Andrew van Der Poel Meng He NC State University Dalhousie University 40 DA18 Abstracts

[email protected] Deeparnab Chakrabarty Dartmouth College Richard Peng USA Georgia Tech [email protected] [email protected] Monika Henzinger Yinzhan Xu Univeristy of Vienna, Austria Massachusetts Institute of Technology [email protected] [email protected] Danupon Nanongkai KTH Royal Institute of Technology CP1 Sweden [email protected] Incremental√ Topological Sort and Cycle Detection in O˜(m n) Expected Total Time CP1 In the incremental cycle detection problem edges are in- ˜ 2 serted to a directed graph (initially empty) and the algo- Dynamic Bridge-Finding in O(log n) Amortized rithm has to report once a directed cycle is formed in the Time graph. A closely related problem to the incremental cycle We present a deterministic fully-dynamic data structure for detection is that of the incremental topological sort prob- maintaining information about the bridges in a graph. We lem, in which edges are inserted to an acyclic graph and support updates in O˜(log2 n) amortized time, and can find the algorithm has to maintain a valid topological sort on a bridge in the component of any given vertex, or a bridge the vertices at all times. Both incremental cycle detection separating any two given vertices, in O(log n/ log log n) and incremental topological sort have a long history. The worst case time. Our bounds match the current best for state of the art is a recent breakthrough of Bender, Fine- bounds for deterministic fully-dynamic connectivity up to man, Gilbert and Tarjan [TALG 2016], with two differ- log log n factors. The previous best dynamic bridge find- ent algorithms with respective total update times of O˜(n2) ing was an O˜(log3 n) amortized time algorithm by Tho- · { 1/2 2/3} and O(m min m ,n ). The two algorithms work for rup [STOC2000], which was a bittrick-based improvement both incremental cycle detection and incremental topolog- on the O(log4 n) amortized time algorithm by Holm et ical sort. In this paper we introduce a novel technique that al.[STOC98, JACM2001]. Our approach is based on a dif- allows us to improve upon the state of the art for a wide ferent and purely combinatorial improvement of the algo- range of graph sparsity. Our√ algorithms has a total ex- rithm of Holm et al., which by itself gives a new combi- ˜ pected update time of O(m n) for both the incremental natorial O˜(log n3n) amortized time algorithm. Combin- cycle detection and the topological sort problems. ing it with Thorup’s bittrick, we get down to the claimed O˜(log2 n) amortized time. Essentially the same new trick Shiri Chechik can be applied to the biconnectivity data structure from Tel-Aviv University, Israel [STOC98, JACM2001], improving the amortized update [email protected] time to O˜(log3 n). We also offer improvements in space. We describe a general trick which applies to both of our Aaron Bernstein new algorithms, and to the old ones, to get down to linear Technical University of Berlin, Germany space, where the previous best use O(m + n log n log log n). [email protected] Our result yields an improved running time for deciding whether a unique perfect matching exists in a static graph. CP1 Dynamic Algorithms for Graph Coloring Jacob Holm University of Copenhagen We design fast dynamic algorithms for proper vertex and University of Copenhagen edge colorings in a graph undergoing edge insertions and [email protected] deletions. In the static setting, there are simple linear time algorithms for (Δ + 1)-vertex coloring and (2Δ − 1)- EvaRotenberg,MikkelThorup edge coloring in a graph with maximum degree Δ. It is University of Copenhagen natural to ask if we can efficiently maintain such color- [email protected], [email protected] ings in the dynamic setting as well. We get the follow- ing three results. (1) We present a randomized algorithm which maintains a (Δ + 1)-vertex coloring with O(log Δ) CP1 expected amortized update time. (2) We present a deter- Decremental Transitive Closure and Shortest Paths ministic algorithm which maintains a (1 + o(1))Δ-vertex for Planar Digraphs and Beyond coloring with O(polylog Δ) amortized update time. (3) We present a simple, deterministic algorithm which main- In this paper we show that the tools used to obtain the tains a (2Δ − 1)-edge coloring with O(log Δ) worst-case best state-of-the-art decremental algorithms for reachabil- update time. This improves√ the recent O(Δ)-edge color- ity and approximate shortest paths in directed graphs can ing algorithm with O˜( Δ) worst-case update time [Baren- be successfully combined with the existence of small sep- boimM17] arators in certain graph classes. In particular,√ for graph classes admitting balanced separators of size O( n), such Sayan Bhattacharya as planar, bounded-genus and minor-free graphs, we show University of Vienna that for both transitive closure and (1 + )-approximate Vienna, Austria all pairs shortest paths (where is constant), there ex- [email protected] ist decremental algorithms with O(n3/2) total update time DA18 Abstracts 41

√ and O( n) worst-case query time. Additionally, for the curve on a surface with non-positive Euler characteristic, case of planar graphs, we show that for any t ∈ [1,n], where n is the number of self-intersection points. Results 2 there exists a decremental transitive closure√ algorithm with of Hass and Scott imply a matching O(n ) upper bound O(n2/t) total update time and O( t) worst-case query for contractible curves on orientable surfaces. Second, we time. In particular, for t = n2/3, if all the edges are even- prove that any closed curve on any orientable surface can be tightened as much as possible using at most O(n4)ho- tually deleted, we obtain O(n1/3) amortized update and motopy moves. Except for a few special cases, only na¨ıve query times. Most of the algorithms we obtain are correct exponential upper bounds were previously known for this with high probability against an oblivious adversary. problem. Adam Karczmarz University of Warsaw Hsien-Chih Chang [email protected] University of Illinois, Urbana-Champaign [email protected]

CP1 Jeff Erickson Incremental DFS Algorithms: a Theoretical and Department of Computer Science Experimental Study University of Illinois at Urbana-Champaign jeff[email protected] Depth first search (DFS) tree is a fundamental data struc- ture for solving graph problems, which can be built in David Letscher O(m+n)timeforagraphwithn vertices and m edges. For Saint Louis University undirected graphs, the two prominent incremental DFS al- [email protected] gorithms are ADFS1√ and ADFS2, achieving total update 3/2 2 time of O(n m)andO(n ) respectively. For DAGs, Arnaud de Mesmay the only non-trivial incremental DFS algorithm is FDFS, CNRS, GIPSA-lab requiring total O(mn) update time. However, no such al- 2 Universit´e Grenoble-Alpes gorithm with o(m ) bound exist for directed graphs. We [email protected] carry out extensive experimental and theoretical analysis of incremental DFS algorithms in random and real graphs, Saul Schleimer deriving the following  results. n Warwick Mathematics Institute 1. For inserting 2 edges uniformly randomly, ADFS1, University of Warwick ADFS2 and FDFS perform equally well taking Θ(n2) [email protected] time experimentally, which is much better than their worst case bounds. We complement this result with Eric Sedgwick 2 probabilistic analysis proving O˜(n ) bound on their DePaul University time complexities. [email protected] 2. We also design a simple algorithm for both undirected and directed graphs, which theoretically matches and Dylan Thurston experimentally outperforms the state-of-the-art algo- Department of Mathematics rithm in dense random graphs. Indiana University 3. Even for real world graphs, both ADFS1 and FDFS [email protected] perform much better than their known bounds. Again, we design a simple algorithm each for directed Stephan Tillmann and undirected graphs, which perform very well on School of Mathematics and Statistics real graphs, and almost always matches FDFS in di- The University of Sydney rected graphs. [email protected]

Surender Baswana IIT Kanpur CP2 [email protected] The Classical Complexity of Boson Sampling

Ayush Goel We study the classical complexity of the exact Boson Sam- Indian Institute of Technology Kanpur pling problem where the objective is to produce provably India correct random samples from a particular quantum me- [email protected] chanical distribution. The computational framework was proposed in STOC ’11 by Aaronson and Arkhipov in 2011 Shahbaz Khan as an attainable demonstration of ‘quantum supremacy’. IIT Kanpur Since its introduction Boson Sampling has been the subject [email protected] of intense international research in the world of quantum computing. On the face of it, the problem is challenging for classical computation. Aaronson and Arkhipov show that CP2 exact Boson Sampling is not efficiently solvable by a clas- #P NP Tightening Curves on Surfaces Via Local Moves sical computer unless P = BPP and the polynomial hierarchy collapses to the third level. The fastest known We prove new upper and lower bounds on the number of exact classical algorithm  for the standard Boson Sampling m n homotopy moves required to tighten a closed curve on a problem requires O(( n )n2 ) time to produce samples for compact orientable surface (with or without boundary) as a system with input size n and m output modes, making much as possible. First we prove that Ω(n2)movesare it infeasible for anything but the smallest values of n and required in the worst case to simplify a contractible closed m. We give an algorithm that is much faster, running in 42 DA18 Abstracts

O(n2n + poly(m, n)) time and O(m) additional space. The an improved approximation ratio of 14. algorithm is simple to implement and has low constant fac- tor overheads. As a consequence our classical algorithm is Sharath Raghvendra, Mariette Wessels able to solve the exact Boson Sampling problem for sys- Virginia Tech tem sizes far beyond current photonic quantum computing [email protected], [email protected] experimentation, thereby significantly reducing the likeli- hood of achieving near-term quantum supremacy in the context of Boson Sampling. CP2 Polycubes with Small Perimeter Defect Raphael Clifford University of Bristol, UK A polycube is a face-connected set of cubical cells on Z3. raphael.cliff[email protected] to-date, no formulae enumerating polycubes by volume (number of cubes) or perimeter (number of empty cubes Peter Clifford neighboring the polycube) are known. We present a few University of Oxford formulae enumerating polycubes with a fixed deviation peter.cliff[email protected] from the maximum possible perimeter. Gill Barequet CP2 Technion - Israel Institute of Technology [email protected] A Near-Quadratic Lower Bound for the Size of Quantum Circuits of Constant Treewidth Andrei Asinowski We show that any quantum circuit of treewidth t, built Vienna University of Technology 2 [email protected] from r-qubit gates, requires at least Ω( n ) gates 2O(r·t) ·log4 n to compute the element distinctness function. Our result Yufei Zheng generalizes a near-quadratic lower bound for quantum for- Technion - Israel Institute of Technology mula size obtained by Roychowdhury and Vatan [SIAM J. [email protected] on Computing, 2001]. The proof of our lower bound fol- lows by an extension of Neˇciporuk’s method to the context of quantum circuits of constant treewidth. This extension CP3 is made via a combination of techniques from structural Metric Violation Distance: Hardness and Approx- graph theory, tensor-network theory, and the connected- imation component counting method, which is a classic tool in al- gebraic geometry. In particular, an essential key to proving Metric data plays an important role in various settings, our lower bound is the development of a new algorithm for for example, in metric-based indexing, clustering, classi- tensor network contraction which may be of independent fication, and approximation algorithms in general. Due interest. to measurement error, noise, or an inability to completely gather all the data, a collection of distances may not sat- Mateus De Oliveira Oliveira isfy the basic metric requirements, most notably the trian- University of Bergen gle inequality. In this paper we initiate the study of the [email protected] metric violation distance problem: given a set of pairwise distances, modify the minimum number of distances such CP2 that the resulting set forms a metric. Three variants of the problem are considered, based on whether distances are al- A Grid-Based Approximation Algorithm for the lowed to only decrease, only increase, or the general case Minimum Weight Triangulation Problem which allows both decreases and increases. We show that while the decrease only variant is polynomial time solvable, Given a set of n points on a plane, in the Minimum Weight the increase only and general variants are NP-Complete, Triangulation problem, we wish to find a triangulation that and moreover cannot in polynomial time be approximated minimizes the sum of Euclidean length of its edges. This in- to any ratio better than the minimum vertex cover prob- credibly challenging problem was only recently shown to be lem. We then provide approximation algorithms for the NP-Hard. In this paper we present a novel polynomial-time increase only and general variants of the problem, by prov- algorithm that computes an expected 14-approximation of ing interesting necessary and sufficient conditions on the the minimum weight triangulation—a constant that is sig- optimal solution, which are used to approximately reduce nificantly smaller than what has been previously known. In to a purely combinatorial problem for which we provide our algorithm, we use grids to partition the edges into lev- matching asymptotic upper and lower bounds. els where shorter edges appear at smaller levels and edges with similar lengths appear at the same level. We then tri- Chenglin Fan, Benjamin A. Raichel, Gregory Van Buskirk angulate the point set incrementally by introducing edges University of Texas at Dallas in increasing order of their levels. Edges of any level i +1 [email protected], [email protected], are added in two steps. In the first step, we partition the [email protected] boundary of any non-triangulated face into reflex chains and add edges between successive chains using a variant of the well-known ring heuristic to generate a partial tri- CP3 ˆ angulation Ai. In the second step, we greedily add non- Race Detection and Reachability in Nearly Series- ˆ intersecting level i +1 edgesto Ai in increasing order of Parallel Dags their length and obtain a partial triangulation Ai+1.The ring heuristic yields only an O(log n)-approximation√ and A program is said to have a determinacy race if logically the greedy heuristic achieves only a Θ( n)-approximation. parallel parts of a program access the same memory loca- Therefore, it is surprising that their combination leads to tion and one of the accesses is a write. These races are DA18 Abstracts 43

generally bugs in the program, as different schedules of the u to v. It was recently discovered that λo(u, v)canbe program can lead to different results. Most prior work on approximated up to a constant multiplicative factor us- detecting these races focuses on a subclass of programs with ing edge-connectivity between u and v and the minimum series-parallel or nested parallelism. This paper presents value of another parameter that measures “how far from a race-detection algorithm for detecting races in a more a bipartite graph’ the part of the graph around u and v general class of programs, namely programs that include is. In this paper, we formalize this second ingredient and arbitrary ordering constraints in additional to the series- call it the perimeter. It is proved that it is a submodu- parallel constructs. Our race-detection algorithm performs lar function on the vertex-sets of a graph, and using this a serial execution of the program, augmented to detect fact, we obtain a version of the Gomory-Hu Theorem in 2 races, in O(T1 + k ) time, where T1 is the sequential run- which minimum edge-cuts are replaced by sets of minimum ning time of the original program and k is the number of perimeter. We construct (in polynomial time) a rooted for- non series-parallel constraints. The main technical novelty est structure, analogous to the Gomory-Hu tree of a graph, is a new data structure for answering reachability queries in which encodes a collection of minimum-perimeter vertex- nearly series-parallel (SP) directed acyclic graphs (DAGs). sets. Although the classical Gomory-Hu Theorem extends Given as input a graph comprising an n-node series par- to arbitrary symmetric submodular functions, this result is allel graph and k additional non-SP edges, the total con- novel and indicates a possibility for further generalizations. struction time of the data structure is O(n + k2), and each These results have implications to the study of path and reachability query can be answered in O(1) time. The data trail systems with parity constraints. Two such applica- structure is traversally incremental, meaning that it sup- tions are presented: an efficient data structure for storing ports the insertion of nodes/edges, but only as they are approximate odd edge-connectivities for all pairs of vertices discovered through a graph traversal. in a graph, and a rough structure theorem for graphs with no “totally odd’ immersion of a large complete graph. Jeremy Fineman Georgetown University Bojan Mohar,RossChurchley jfi[email protected] Simon Fraser University [email protected], [email protected] Kunal Agrawal Washington University in St. Louis [email protected] CP3 The Complexity of Independent Set Reconfigura- Joseph Devietti tion on Bipartite Graphs University of Pennsylvania [email protected] We settle the complexity of the Independent Set Reconfig- uration problem on bipartite graphs under all three com- monly studied reconfiguration models. We show that un- I-Ting Angelina Lee, Robert Utterback, Changming Xu der the token jumping or token addition/removal model Washington University in St. Louis the problem is NP-complete. For the token sliding model, [email protected], [email protected], we show that the problem remains PSPACE-complete. [email protected] Daniel Lokshtanov University of Bergen CP3 [email protected] Planar Graphs As L-Intersection Or L-Contact Graphs Amer Mouawad The L-intersection graphs are the graphs that have a rep- University of Bergen, Norway resentation as intersection graphs of axis-parallel L shapes [email protected] in the plane. A subfamily of these graphs are {L, |, −}- contact graphs which are the contact graphs of axis par- CP4 allel L, |,and− shapes in the plane. We prove here two results that were conjectured by Chaplick and Ueckerdt Recognizing Weak Embeddings of Graphs in 2013. We show that planar graphs are L-intersection graphs, and that triangle-free planar graphs are {L, |, −}- We present an efficient algorithm for a problem in the in- terface between clustering and graph embeddings. An em- contact graphs. These results are obtained by a new and → simple decomposition technique for 4-connected triangu- bedding ϕ : G M of a graph G into a 2-manifold M lations. Our results also provide a much simpler proof of maps the vertices in V (G) to distinct points and the edges the known fact that planar graphs are segment intersection in E(G) to interior-disjoint Jordan arcs between the corre- graphs. sponding vertices. In applications in clustering, cartogra- phy, and visualization, nearby vertices and edges are often Daniel Goncalves, Lucas Isenmann, Claire Pennarun bundled to a common node or arc, due to data compression LIRMM (CNRS & Univ. Montpellier) or low resolution. This raises the computational problem [email protected], [email protected], pen- of deciding whether a given map ϕ : G → M comes from [email protected] an embedding. A map ϕ : G → M is a weak embedding if it can be perturbed into an embedding ψε : G → M with ϕ−ψε <εfor every ε>0. A polynomial-time algorithm CP3 for the problem was recently found by [Fulek and Kynˇcl, A Submodular Measure and Approximate 2017], which reduces to solving a system of linear equa- 2ω ≤ 4.75 Gomory-Hu Theorem for Packing Odd Trails tions over Z2. It runs in O(n ) O(n )time,where ω ≈ 2.373 is the matrix multiplication exponent and n is Motivated by a problem about totally odd immersions of the number of vertices and edges of G.Weimprovethe graphs, we define the odd edge-connectivity λo(u, v)asthe running time to O(n log n) by generalizing a technique de- maximum number of edge-disjoint trails of odd length from veloped for the case that G is a cycle and the embedding 44 DA18 Abstracts

n(1− 1 ) is a simple polygon [Akitaya et al., 2016], which combines which runs in time 2 O(s·ω·4ω ) . This is the first local constraints on the orientation of subgraphs directly, algorithm to achieve exponential speed-up over brute thereby eliminating the need for solving large systems of force for the satisfiability of linear size circuits with linear equations. treewidth bounded by a constant greater than 1. For treewidth 1, our algorithm significantly outperforms Hugo A. Akitaya − 2 the previously fastest 2n(1 1/O(s )) time satisfiability Tufts University algorithm by Santhanam. hugo.alves [email protected] • Our second main result is an algorithm for True Radoslav Fulek Quantified Boolean Circuit Satisfiability for circuits Institute of Science and Technology Austria of treewidth ω, in which every input gate has fanout ω [email protected] at most s, which runs in time 2n(1−1/O(s·ω·4 )). Our algorithm is the first to achieve exponential speedup Csaba D. T´oth over brute force for such circuits. California State University Northridge [email protected] • We also show that the number of wires of any constant treewidth circuit that computes the majority function must be super-linear by utilizing the structural prop- CP4 erties of low treewidth circuits. A Polynomial Excluded-Minor Approximation of Treedepth Daniel Lokshtanov Treedepth is a well-studied graph invariant in the family of University of Bergen “width measures’ that includes treewidth and pathwidth. [email protected] Understanding these invariants in terms of excluded mi- nors has been an active area of research. The recent Grid Ivan Mikhailin Minor Theorem of Chekuri and Chuzhoy (2014) establishes UC San Diego that treewidth is polynomially approximated by the largest [email protected] k × k grid minor. In this paper, we give a similar polyno- mial excluded-minor approximation for treedepth in terms Ramamohan Paturi of three basic obstructions: grids, tree, and paths. Specif- University of California, San Diego ically, we show that there is a constant c such that every [email protected] graph of treedepth ≥ kc contains one of the following mi- nors (each of treedepth ≥ k): Pavel Pudlak • × the k k grid, Institute of Mathematics of the Czech Academy of • the complete binary tree of height k, Sciences [email protected] • the path of order 2k. Let us point out that we cannot drop any of the above graphs for our purpose. Moreover, given a graph G we CP4 can, in polynomial time, find either an embedding of one of these minors or conclude that treedepth of G is at most Minor-Matching Hypertree Width kc. This result has potential applications in a variety of settings where bounded treedepth plays a role. In addition In this paper we present a new width measure for a tree to some graph structural applications, we describe a sur- decomposition, minor-matching hypertree width, μ-tw,for prising application in circuit complexity and finite model graphs and hypergraphs, such that bounding the width theory from recent work of the second author. guarantees that set of maximal independent sets has a polynomially-sized restriction to each decomposition bag. Ken-ichi Kawarabayashi The relaxed conditions of the decomposition allow a much National Institute of Informatics, Japan wider class of graphs and hypergraphs to have bounded width compared to other tree decompositions. We show k [email protected] n (1− 1 +o(1)) that, for fixed k,thereare2 k (2) n-vertex graphs Benjamin Rossman of minor-matching hypertree width at most k.Anum- University of Toronto ber of problems including Maximum Independence Set, [email protected] k-Colouring, and Homomorphism of uniform hypergraphs permit polynomial-time solutions for hypergraphs with bounded minor-matching hypertree width and bounded CP4 rank. We show that for any given k and any graph Beating Brute Force for (Quantified) Satisfiability G, it is possible to construct a decomposition of minor- of Circuits of Bounded Treewidth matching hypertree width at most O(k3), or to prove that 3 μ-tw(G) >kin time nO(k ).Thisisdonebypresentinga We investigate the algorithmic properties of circuits of general algorithm for approximating the hypertree width bounded treewidth. Here the treewidth of a circuit C is de- of well-behaved measures, and reducing μ-tw to such mea- fined as the treewidth of the underlying undirected graph sure. The result relating the restriction of the maximal in- of C, after the vertices corresponding to input gates have dependent sets to a set S with the set of induced matchings been removed. Thus, boolean formulae correspond to cir- intersecting S in graphs, and minor matchings intersecting cuits of treewidth 1. S in hypergraphs, might be of independent interest. • Our first main result is an algorithm for counting the number of satisfying assignments of circuits with n Nikola G. Yolov input gates, treewidth ω,andatmosts · n gates, University of Oxford DA18 Abstracts 45

3 [email protected] • FVST and TPT admits a kernel with O(k 2 )vertices.

• CVD and Induced P3-Packing admits a kernel with 5 CP4 O(k 3 )vertices. Cliquewidth III: The Odd Case of Graph Coloring Our results resolve an open problem from WorKer 2010 on Parameterized by Cliquewidth the existence of kernels with O(k2−)verticesforFVST and CVD. All of our results are based on novel uses of old Max-Cut (MC), Edge Dominating Set (DS), Graph Col- and new “expansion lemmas’, and a weak form of crown oring (GC) and Hamiltonian Path (HP) on graphs decomposition. of bounded cliquewidth can be formulated in MSO2 (and therefore have linear-time algorithms on bounded Tien-Nam Le treewidth graphs), but cannot be formulated in MSO1 ENS de Lyon (which would have yielded linear-time algorithms on [email protected] bounded cliquewidth graphs). Each of these problems can be solved in time g(k)nf(k) on graphs of cliquewidth k. Daniel Lokshtanov Fomin et al. [SICOMP 2010] showed that the running times University of Bergen cannot be improved to g(k)nO(1) assuming W[1]=FPT. [email protected] However, this does not rule out non-trivial improvements to the exponent f(k) in the running times. Fomin et Saket Saurabh al. [SICOMP 2014] improved the running times for EDS IMSc +UiB and MC to nO(k), and proved g(k)no(k) lower bounds for [email protected] EDS, MC and HP assuming the ETH. Recently, Bergoug- noux, Kant´e and Kwon [WADS 2017] gave an nO(k)-time St´ephan Thomass´e algorithm for HP. Prior to this work, EDS, MC and HP ENS de Lyon were known to have tight nΘ(k) algorithmic upper and [email protected] lower bounds. In contrast, GC has an√ upper bound of k 4 nO(2 ) and a lower bound of merely no( k) (implicit from Meirav Zehavi the W[1]-hardness proof). We close the gap for GC by University of Bergen o(k) [email protected] proving a lower bound of n2 . This shows that GC be- haves qualitatively different from the other three problems. To the best of our knowledge, GC is the first natural prob- CP5 lem known to require exponential dependence on the pa- Stochastic Packing Integer Programs with Few rameter in the exponent of n. Queries Petr Golovach We consider a stochastic variant of the packing-type inte- University of Bergen, Norway ger linear programming problem, which contains random [email protected] variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, Daniel Lokshtanov and the task is to find a good solution by conducting a University of Bergen small number of queries. We propose a general framework [email protected] of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the per- Saket Saurabh formance of those algorithms. We also demonstrate our IMSc +UiB framework by applying it to a variety of stochastic combi- [email protected] natorial optimization problems such as matching, matroid, and stable set problems. Meirav Zehavi Ben-Gurion University Takanori Maehara [email protected] RIKEN Center for Advanced Intelligence Project Discrete Optimization Unit [email protected] CP5 Subquadratic Kernels for Implicit 3-Hitting Set Yutaro Yamaguchi and 3-Set Packing Problems University of Tokyo Department of Mathematical Informatics We consider four well-studied NP-complete pack- yutaro [email protected] ing/covering problems on graphs: Feedback Vertex Set in Tournaments (FVST), Cluster Vertex Deletion (CVD), Triangle Packing in Tournaments CP5 (TPT) and Induced P3-Packing. For these four prob- Randomized MWU for Positive LPs lems kernels with O(k2) vertices have been known for a long time. In fact, such kernels can be obtained by We describe and analyze a simple randomized multiplica- interpreting these problems as finding either a packing of tive weight update (MWU) based algorithm for approxi- k pairwise disjoint sets of size 3 (3-Set-Packing)ora mately solving positive linear programming problems, in hitting set of size at most k for a family of sets of size at particular, mixed packing and covering LPs. Given m ex- most 3 (3-Hitting-Set). In this paper, we give the first plicit linear packing and covering constraints over n vari- kernelsforFVST,CVD,TPTandInduced P3-Packing ables specified by N nonzero entries, Young [2014] gave a with a subquadratic number of vertices. Specifically, we deterministic algorithm returning an (1 + )-approximate obtain the following results. feasible solution (if a feasible solution exists) in O˜(N/ 2) 46 DA18 Abstracts

time. We show that a simple randomized implementation resource. matches this bound, and that randomization can be fur- ther exploited to improve the running time to O˜(N/ + Xue Zhu,ZhiyiHuang m/ 2 + n/ 3) (both with high probability). For instances The University of Hong Kong that are not very sparse (with at leastω ˜(1/ )nonzeroes [email protected], [email protected] per column on average), this improves the running time of O˜(N/ 2). The randomized algorithm also gives improved CP6 running times for several implicitly defined problems that arise in combinatorial and geometric optimization. The A Fast Approximation Scheme for Low- analysis of the general algorithm and the improvements Dimensional k-Means rely on techniques that we believe are of independent in- terest. We consider the popular k-means problem in d- dimensional Euclidean space. Recently Friggstad, Reza- Chandra Chekuri, Kent Quanrud pour, Salavatipour [FOCS’16] and Cohen-Addad, Klein, University of Illinois at Urbana-Champaign Mathieu [FOCS’16] showed that the standard local search [email protected], [email protected] algorithm yields a (1 + )-approximation in time (n · O(d) k)1/ , giving the first polynomial-time approximation scheme for the problem in low-dimensional Euclidean CP5 space. While local search achieves optimal approximation guarantees, it is not competitive with the state-of-the-art Algorithms to Approximate Column-Sparse Pack- 2 ing Problems heuristics such as the famous k-means++ and D -sampling algorithms. In this paper, we aim at bridging the gap be- Column-sparse packing problems arise in several contexts tween theory and practice by giving a (1+ )-approximation in both deterministic and stochastic discrete optimization. algorithm for low-dimensional k-means running in time −1 O(d) We present two unifying ideas, (non-uniform) attenuation n·k ·(log n)(d ) , and so matching the running time of and multiple-chance algorithms, to obtain improved ap- the k-means++ and D2-sampling heuristics up to polylog- proximation algorithms for some well-known families of arithmic factors. We speed-up the local search approach such problems. As three main examples, we attain the by making a non-standard use of randomized dissections integrality gap, up to lower-order terms, for known LP that allows to find the best local move efficiently using a relaxations for k-column sparse packing integer programs quite simple dynamic program. We hope that our tech- (Bansal et al., Theory of Computing, 2012) and stochas- niques could help design better local search heuristics for tic k-set packing (Bansal et al., Algorithmica, 2012), and geometric problems. go “half the remaining distance” to optimal for a major integrality-gap conjecture of F¨uredi, Kahn and Seymour Vincent Cohen-Addad on hypergraph matching (Combinatorica, 1993). CNRS, LIP6, Universit´e Pierre et Marie Curie Paris, France Brian Brubach, Karthik Abinav Sankararaman [email protected] University of Maryland College Park [email protected], [email protected] CP6 Aravind Srinivasan Hierarchical Clustering: Objective Functions and University of Maryland Algorithms [email protected] Hierarchical clustering is a recursive partitioning of a Pan Xu dataset into clusters at an increasingly finer gran- ular- University of Maryland College Park ity. Motivated by the fact that most work on hierarchi- [email protected] cal clustering was based on providing algo- rithms, rather than optimizing a specific objective, [18] framed similarity- based hierarchical clustering as a combinatorial optimiza- CP5 tion problem, where a good hierarchical clustering is one that minimizes some cost function. He showed that this Near Optimal Jointly Private Packing Algorithm cost function has certain desirable properties, such as in Via Dual Multiplicative Weight Update order to achieve optimal cost, disconnected components must be separated first and that in structureless graphs, We present an improved ( , δ)-jointly differentially private i.e., cliques, all clusterings achieve the same cost. We take algorithm for packing problems. Our algorithm gives a an axiomatic approach to defining good objective func- feasible output that is approximately optimal up to an αn tions for both similarity and dissimilarity-based hierarchi- additive factor√ as long as the supply of each resource is cal clustering. We char- acterize a set of admissible ob- at least O˜( m/α ), where m is the number of resources. jective functions (that includes the one introduced by Das- This improves the previous result by Hsu et al. (SODA ’16), gupta) that have the property that when the input admits a which requires the total supply to be at least O˜(m2/α ), natu- ral ground-truth hierarchical clustering, the ground- and only guarantees approximate feasibility in terms of truth clustering has an optimal value. total violation. Further, we complement our algorithm with an almost matching hardness result, showing that Vincent Cohen-Addad Ω( m ln(1/δ)/α ) supply is necessary for any ( , δ)-jointly CNRS, LIP6, Universit´e Pierre et Marie Curie differentially private algorithm to compute an approxi- Paris, France mately optimal packing solution. Finally, we introduce an [email protected] alternative approach that runs in linear time, is exactly truthful, can be implemented online, and can be -jointly Varun Kanade differentially private, but requires a larger supply of each University of Oxford DA18 Abstracts 47

[email protected] mum (while still using at most z outliers). Furthermore, we show how our analysis can be extended to general met- Claire Mathieu rics for k-Means with outliers to obtain a (25 + , 1+ ) CNRS, Ecole normale sup´erieure bicriteria. [email protected] Zachary Friggstad University of Alberta, Canada Frederik Mallmann-Trenn [email protected] MIT [email protected] Kamyar Khodamoradi, Mohsen Rezapour, Mohammad Salavatipour CP6 University of Alberta Adaptive Hierarchical Clustering Using Ordinal [email protected], [email protected], Queries [email protected] In many applications of clustering (for example, ontolo- gies or clusterings of animal or plant species), hierarchical CP6 clusterings are more descriptive than a flat clustering. A The Bane of Low-Dimensionality Clustering hierarchical clustering over n elements is represented by a rooted binary tree with n leaves, each corresponding to one In this paper, we give a conditional lower bound of nΩ(k) element. The subtrees rooted at interior nodes capture the for the classic k-median and k-means clustering objectives clusters. In this paper, we study active learning of a hier- (where n is the size of the input), even in low-dimensional archical clustering using only ordinal queries. An ordinal Euclidean space of dimension four, assuming the Exponen- query consists of a set of three elements, and the response tial Time Hypothesis (ETH). We also consider k-median to a query reveals the two elements (among the three ele- (and k-means) with penalties where each point need not be ments in the query) which are “closer’ to each other than to assigned to a center, in which case it must pay a penalty, the third one. We say elements x and y are closer to each and extend our lower bound to at least three-dimensional other than z if there exists a cluster containing x and y, but Euclidean space. This stands in stark contrast to many not z. Our main result is a deterministic algorithm that other geometric problems such as the traveling salesman learns the underlying hierarchical clustering using at most problem, or computing an independent set of unit spheres. n log2 n adaptive ordinal queries. We generalize our algo- While these problems benefit from the so-called (limited) rithm to be robust in a model in which each query response blessing of dimensionality, as they can be solved in time − /d − /d is correct independently with probability p>1/2, and ad- O(k1 1 ) n1 1 − n or 2 in d dimensions, our work shows that versarially incorrect with probability 1 p. We show that widely-used clustering objectives have a lower bound of in the presence of noise, our algorithm outputs the correct nΩ(k), even in dimension four. We complete the picture by hierarchical clustering with probability at least 1−δ,using considering the two-dimensional case: we show that there O(n(log n +log(1/δ))) adaptive ordinal queries. For our is no algorithm that solves the penalized version in time results, adaptivity is crucial: we prove that even in the ab- √ 3 o( k) sence of noise, every non-adaptive algorithm requires Ω(n ) less√ than n , and provide a matching upper bound of ordinal queries in the worst case. nO( k). The main tool we use to establish these lower bounds is the placement of points on the moment curve, Ehsan Emamjomeh-Zadeh,DavidKempe which takes its inspiration from constructions of point sets University of Southern California yielding Delaunay complexes of high complexity. [email protected], [email protected] Vincent Cohen-Addad CNRS, LIP6, Universit´e Pierre et Marie Curie CP6 Paris, France Approximation Schemes for Clustering with Out- [email protected] liers Arnaud de Mesmay Clustering problems are well-studied in a variety of fields Ecole Normale Superieur such as data science, operations research, and computer [email protected] science. Such problems include variants of centre loca- tion problems, k-Median, and k-Means to name a few. In some cases, not all data points need to be clustered; some Eva Rotenberg may be discarded for various reasons. For instance, some Department of Applied Mathematics and Computer points may arise from noise in a data set or one might be Science willing to discard a certain fraction of the points to avoid Technical University of Denmark, Denmark incurring unnecessary overhead in the cost of a clustering [email protected] solution. We study some clustering problems with out- liers: Uncapaciated Facility Location (UFL) with uniform Alan Roytman opening costs, k-Median, and k-Means. Our main focus Department of Computer Science is when the metric is a doubling metric (including fixed- University of Copenhagen, Denmark dimensional Euclidean metrics) or is the shortest path met- [email protected] rics of a graph from a minor-closed family of graphs. For Uncapacitated Facility Location with outliers on such met- rics we show that a multiswap simple local search heuristic CP7 yields a PTAS. With a bit more work, we extend this to bi- Near-Optimal Compression for the Planar Graph criteria approximations for k-Median and k-Means where, Metric for any constant >0, we can find a solution using (1+ )k centres whose cost is at most a (1 + )-factor of the opti- The Planar Graph Metric Compression Problem is to com- 48 DA18 Abstracts

pactly encode the distances among k nodes in a planar Oren Weimann graph of size n. Two naive solutions are to store the graph University of Haifa using O(n) bits, or to explicitly store the distance matrix [email protected] with O(k2 log n) bits. The only lower bounds are from the seminal work of Gavoille, Peleg, Prennes, and Raz Christian Wulff-Nilsen [SODA’01], who rule out compressions into a polynomi- Department of Computer Science ally smaller number of bits, for weighted planar graphs, University of Copenhagen but leave a large gap√ for unweighted planar graphs. For [email protected] example, when k = n, the upper bound is O(n)and their constructions imply an Ω(n3/4) lower bound. Our main result is a new√ compression of the planar graph met- CP7 ric into O˜(min(k2, kn)) bits, which is optimal up to log A Faster Algorithm for Minimum-Cost Bipartite factors. Our data structure circumvents a lower bound for Perfect Matching in Planar Graphs compression using minors, and the lower bound of Gavoille et al. for weighted planar graphs. This is an unexpected Given a weighted planar bipartite graph G(A∪B,E)where and decisive proof that weights can make planar graphs in- each edge has a positive integer edge cost, we give an herently more complex. Moreover, we design√ a new Subset O˜(n4/3 log nC) time algorithm to compute minimum-cost Distance Oracle for planar graphs with O˜( kn) space, and perfect matching; here C is the maximum edge cost in O˜(n3/4) query time. Our work carries strong messages to the graph. The previous best-known planarity exploit- 3/2 related fields. In particular, the O(n1/2)vs.Ω(n1/3) gap ing algorithm has a running time of O(n log n)andis for distance labeling schemes in planar graphs cannot be achieved by using planar separators (Lipton and Tarjan resolved with current lower bound techniques. On the pos- ’78). Our algorithm is based on the bit-scaling paradigm itive side, we introduce the powerful tool of unit-monge to (Gabow and Tarjan ’89). For each scale, our algorithm ex- planar graph algorithms. ecutes O(n1/3) iterations of Gabow and Tarjan’s algorithm in O(n4/3) time. Next, it constructs a compressed residual Amir Abboud graph H with O(n2/3)verticesandO(n) edges. This is Stanford University achieved by constructing an r-division with r = n2/3.For [email protected] each partition of the r-division, there is an edge between two vertices of H if and only if they are connected by a Pawel Gawrychowski directed path inside the partition. Using existing efficient University of Wroclaw shortest-path data structures, the remaining O(n2/3)ver- [email protected] tices are matched by iteratively computing a minimum-cost augmenting path each taking O˜(n2/3) time. Augmenta- Shay Mozes tion changes the residual graph, so the algorithm updates IDC Herzliya, Israel the compressed representation for each affected partition [email protected] in O˜(n2/3) time. We bound the total number of affected partitions over all the augmenting paths by O(n2/3 log n). Oren Weimann ˜ 4/3 University of Haifa Therefore, the total time taken by the algorithm is O(n ). [email protected] Mudabir Kabir Asathulla CP7 Virginia Tech [email protected] Better Tradeoffs for Exact Distance Oracles in Pla- nar Graphs Sanjeev Khanna We present an O(n1.5)-space distance oracle for directed University of Pennsylvania planar graphs that answers distance queries in O(log n) [email protected] time. Our oracle both significantly simplifies and signifi- cantly improves the recent oracle of Cohen-Addad, Dahl- Nathaniel Lahn, Sharath Raghvendra gaard and Wulff-Nilsen [FOCS 2017], which uses O(n5/3)- Virginia Tech space and answers queries in O(log n)time.Weachieve [email protected], [email protected] this by designing an elegant and efficient point location data structure for Voronoi diagrams on planar graphs. We CP7 further show a smooth tradeoff between space and query- time. For any S ∈ [n, n2], we show an oracle of size S Voronoi Diagrams on Planar Graphs, and Comput- 5/3 that answers queries in O˜(max{1,n1.5/S}) time. This new ing the Diameter in Deterministic O˜(n ) Time tradeoff is currently the best (up to polylogarithmic fac- tors) for the entire range of S and improves by polynomial We present an explicit and efficient construction of addi- factors over all previously known tradeoffs for the range tively weighted Voronoi diagrams on planar graphs. Let S ∈ [n, n5/3]. G be a planar graph with n vertices and b sites that lie on a constant number of faces. We show how to prepro- 2 Pawel Gawrychowski cess G in O˜(nb ) time so that one can compute any ad- University of Wroclaw ditively weighted Voronoi diagram for these sites in O˜(b) [email protected] time. We use this construction to compute the diameter of a directed planar graph with real arc lengths in O˜(n5/3) Shay Mozes time. This improves the recent breakthrough result of IDC Herzliya, Israel Cabello (SODA’17), both by improving the running time [email protected] (from O˜(n11/6)), and by using a deterministic algorithm. DA18 Abstracts 49

It is in fact the first truly subquadratic deterministic al- of options. In this setting each user draws i.i.d. from some gorithm for this problem. Our use of Voronoi diagrams to distribution a utility function mapping each item in the compute the diameter follows that of Cabello, but he used universe to a real-valued utility. The user is then offered abstract Voronoi diagrams, which makes his diameter al- a subset of the items, and selects the one of maximum gorithm more involved, more expensive, and randomized. utility. A max-distribution oracle for this choice model As in Cabello’s work, our algorithm can also compute the takes any subset of items and returns the probability (over Wiener index of a planar graph (i.e., the sum of all pairwise the distribution of utility functions) that each will be se- distances) within the same bounds. Our construction of lected. A discrete choice algorithm, given access to a max- Voronoi diagrams for planar graphs is of independent inter- distribution oracle, must return a function that approxi- est. It has already been used to obtain fast exact distance mates the oracle. We show three primary results. First, oracles for planar graphs [Cohen-Addad et al. FOCS’17]. we show that any algorithm exactly reproducing the or- acle must make exponentially many queries. Second, we Pawel Gawrychowski show an equivalent representation of the distribution over University of Wroclaw utility functions, based on permutations, and show that [email protected] if this distribution has support size k, then it is possible to approximate the oracle using O(nk) queries. Finally, Haim Kaplan we consider settings in which the subset of items is always Tel-Aviv University small. We give an algorithm that makes less than n(1−/2)K [email protected] queries, each to sets of size at most (1 − /2)K,inorder to approximate the max-distribution oracle on every set of Shay Mozes size |T |≤K with statistical error at most . IDC Herzliya, Israel [email protected] Flavio Chierichetti Sapienza University Micha Sharir Dipartimento di Informatica TelAvivUniversity&NewYorkUniversity fl[email protected] [email protected] Ravi Kumar Oren Weimann Google Inc. University of Haifa [email protected] [email protected] Andrew Tomkins CP7 Google [email protected] Minimum Cut of Directed Planar Graphs in O(n log log n) Time

We give an O(n log log n) time algorithm for computing CP8 the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the pre- Nearly Tight Bounds for Sandpile Transience on vious fastest O(n log3 n) solution. Interestingly, while in the Grid undirected planar graphs both min cut and min st-cut have O(n log log n) solutions, in directed planar graphs our re- sult makes min cut faster than min st-cut, which currently We use techniques from the theory of electrical networks requires O(n log n). to give nearly tight bounds for the transience class of the Abelian sandpile model on the two-dimensional grid up to Shay Mozes polylogarithmic factors. The Abelian sandpile model is a IDC Herzliya, Israel discrete process on graphs that is intimately related to the [email protected] phenomenon of self-organized criticality. In this process, vertices receive grains of sand, and once the number of Cyril Nikolaev grains exceeds their degree, they topple by sending grains University of Haifa, Israel to their neighbors. The transience class of a model is the [email protected] maximum number of grains that can be added to the sys- tem before it necessarily reaches its steady-state behavior Yahav Nussbaum or, equivalently, a recurrent state. Through a more re- Tel-Aviv University fined and global analysis of electrical potentials and ran- [email protected] dom walks, we give an O(n4 log4 n) upper bound and an Ω(n4) lower bound for the transience class of the n×n grid. Oren Weimann Our methods naturally extend to nd-sized d-dimensional − − University of Haifa grids to give O(n3d 2 logd+2 n) upper bounds and Ω(n3d 2) [email protected] lower bounds.

CP8 David Durfee, Matthew Fahrbach,YuGao Discrete Choice, Permutations, and Reconstruc- Georgia Institute of Technology tion [email protected], [email protected], [email protected] In this paper we study the well-known family of Random Utility Models, developed over 50 years ago to codify ra- Tao Xiao tional user behavior in choosing one item from a finite set Shanghai Jiao Tong University 50 DA18 Abstracts

xt [email protected] mutation is transformed into the next by applying either the operation σ, a rotation to the left, or τ, a transposition of the first two symbols? Knuth rated the challenge of find- CP8 ing a cyclic solution for odd n (cycles do not exist for even Time and Space Efficient Representations of Dis- n>2) at 48/50 in The Art of Computer Programming, tributive Lattices which makes it Volume 4’s hardest open problem since the ‘middle levels’ problem was solved by M¨utze. In this paper We present a space-efficient data structure using O(n log n) we solve the 40 year-old question by Nijenhuis and Wilf, bits that represents a distributive lattice on n elements and by providing a simple successor rule to generate each suc- supports finding meets and joins in O(log n)time.Our cessive permutation. We also present insights into how our data structure extends the ideal tree structure of Habib solution can be modified to find a Hamilton cycle for odd and Nourine which occupies O(n log n)bitsofspaceand n. requires O(m) time to compute a meet or join, where m depends on the specific lattice and may be as large as n−1. Joe Sawada We also give an encoding of a distributive lattice using University of Guelph 10 7 n + O(log n) bits, which is very close to the information School of Computer Science theoretic lower bound. This encoding can be created or [email protected] decompressed in O(n log n)time. Aaron Williams Corwin Sinnamon Simon’s Rock University of Waterloo, Waterloo, Ontario [email protected] [email protected]

CP9 CP8 The Gotsman-Linial Conjecture is False Consistent Hashing with Bounded Loads In 1991, Craig Gotsman and Nathan Linial conjectured In dynamic load balancing, we wish to allocate a set of that for all n and d, the average sensitivity of a degree-d clients (balls) to a set of servers (bins) with the goal of polynomial threshold function on n variables is maximized minimizing the maximum load of any server and also min- by the degree-d symmetric polynomial which computes the imizing the number of moves after adding or removing a parity function on the d layers of the hypercube with Ham- server or a client. We want a hashing-style solution where ming weight closest to n/2. We refute the conjecture for we given the ID of a client can efficiently find its server in almost all d and for almost all n, and we confirm the con- a distributed dynamic environment. In such a dynamic en- jecture in many of the remaining cases. vironment, both servers and clients may be added and/or removed from the system in any order. In particular, we Brynmor Chapman consider a problem with balls and bins, and given a user- MIT specified balancing parameter c =1+ >1, we aim to [email protected] find a hashing scheme with no load above c/, referred to as the capacity of the bins. We show that in our hashing scheme when a ball or bin is inserted or deleted, the ex- CP9 pected number of balls that have to be moved is within Approximate Local Decoding of Cubic Reed- 1 ≤ a multiplicative factor of O( 2 ) of the optimum for 1 Muller Codes Beyond the List Decoding Radius log c (Theorem ??) and within a factor 1 + O( c )oftheop- timum for ≥ 1(Theorem??). Technically, the latter We consider the question of decoding Reed-Muller codes n bound is the most challenging to prove. It implies that we over F2 beyond their list-decoding radius. Since, by def- for superconstant c, we only pay a negligible cost in ex- inition, in this regime one cannot demand a list-decoder tra moves. We also get the same bounds for the simpler efficient in the message length, we seek an approximate de- coder: Given a word F and radii r >r>0, the goal is problem where we instead of a user specified balancing pa-  rameter have a fixed bin capacity C for all bins, and define to output a codeword within radius r of F ,ifthereex- c =1+ = C/. ists a codeword within distance r. As opposed to the list decoding problem, it suffices here to output any codeword Vahab Mirrokni with this property, since the list may be too large if r ex- Google Inc. ceeds the list decoding radius. Prior to our work, such [email protected] decoders were known for Reed-Muller codes of degree 2, due to works of Wolf and the second author [FOCS 2011]. Mikkel Thorup In this work we make the first progress on this problem University of Copenhagen for the degree 3 where the list decoding radius is 1/8. We [email protected] show that there is a constant δ =1/2 − 1/8 > 1/8and an efficient approximate decoder, that given query access n → Morteza Zadimoghaddam to a function F : F2 F2, such that F is within distance Google r = δ − from a cubic polynomial, runs in time polynomial [email protected] in message length and outputs with high probability a cu- bic polynomial which is at distance at most r =1/2 −  from F ,where  is a quasi polynomial function of . CP8 A Hamilton Path for the Sigma-Tau Problem Pooya Hatami UT Austin Nijenhuis and Wilf asked the following question in their [email protected] Combinatorial Algorithms textbook from 1975: Can the permutations of {1, 2,...,n} be ordered so that each per- Madhur Tulsiani DA18 Abstracts 51

TTI Chicago ingredient is an algorithm for solving certain kinds of [email protected] systems of polynomial equations.

CP9 Aditya Potukuchi, Swastik Kopparty Rutgers University Coding Against Deletions in Oblivious and Online [email protected], [email protected] Models

We consider binary error correcting codes when errors are deletions. A basic challenge concerning deletion codes is CP9 (adv) Average-Radius List-Recoverability of Random determining p0 , the zero-rate threshold of adversarial deletions, defined to be the supremum of all p for which Linear Codes there exists a code family with rate bounded away from 0 We analyze the list-decodability, and related notions, of capable of correcting a fraction p of adversarial√ deletions. (adv) ≥ − random linear codes. This has been studied extensively be- A recent construction shows p0 2 1, and the triv- fore: there are many different parameter regimes and many (adv) ≤ 1 ial upper bound, p0 2 , is the best known. Perhaps different variants. Previous works have used complemen- (adv) surprisingly, we do not know whether p0 =1/2. In tary styles of arguments—which each work in their own this work, we explore two related error models: oblivious parameter regimes but not in others—and moreover have deletions and online deletions, which are in between ran- left some gaps in our understanding of the list-decodability dom and adversarial deletions in power. In the oblivious of random linear codes. In particular, none of these ar- model, the channel can inflict an arbitrary pattern of pn guments work well for list-recovery, a useful generaliza- deletions, picked without knowledge of the codeword. We tion of list-decoding. In this work, we present a new ap- prove the existence of binary codes of positive rate that proach, which works across parameter regimes and fur- can correct any fraction p<1 of oblivious deletions, es- ther generalizes to list-recovery. This argument unifies the (obliv) landscape of this problem, and can establish the follow- tablishing that the associated zero-rate threshold p0 equals 1. For online deletions, where the channel decides ing new results: (*) Random linear codes over large fields are list-recoverable and list-decodable up to near-optimal whether to delete bit xi based only on knowledge of bits rates (within a multiplicative factor of 0.99), with list sizes x1x2 ...xi, define the deterministic zero-rate threshold for (on,d) that depend quasi-polynomially on the gap-to-capacity. (*) online deletions p to be the supremum of p for which 0 First quasipolynomial list sizes for high-rate list-recovery there exist deterministic codes against an online channel of random linear codes. (*) Our results exponentially im- causing pn deletions with low average probability of error. (adv) 1 (on,d) 1 prove the list size bounds in the best known results on We prove p0 = 2 if and only if p0 = 2 . linear-time list-recoverable codes and the near-linear time list decodable codes (with optimal rate). Venkatesan Guruswami Carnegie Mellon University Atri Rudra [email protected] Univ. of Washington atri@buffalo.edu Ray Li Stanford University Mary Wootters [email protected] Stanford University [email protected] CP9 Syndrome Decoding of Reed-Muller Codes and CP10 Tensor Decomposition over Finite Fields Prophet Secretary for Combinatorial Auctions and Reed-Muller codes are some of the oldest and most widely Matroids studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic prop- The secretary and the prophet inequality problems are cen- erties. A recent beautiful result of Saptharishi, Shpilka tral to the field of Stopping Theory. Recently, there has and Volk showed that for binary Reed-Muller codes of been a lot of work in generalizing these models to multi- length n and distance d = O(1), one can correct polylog(n) ple items because of their applications in mechanism de- random errors in poly(n) time. In this paper, we con- sign. The most important of these generalizations are to sider the problem of deciding Reed-Muller codes from the matroids and to combinatorial auctions (extends bipartite polylog(n)-bit long syndrome vector of a codeword cor- matching). Kleinberg-Weinberg [KW12] and Feldman et rupted in polylog(n) random coordinates. This problem al. [FGL15] show that for adversarial arrival order of ran- turns out to be equivalent to a basic question about com- dom variables the optimal prophet inequalities give a 1/2- puting tensor decomposition of random low-rank tensors approximation. For many settings, however, it’s conceiv- over finite fields. Our main result is that syndrome de- able that the arrival order is chosen uniformly at random, coding of Reed-Muller codes (and the equivalent tensor akin to the secretary problem. For such a random arrival decomposition problem) can be solved efficiently, i.e., in model, we improve upon the 1/2-approximation and ob- polylog(n) time. We give two algorithms for this problem: tain (1-1/e)- approximation prophet inequalities for both matroids and combinatorial auctions. This also gives im- 1. The first algorithm is a finite field variant of a classical provements to the results of Yan [Yan11] and Esfandiari algorithm for tensor decomposition over real numbers et al. [EHLM17] who worked in the special cases where due to Jennrich. This also gives an alternate proof for we can fully control the arrival order or when there is only the main result by Saptharshi et al. a single item. Our techniques are threshold based. We 2. The second algorithm is obtained by implementing convert our discrete problem into a continuous setting and the steps of the Berlekamp-Welch-style decoding al- then give a generic template on how to dynamically adjust gorithm of Saptharshi et al. in sublinear-time. A new these thresholds to lower bound the expected total welfare. 52 DA18 Abstracts

has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments af- Soheil Ehsani ter knowing how many items arrived. For this problem we University of Maryland at College Park show that there is no deterministic truthful and individu- [email protected] ally rational mechanism that, even with unbounded com- putational resources, gets any finite approximation factor MohammadTaghi Hajiaghayi to the optimal social welfare. University of Maryland [email protected] Vasilis Syrgkanis Microsoft Research Thomas Kesselheim [email protected] TU Dortmund [email protected] Nikhil R. Devanur Microsoft Research, Redmond Sahil Singla [email protected] CMU [email protected] Balasubramanian Sivan Google Research [email protected] CP10 A Framework for the Secretary Problem on the Intersection of Matroids CP10 Strong Algorithms for the Ordinal Matroid Secre- The secretary problem became one of the most promi- tary Problem nent online selection problems due to its numerous appli- cations in online mechanism design. The task is to select a In the ordinal Matroid Secretary Problem (MSP), elements maximum weight subset of elements subject to given con- from a weighted matroid are presented in random order to straints, where elements arrive one-by-one in random order, an algorithm that must incrementallty select a large weight revealing a weight upon arrival. The decision whether to independent set. However, the algorithm can only com- select an element has to be taken immediately after its ar- pare pairs of revealed elements without using its numerical rival. The different applications that map to the secretary value. An algorithm is α probability-competitive (PC) if problem ask for different constraint families to be handled. every element from the optimum appears with probability The most prominent ones are matroid constraints, which 1/α in the output. both capture many relevant settings and admit strongly We present a technique to design algorithms with strong competitive secretary algorithms. However, dealing with PC ratios, improving the guarantees for almost every ma- more involved constraints proved to be much more diffi- troid class considered in the literature: e.g., we get PC cult, and strong algorithms are known only for a few spe- ratios of 4 for graphic matroids (improving on 2e by Ko- cific settings. In this paper, we present a general frame- rula and P´al [ICALP 2009]) and of 5.19 for laminar ma- work for dealing with the secretary problem over the inter- troids (improving on 9.6 by Ma et al. [THEOR COM- section of several matroids. This framework allows us to PUT SYST 2016]). We also obtain new results for su- combine and exploit the large set of matroid secretary al- perclasses of k column sparse matroids, for hypergraphic gorithms known in the literature. As one consequence, we matroids, certain gammoids and graph packing matroids, get constant-competitive secretary algorithms over the in- and a 1 + O( log ρ/ρ) PC algorithm for uniform ma- tersection of any constant number of matroids whose corre-  sponding (single-)matroid secretary problems are currently troids of rank ρ based on Kleinberg’s 1 + O( 1/ρ) utility- known to have a constant-competitive algorithm. More- competitive algorithm [SODA 2005] for that class. over, we show that our results extend to submodular ob- Our second contribution are algorithms for the ordi- jectives. nal MSP on arbitrary matroids of rank ρ.Wedevise an O(log ρ) PC algorithm and an O(log log ρ)ordinal- Moran Feldman competitive algorithm, a weaker notion of competitiveness Open University of Israel but stronger than the utility variant. These are based on [email protected] the O(log log ρ) utility-competitive algorithm by Feldman et al. [SODA 2015]. Ola Svensson Jose A. Soto EPFL Universidad de Chile ola.svensson@epfl.ch [email protected] Rico Zenklusen Abner Turkieltaub ETH Zurich Universidad de chile [email protected] [email protected]

CP10 Victor Verdugo Universidad de Chile & Truthful Multi-Parameter Auctions with Online Ecole´ normale sup´erieure, Supply: An Impossible Combination [email protected] We study a basic auction design problem with online sup- ply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the CP10 second item type may or may not arrive. The auctioneer Variance Reduced Value Iteration and Faster Al- DA18 Abstracts 53

gorithms for Solving Markov Decision Processes build upon a new decomposition technique that, for any convex set C, allows for approximating any mixed-integer In this paper we provide faster algorithms for approxi- description of C by the intersection of C with the union of mately solving discounted Markov Decision Processes in a small number of affine subspaces. multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with |S| states, |A| actions, dis- Alfonso Cevallos, Stefan Weltge, Rico Zenklusen count factor γ ∈ (0, 1), and rewards in the range [−M, M], ETH Zurich we show how to compute an -optimal policy, with proba- [email protected], ste- bility 1 − δ in time [email protected], [email protected]       |S||A| M 1 O |S|2|A| + log log . (1 − γ)3 δ CP11 Proximity Results and Faster Algorithms for Inte- This contribution reflects the first nearly linear time, nearly ger Programming Using the Steinitz Lemma linearly convergent algorithm for solving DMDP’s for inter- mediate values of γ. We also show how to obtain improved We consider integer programming problems in standard sublinear time algorithms and provide an algorithm which form max{cT x : Ax = b, x ≥ 0,x∈ Zn} where A ∈ Zm×n, − computes an -optimal policy with probability 1 δ in time b ∈ Zm and c ∈ Zn. We show that such an integer program    O(m) O(m) |S||A|M 2 1 canbesolvedintimem · Δ , where Δ is an upper O log (1 − γ)4 2 δ bound on each absolute value of an entry in A and b.This improves upon the longstanding best bound of Papadim- 2 2 provided we can sample from the transition function in itriou (1981) of mO(m ) · ΔO(m ) andaddressesanopen O(1) time. We obtain our results by combining approx- problem raised by Fomin. Our result relies on a lemma imate value iteration with new techniques in variance re- of Steinitz that states that a set of vectors in Rm that is duction. Our fastest algorithms leverage further insights contained in the unit ball and that sum up to zero can be to ensure that our algorithms make monotonic progress ordered such that all partial sums are of norm bounded by towards the optimal value. This paper is one of few in- m. We also use the Steinitz lemma to show that the 1- stances in using sampling to obtain a linearly convergent distance of an optimal integer and fractional solution of the linear programming algorithm and we hope that the anal- integer program, also under the presence of upper bounds m ysis may be useful more broadly. on the variables, is bounded by m · (2 · m · ΔA +1) .Here ΔA is an upper bound on the absolute values of the entries Xian Wu, Aaron Sidford of A only. The novel strength of our bound is that it is Stanford University independent of n. We provide evidence for the significance [email protected], [email protected] of our bound by applying it to general knapsack problems where we obtain structural and algorithmic results that Mengdi Wang improve upon the recent literature. Department of Operations Research and Financial Engineering Friedrich Eisenbrand Princeton University Ecole Polytechnique Federale de Lausanne [email protected] friedrich.eisenbrand@epfl.ch

Yinyu Ye Robert Weismantel Stanford University ETH Zuerich [email protected] [email protected]

CP11 CP11 Lifting Linear Extension Complexity Bounds to the Approximating Weighted Tree Augmentation Via Mixed-Integer Setting Chv´atal-Gomory Cuts

Mixed-integer mathematical programs are ubiquitous in In the weighted tree augmentation problem (WTAP), we Operations Research and related fields. However, there are given an undirected tree G =(V,E) and an additional is still very little known about what can be expressed by set of edges L called links, with costs c ≥ 1 for all links. small mixed-integer programs. In particular, prior to this The goal is to choose a minimum cost subset S ⊆ L such work, it was open whether some classical problems, like the that G =(V,E∪S) is 2-edge-connected. In the unweighted minimum odd-cut problem, can be expressed by a compact case, with c = 1 for all links, the problem is called the tree mixed-integer program with few (even constantly many) augmentation problem (TAP). Both problems are known integer variables. We provide a general framework for lift- to be APX-hard, and the best known approximation fac- ing inapproximability results of extended formulations to tors are 2 for WTAP [Frederickson and J´aJ´a] and 1.5 for the setting of mixed-integer extended formulations, and ob- TAP [Kortsarz and Nutov]. Adjiashvili (SODA ’17) gave tain almost tight lower bounds on the number of integer a1.96418 + -approximation algorithm for WTAP under variables needed to describe a variety of classical combina- the assumption that all link costs are bounded by a con- torial optimization problems. Among the implications we stant. This is the first approximation with a better guar- obtain, we show that any mixed-integer extended formu- antee than 2 not requiring a special structure of the tree or lation of sub-exponential size for the matching polytope, the links. In this paper, we improve Adjiashvili’s approx- cut polytope, or dominant of the odd-cut polytope, needs imation to a 1.5+ -approximation for WTAP under the Ω(n/ log n) many integer variables, where n is the number bounded cost assumption. We achieve this by introducing a of vertices of the underlying graph. Conversely, the above- strong LP that combines {0, 0.5}-Chv´atal-Gomory cuts for mentioned polyhedra admit polynomial-size mixed-integer the standard LP for the problem with bundle constraints formulations with only O(n)orO(n log n)(forthetravel- from Adjiashvili. We show that our LP can be solved ef- ing salesman polytope) many integer variables. Our results ficiently and that it is exact for some instances that arise 54 DA18 Abstracts

at the core of Adjiashvili’s approach. This results in an algorithms, including pseudo-polynomial ones. In partic- improved performance guarantee of 1.5+ . ular, we can obtain strongly polynomial algorithms by a repeated application of the conditional gradient or of the Martin Gro Fujishige-Wolfe algorithm. Combined with the geomet- University of Waterloo ric rescaling technique, the black-box approach provides [email protected] a O((n5EO + n6)log2 n) algorithm. Finally, we show that our technique can be used to obtain a simplifed variant of Samuel Fiorini the O(n3 log2 nEO +n4 logO(1) n) cutting-plane SFM algo- Universit´e Libre de Bruxelles rithm of Lee, Sidford, and Wong. sfi[email protected] Daniel Dadush Jochen K¨onemann, Laura Sanit`a New York University University of Waterloo [email protected] [email protected], [email protected] Laszlo A. Vegh, Giacomo Zambelli London School of Economics CP11 [email protected], [email protected] Submodular Minimization Under Congruency Constraints CP12 Submodular function minimization (SFM) is a fundamen- More Logarithmic-Factor Speedups for 3SUM, tal and efficiently solvable problem class in combinatorial (median,+)-Convolution, and Some Geometric optimization with a multitude of applications in various 3SUM-Hard Problems fields. Surprisingly, there is only very little known about constraint types under which SFM remains efficiently solv- We present an algorithm that solves the 3SUM problem able. The arguably most relevant non-trivial constraint for n real numbers in O((n2/ log2 n)(log log n)O(1))time, class for which polynomial SFM algorithms are known improving previous solutions by about a logarithmic fac- are parity constraints. Parity constraints capture classi- tor. Our framework for shaving off two logarithmic factors cal combinatorial optimization problems like the odd-cut can be applied to other problems, such as (median,+)- problem, and they are a key tool in a recent technique to convolution/matrix multiplication and algebraic general- efficiently solve integer programs with a constraint matrix izations of 3SUM. We also obtain the first subquadratic whose subdeterminants are bounded by two in absolute results on some 3SUM-hard problems in computational ge- value. We show that efficient SFM is possible even for ometry, for example, deciding whether (the interiors of) a a significantly larger class than parity constraints, by in- constant number of simple polygons have a common inter- troducing a new approach that combines techniques from section. Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we can show that efficient SFM is Timothy M. Chan possible over all sets of cardinality r mod m, as long as University of Illinois at Urbana-Champaign m is a constant prime power. This covers generalizations [email protected] of the odd-cut problem with open complexity status, and with relevance in the context of integer programming with higher subdeterminants. Moreover, our results settle two CP12 open questions raised by Geelen and Kapadia [Combina- Voronoi Tessellations in the Crt and Continuum torica, 2017] in the context of computing the girth and Random Maps of Finite Excess cogirth of certain types of binary matroids. Given a large graph G and k agents on this graph, we Martin N¨agele, Benny Sudakov, Rico Zenklusen consider the Voronoi tessellation induced by the graph dis- ETH Zurich tance. Each agent gets control of the portion of the graph [email protected], ben- that is closer to itself than to any other agent. We study [email protected], [email protected] the limit law of the vector Vor := (V1/n, V2/n, ..., Vk/n), whose i’th coordinate records the fraction of vertices of G controlled by the i’th agent, as n tends to infinity. We CP11 show that if G is a uniform random tree, and the agents Geometric Rescaling Algorithms for Submodular are placed uniformly at random, the limit law of vor is Function Minimization uniform on the (k − 1)-dimensional simplex. In particu- lar, when k = 2, the two agents each get a uniform ran- We present a new class of polynomial-time algorithms for dom fraction of the territory. In fact, we prove the result submodular function minimization (SFM), as well as a uni- directly on the Brownian continuum random tree (CRT), fied framework to obtain strongly polynomial SFM algo- and we also prove the same result for a “higher genus” rithms. Our new algorithms are based on simple iter- analogue of the CRT that we call the continuum random ative methods for the minimum-norm problem. We ex- unicellular map, indexed by a genus parameter g ≥ 0. As hibit two techniques to turn simple iterative methods into a key step of independent interest, we study the case when polynomial-time algorithms. Firstly, we use the geomet- G is a random planar embedded graph with a finite num- ric rescaling technique, which has recently gained atten- ber of faces. The main idea of the proof is to show that tion in linear programming. We adapt this technique to vor has the same distribution as another partition of mass 4 SFM and obtain a weakly polynomial bound O((n EO + Int := (I1/n, I2/n, ..., Ik/n)whereIj is the contour length 5 n )log(nL)). Secondly, we exhibit a general combinato- separating the i-th agent from the first one following it rial black-box approach to turn any strongly polynomial clockwise around the graph. εL-approximate submodular function minimization oracle into a strongly polynomial algorithm. This framework can Louigi Addario-Berry be applied to a wide range of combinatorial and continuous McGill University DA18 Abstracts 55

[email protected] ity of a given point set in the plane.

Omer Angel Sariel Har-Peled University of British Columbia Department of Computer Science [email protected] University of Illinois, Urbana Champaign [email protected] Guillaume Chapuy CNRS, IRIF, Universite Paris Diderot Mitchell F. Jones France University of Illinois at Urbana-Champaign [email protected] [email protected]

Christina Goldschmidt CP12 University of Oxford The Entropy of Backwards Analysis [email protected] Backwards analysis, first popularized by Seidel, is often the Eric´ Fusy simplest most elegant way of analyzing a randomized algo- CNRS, LIX, Ecole´ Polytechnique rithm. It applies to incremental algorithms where elements [email protected] are added incrementally, following some random permuta- tion, e.g., incremental Delauney triangulation of a pointset, where points are added one by one, and where we always CP12 maintain the Delauney triangulation of the points added On the Complexity of Range Searching Among thus far. For backwards analysis, we think of the per- Curves mutation as generated backwards, implying that the ith point in the permutation is picked uniformly at random Modern tracking technology has made the collection of from the i points not picked yet in the backwards direc- large numbers of densely sampled trajectories of moving tion. Backwards analysis has also been applied elegantly objects widely available. We consider a fundamental prob- by Chan to the randomized linear time minimum spanning lem encountered when analysing such data: Given n polyg- tree algorithm of Karger, Klein, and Tarjan. The question onal curves S in Rd,preprocessS into a data structure considered in this paper is how much randomness we need that answers queries with a query curve q and radius ρ for in order to trust the expected bounds obtained using back- the curves of S that have Fr´echet distance at most ρ to q. wards analysis, exactly and approximately. For the exact We initiate a comprehensive analysis of the space/query- case, it turns out that a random permutation works if and time trade-off for this data structuring problem. Our lower only if it is minwise, that is, for any given subset, each bounds imply that any data structure in the pointer model element has the same chance of being first.Minwise permu- model that achieves Q(n)+O(k) query time, where k is tations are known to have Θ(n) entropy, and this is then the output size, has to use roughly Ω (n/Q(n))2 space in also what we need for exact backwards analysis. However, theworstcase,evenifqueriesaremerepointsorlineseg- when it comes to approximation, the two concepts diverge ments. More importantly, we show that the space/query- dramatically. To get backwards analysis to hold within a time trade-off worsens by an exponential factor of input factor α, the random permutation needs entropy Ω(n/α). and query complexity. This behaviour addresses an open This contra ... Cut off due to character limit question in the range searching literature: whether it is possible to avoid the additional logarithmic factors in the Mathias Knudsen, Mikkel Thorup space and query time of a multilevel partition tree. We University of Copenhagen answer this question negatively. On the positive side, we [email protected], [email protected] show we can build data structures for the Fr´echet distance by using semialgebraic range searching. Here, our solution CP13 is in line with our lower bound in terms of the asymptotic number of levels in the data structure. Online Bipartite Matching with Amortized O(log2 N) Replacements Peyman Afshani MADALGO, Aarhus University In the online bipartite matching problem with replace- [email protected] ments, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one by one with all their incident edges. The goal is to main- Anne Driemel tain a maximum matching while minimizing the number of TU Eindhoven, The Netherlands changes (replacements) to the matching. We show that the Department of Mathematics and Computer Science greedy algorithm that always takes a shortest augmenting [email protected] path from the newly inserted vertex (denoted SAP) uses at most amortized O(log2 n) replacements per insertion, where n is the total number of vertices inserted. This is CP12 the first analysis to achieve a polylogarithmic number of re- On Separating Points by Lines placements for any strategy, almost matching the Ω(log n) lower bound.√ The previous best strategy achieved amor- Given a set of n points in the plane, its separability is the tized O( n) replacements [Bosek, Leniowski, Sankowski, minimum number of lines needed to separate all its pairs of Zych, FOCS 2014]. For SAP in particular, nothing better points from each other. We show that the minimum num- than the trivial O(n) bound was known except in special ber of lines needed to separate n points, picked randomly cases. Our analysis immediately implies the same upper (and uniformly) in the unit square, is Θ( n2/3), where Θ bound of O(log2 n) reassignments for the capacitated as- hides polylogarithmic factors. In addition, we provide a signment problem where each vertex on the static side of fast approximation algorithm for computing the separabil- the bipartition is initialized with the capacity to serve a 56 DA18 Abstracts

number of vertices. We also analyze the problem of mini- with competitive ratio O(k2k )andO(k3 log k)respectively. mizing the maximum server load. We show that if the final Our deterministic bound is based on a novel application of graph has maximum server√ load L, then SAP makes amor- the polynomial method to online algorithms, and essen- tized O(min{L log2 n, n log n}) reassignments.√ We also tially matches the long-known lower bound of 2k − 1. We { } O(k) show that this is close to tight because Ω(min L, n )re- also give a 22 -competitive deterministic algorithm for assignments can be necessary. weighted uniform metrics, which also essentially matches the recent doubly exponential lower bound for the problem. Aaron Bernstein Technical University of Berlin, Germany [email protected] Nikhil Bansal Department of Mathematics and Computer Science Jacob Holm Eindhoven University of Technology, Eindhoven, University of Copenhagen Netherlands University of Copenhagen [email protected] [email protected] Marek Elias Eva Rotenberg Eindhoven University of Technology, Netherlands University of Copenhagen [email protected] [email protected] Grigorios Koumoutsos, Jesper Nederlof TU Eindhoven CP13 [email protected], [email protected] Randomized Algorithms for Online Vector Load Balancing CP13 We study randomized algorithms for the online vector bin Online Facility Location Against a t-Bounded Ad- packing and vector scheduling problems. For vector bin versary packing, we achieve a competitive ratio of O˜(d1/B), where d is the number of dimensions and B the size of a bin. This In the streaming model, the order of the stream can ˜ 1/(B−1) improves the previous bound of O(d )byapolyno- significantly affect the difficulty of a problem. A t- mial factor, and is tight up to logarithmic factors. For semirandom stream was introduced as an interpolation be- log d vector scheduling, we show a lower bound of Ω( log log d )on tween random-order (t = 1) and adversarial-order (t = n) the competitive ratio of randomized algorithms, which is streams where an adversary intercepts a random-order the first result for randomized algorithms and is asymp- stream and can delay up to t elements at a time. IITK totically tight. Finally, we analyze the widely used “power Sublinear Open Problem #15 asks to find algorithms of two choices” algorithm for vector scheduling, and show whose performance degrades smoothly as t increases. We log d that its competitive ratio is O(log log n + log log d ), which show that the celebrated online facility location algorithm log t is optimal up to the additive O(log log n)termthatalso achieves an expected competitive ratio of O( log log t ). We appears in the scalar version of this algorithm. present a matching lower bound that any randomized algo- log t rithm has an expected competitive ratio of Ω( log log t ). We Yossi Azar use this result to construct an O(1)-approximate stream- Tel-Aviv University ing algorithm for k-median clustering that stores O(k log t) [email protected] points and has O(k log t) worst-case update time. Our tech- nique generalizes to any dissimilarity measure that sat- Ilan R. Cohen isfies a weak triangle inequality, including k-means, M- Tel Aviv University estimators, and p norms. The special case t =1yieldsan Tel Aviv University optimal O(k) space algorithm for random-order streams [email protected] as well as an optimal O(nk) time algorithm in the RAM model, closing a long line of research on this problem. Debmalya Panigrahi Duke University Harry Lang [email protected] Inria Saclay Johns Hopkins University [email protected] CP13 Competitive Algorithms for Generalized k-Server in Uniform Metrics CP13 Randomized Online Matching in Regular Graphs The generalized k-server problem is a far-reaching exten- sion of the k-server problem with several applications. In this paper we study the classic online matching prob- Here, each server si lies in its own metric space Mi.A lem, introduced in the seminal work of Karp, Vazirani and request is a k-tuple r =(r1,r2,...,rk) and to serve it, Vazirani (STOC 1990), in regular graphs. For such graphs, we need to move some server si to the point ri ∈ Mi, an optimal deterministic algorithm as well as efficient al- and the goal is to minimize the total distance traveled by gorithms under stochastic input assumptions were known. the servers. Despite much work, no f(k)-competitive al- In this work, we present a novel randomized algorithm gorithm is known for the problem for k>2 servers, even with competitive ratio tending to one on this family of for special cases such as uniform metrics and lines. Here, graphs, under adversarial arrival order. Our main con- we consider the problem in uniform metrics and give the tribution is√ a novel√ algorithm which achieves competitive first f(k)-competitive algorithms for general k.Inpartic- ratio 1−O log d/ d in expectation on d-regular graphs. ular, we obtain deterministic and randomized algorithms In contrast, we show that all previously-studied online algo- DA18 Abstracts 57

rithms have competitive ratio strictly bounded away from fied parametrization and algorithm. one. Moreover, we show the convergence rate of our algo- rithm’s competitive ratio to one is nearly tight, as no algo-√  Christopher De Sa rithm achieves competitive ratio better than 1 − O 1/ d . Cornell University Finally, we show that our algorithm yields a similar com- [email protected] petitive ratio with high probability, as well as guaranteeing each vertex a probability of being matched tending to one. Albert Gu Stanford University David Wajc [email protected] Carnegie Mellon University [email protected] Rohan Puttagunta Instagram Ilan R. Cohen [email protected] Tel Aviv University Tel Aviv University Christopher Re [email protected] Stanford University [email protected] CP14 Atri Rudra Approximating the Largest Root and Applications Univ. of Washington to Interlacing Families atri@buffalo.edu Abstract not available at time of publication CP14 Nima Anari Stanford University Improved Rectangular Matrix Multiplication Us- [email protected] ing Powers of the Coppersmith-Winograd Tensor In the past few years, successive improvements of the Shayan Oveis Gharan asymptotic complexity of square matrix multiplication University of Washington have been obtained by developing methods to analyze the [email protected] powers of the Coppersmith-Winograd tensor, a construc- tion introduced thirty years ago. We show how to gener- Amin Saberi alize this approach to make progress on the complexity of Management Science and Engineering rectangular matrix multiplication as well, by developing a Stanford University framework to analyze powers of tensors in an asymmetric [email protected] way. By applying this methodology to the fourth power of the Coppersmith-Winograd tensor, we improve the com- Nikhil Srivastava plexity of rectangular matrix multiplication. Let α denote U.C. Berkeley the maximum value such that the product of an n×nα ma- [email protected] trix by an nα × n matrix can be computed with O(n2+) arithmetic operations for any >0. By analyzing the fourth power of the Coppersmith-Winograd tensor, we ob- CP14 tain the new lower bound α>0.31389, which improves A Two-Pronged Progress in Structured Dense Ma- the previous lower bound α>0.30298 obtained five years trix Vector Multiplication ago by Le Gall (FOCS’12) from the analysis of the second power of the Coppersmith-Winograd tensor. More gener- We address the broad question of identifying classes of ally, we give faster algorithms computing the product of an structured dense square matrices that can be represented n × nk matrix by an nk × n matrix for any k =1.These with a linear (in dimension) number of parameters, and improvements lead to improvements in the complexity of for which operations such as matrix-vector multiplication a multitude of fundamental problems for which the bot- can be performed in a near-linear number of operations. In tleneck is rectangular matrix multiplication, such as com- this paper, we make progress on two fronts: First, we iden- puting the all-pair shortest paths in directed graphs with tify a notion of recurrence width of matrices. For matrices bounded weights. A with constant recurrence width, we design algorithms to compute Ab, AT b, and more with a near-linear number of Fran¸cois Le Gall operations. This notion of width is more fine-grained than Kyoto University classic structures such as orthogonal polynomial transforms [email protected] and Toeplitz/Cauchy/Vandermonde matrices, and thus we can compute superfast matrix-vector multiplication for all Florent Urrutia of them using the same core algorithm. Second, we adapt IRIF this algorithm to a matrix-vector multiplication algorithm Universit´eParisDiderot for a much more general class of matrices with displace- [email protected] ment structure: those with low displacement rank with respect to quasiseparable matrices. This result is a novel connection between matrices with displacement structure CP14 and those with rank structure, two large but previously A Tight Lower Bound for Counting Hamiltonian separate classes of structured matrices. This class includes Cycles Via Matrix Rank Toeplitz-plus-Hankel-like matrices, the Discrete Trigono- metric Transforms, and more, and captures all previously For even k, the matchings connectivity matrix Mk is a bi- known matrices with displacement structure under a uni- nary matrix that is indexed by the perfect matchings on 58 DA18 Abstracts

k vertices; it encodes whether the union of two matchings by its natural insensitivity to asymmetry. We extend a con- forms a single cycle. In [Cygan et al., Fast hamiltonicity struction of homology of digraphs due to Grigoryan, Lin, checking via bases of perfect matchings, STOC 2013], it Muranov and Yau to the persistent framework. The result, was shown√ that the rank of Mk over the integers√ modulo 2 which we call persistent path homology or PPH, encodes a k is Θ( 2 ). This was used to give an O∗((2 + 2)w)time rich level of detail about the asymmetric structure of the algorithm for counting Hamiltonian cycles modulo 2 on input directed network. For example, we prove that PPH graphs of pathwidth w. Furthermore, a tight lower bound identifies a class of directed cyclic networks as directed ana- under the Strong Exponential Time Hypothesis (SETH) logues of the circle. In general, PPH produces signatures ˇ was shown; this relied on finding a large permutation sub- that differ from natural extensions of Rips or Cech per- matrix within M . We present a new technique to obtain sistence to the directed setting, but we prove that PPH k ˇ similar complexity lower bounds when only a black-box agrees with Cech persistence on symmetric spaces. Addi- tionally, we prove that PPH agrees with Cechˇ persistence lower bound on the rank of Mk is given. To apply this on directed networks satisfying a local condition that we technique, we prove that the rank of Mk over the rationals is 4k, up to polynomial factors in k, using the represen- call square-freeness. We prove stability of PPH by utilizing tation theory of the symmetric group. We also show that a separate theory of homotopy of digraphs that is compat- k ible with path homology. Finally, we study computational the rank of Mk over the integers mod p is Ω(1.56 ) for any prime p = 2. As a consequence, we obtain that Hamilto- aspects of PPH, and derive an algorithm showing that over nian cycles cannot be counted in time O∗((6 − )w) for any field coefficients, computing PPH requires the same worst >0 unless SETH fails. This is essentially tight. We also case running time as standard persistent homology. obtain that Hamiltonian cycles cannot be counted modulo primes p =2intime O∗(3.56w ). Samir Chowdhury The Ohio State University Radu Curticapean [email protected] Simons Institute, Berkeley [email protected] Facundo Memoli Ohio State University Nathan Lindzey [email protected] Department of Combinatorics and Optimization University of Waterloo CP15 [email protected] On the Decidability of the Frechet Distance Be- Jesper Nederlof tween Surfaces TU Eindhoven We show that the Frechet distance between two piecewise [email protected] linear surfaces can be decided in finite time, hence, the problem is decidable. For the special case that one of the surfaces is a triangle, we show that the problem is CP14 in PSAPCE. In both cases, our computational model is A Fast Generalized DFT for Finite Groups of Lie a Turing Machine, and our algorithms rely on Cannys re- Type sult [STOC 1988] that the existential theory of the real numbers is decidable in PSPACE. We give an arithmetic algorithm using O(|G|ω/2+o(1))oper- ations to compute the generalized Discrete Fourier Trans- Amir Nayyeri form (DFT) over group G for finite groups of Lie type, School of Electrical Eng and Computer Science including the linear, orthogonal, and symplectic families Oregon State University and their variants, as well as all finite simple groups of Lie [email protected] type. Here ω is the exponent of matrix multiplication, so the exponent ω/2 is optimal if ω = 2. Previously, “expo- nent one’ algorithms were known for supersolvable groups CP15 and the symmetric and alternating groups. No exponent On the Complexity of Optimal Homotopies one algorithms were known (even under the assumption ω = 2) for families of linear groups of fixed dimension, and In this article, we provide new structural results and algo- indeed the previous best-known algorithm for SL2(Fq )had rithms for the Homotopy Height problem. In broad terms, exponent 4/3 despite being the focus of significant effort. this problem quantifies how much a curve on a surface We unconditionally achieve exponent at most 1.19 for this needs to be stretched to sweep continuously between two group, and exponent√ one if ω = 2. We also show that positions. More precisely, given two homotopic curves γ1 ω = 2 implies a 2 exponent for general finite groups G, and γ2 on a combinatorial (say, triangulated) surface, we which beats the longstanding previous best upper bound investigate the problem of computing a homotopy between (assuming ω =2)of3/2. γ1 and γ2 where the length of the longest intermediate curve is minimized. Such optimal homotopies are rele- Chris Umans,ChloeHsu vant for a wide range of purposes, from very theoretical California Institute of Technology questions in quantitative homotopy theory to more prac- [email protected], [email protected] tical applications such as similarity measures on meshes and graph searching problems. We prove that Homotopy Height is in the complexity class NP, and the correspond- CP15 ing exponential algorithm is the best one known for this Persistent Path Homology of Directed Networks problem. This result builds on a structural theorem on monotonicity of optimal homotopies, which is proved in a While standard persistent homology has been successful in companion paper. Then we show that this problem encom- extracting information from metric datasets, its applicabil- passes the Homotopic Fr´echet distance problem which we ity to more general data, e.g. directed networks, is hindered therefore also establish to be in NP, answering a question DA18 Abstracts 59

which has previously been considered in several different number of simplices of X. Moreover, we prove that this is settings. We also provide an O(log n)-approximation al- optimal: For every fixed d ≥ 2, we construct a family of gorithm for Homotopy Height on surfaces by adapting an simply connected simplicial complexes X such that for any earlier algorithm of Har-Peled, Nayyeri, Salvatipour and simplicial map representing a generator of πd(X), the size Sidiropoulos in the planar setting. of the triangulation of Sd on which the map is defined is exponential in size(X). Erin Chambers Saint Louis University Peter Franek [email protected] Institute of Computer Science Academy of Sciences of the Czech Republic Arnaud de Mesmay [email protected] Ecole Normale Superieur [email protected] Marek Filakovsky Masaryk University Tim Ophelders Brno Department of Mathematics and Computer Science m.fi[email protected] TU Eindhoven [email protected] Uli Wagner, Stephan Zhechev IST Austria [email protected], [email protected] CP15 Frechet-Stable Signatures Using Persistence Ho- mology CP16 Multivariate Fine-Grained Complexity of Longest For a metric space Y ,theFr´echet distance is a met- Common Subsequence ric on trajectories f,g :[0, 1] → Y that mini- mizes over continuous reparameterizations h of time of We revisit the classic combinatorial pattern matching prob- maxt∈[0,1] dY (f(t),g(h(t))). One can define the generalized lem of finding a longest common subsequence (LCS). For Fr´echet distance between more complex objects, functions strings x and y of length n, a textbook algorithm solves f : X → Y where X is some topological space that min- 2 2−ε → LCSintimeO(n ), but despite much effort, no O(n )- imizes over homeomorphisms from X X.Thismore time algorithm is known. Recent work indeed shows that general definition has been studied for surfaces and often such an algorithm would refute the Strong Exponential leads to computationally hard problems. We show how to Time Hypothesis (SETH). In spite of the quadratic-time compute in polynomial-time signatures for these functions barrier, an enduring scientific interest produced strongly for which the resulting metric on the signatures can also subquadratic time algorithms for special cases of interest, be computed in polynomial-time and provides a meaning- e.g., differential file comparison. In this paper, using the ful lower bound on the generalized Fr´echet distance. Our lens of fine-grained complexity, our goal is to (1) justify approach uses persistent homology and exploits the natural the lack of faster specialized algorithms since 1990 and invariance of persistence diagrams of functions to homeo- (2) determine whether some special cases of LCS admit morphisms of the domain. Our algorithm for computing faster algorithms than currently known. To this end, we the signatures in Euclidean spaces uses a new method for provide a systematic study of the multivariate complexity computing persistent homology of convex functions on sim- of LCS, taking into account all parameters previously dis- plicial complexes which may be of independent interest. cussed in the literature: the input size n := max{|x|, |y|}, {| | | |} Donald Sheehy the length of the shorter string m := min x , y ,the length L of an LCS of x and y, the numbers of deletions University of Connecticut − − [email protected] δ := m L and Δ := n L, the alphabet size, as well as the numbers of matching pairs M and dominant pairs d. For any class of instances defined by fixing each pa- CP15 rameter individually to a polynomial in terms of the input Computing Simplicial Representatives of Homo- size, we determine the optimal running time under SETH { } 1±o(1) topy Group Elements as (n +min d, δΔ,δm ) , up to lower order factors.

A central problem of algebraic topology is to understand Karl Bringmann the homotopy groups πd(X) of a topological space X.For Max Planck Institute for Informatics, the computational version of the problem, it is well known Saarland Informatics Campus, Germany that there is no algorithm to decide whether the funda- [email protected] mental group π1(X) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms Marvin K¨unnemann that, given a finite simplicial complex X that is simply Max-Planck-Institut f¨ur Informatik, Saarbr¨ucken, connected (i.e., with π1(X) trivial), compute the higher Germany homotopy group πd(X) for any given d ≥ 2. However, [email protected] these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≥ 2asanabstract finitely generated abelian group given by generators and relations, CP16 but they work with very implicit representations of the Tight Hardness for Shortest Cycles and Paths in elements of πd(X). Here we present an algorithm that, Sparse Graphs given a simply connected simplicial complex X, computes πd(X) and represents its elements as simplicial maps from Fine-grained reductions have established equivalences be- a suitable triangulation of the d-sphere Sd to X.Forfixed tween many core problems with O˜(n3)-time algorithms d, the algorithm runs in time exponential in size(X), the on n-node weighted graphs, such as Shortest Cycle, All- 60 DA18 Abstracts

Pairs Shortest Paths (APSP), Radius, Replacement Paths, University of Maryland Second Shortest Paths, and so on. These problems also [email protected] have O˜(mn)-time algorithms on m-edge n-node weighted graphs, and such algorithms have wider applicability. Are Mohammad Ghodsi these mn bounds optimal when m  n2? Starting from Sharif University of Technology the hypothesis that the minimum weight (2 + 1)-Clique Institute for Research in Fundamental Sciences (IPM) problem in edge weighted graphs requires n2+1−o(1) time, [email protected] we prove that for all sparsities of the form m =Θ(n1+1/), − there is no O(n2 +mn1 ) time algorithm for >0forany MohammadTaghi Hajiaghayi, Saeed Seddighin of the below problems: University of Maryland, College Park • Minimum Weight (2+1)-Cycle in a directed weighted [email protected], [email protected] graph, • Shortest Cycle in a directed weighted graph, CP16 • APSP in a directed or undirected weighted graph, Tree Edit Distance Cannot Be Computed in • Radius (or Eccentricities) in a directed or undirected Strongly Subcubic Time (unless Apsp Can) weighted graph, The edit distance between two rooted ordered trees with • Wiener index, Replacement Paths, Second Shortest n nodes labeled from an alphabet Σ is the minimum cost Path, and Betweenness Centrality in directed or undi- of transforming one tree into the other by a sequence of rected weighted graphs. elementary operations consisting of deleting and relabel- That is, we prove hardness for a variety of sparse graph ing existing nodes, as well as inserting new nodes. Tree problems from the hardness of a dense graph problem. Our edit distance is a well known generalization of string edit results also lead to new conditional lower bounds from sev- distance. The fastest known algorithm for tree edit dis- eral hypothesis for unweighted sparse graph problems in- tance runs in cubic O(n3) time and is based on a similar cluding k-cycle, shortest cycle, Radius, Wiener index and dynamic programming solution as string edit distance. In APSP. this paper we show that a truly subcubic O(n3−ε) time al- gorithm for tree edit distance is unlikely: For |Σ| =Ω(n), Andrea Lincoln, Virginia Vassilevska Williams a truly subcubic algorithm for tree edit distance implies MIT a truly subcubic algorithm for the all pairs shortest paths [email protected], [email protected] problem. For |Σ| = O(1), a truly subcubic algorithm for tree edit distance implies an O(nk−ε) algorithm for finding Ryan Williams a maximum weight k-clique. Thus, while in terms of up- Stanford University per bounds string edit distance and tree edit distance are [email protected] highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hy- CP16 pothesis [Backurs, Indyk STOC’15] whereas tree edit dis- tance exhibits the hardness of all pairs shortest paths. Our Approximating Edit Distance in Truly Sub- result provides a matching conditional lower bound for one quadratic Time: Quantum and MapReduce of the last remaining classic dynamic programming prob- The edit distance between two strings is defined as the lems. smallest number of insertions, deletions,andsubstitutions Karl Bringmann that need to be made to transform one of the strings to Max Planck Institute for Informatics, another one. Approximating edit distance in subquadratic Saarland Informatics Campus, Germany time is “one of the biggest unsolved problems in the field [email protected] of combinatorial pattern matching.” Our main result is a quantum constant approximation algorithm for comput- ing the edit distance in truly subquadratic time. More Pawel Gawrychowski precisely, we give an O(n1.858 ) quantum algorithm that University of Wroclaw approximates the edit distance within a factor of 7. We [email protected] further extend this result to an O(n1.781 ) quantum algo- rithm that approximates the edit distance within a larger Shay Mozes constant factor. Our solutions are based on a framework IDC Herzliya, Israel for approximating edit distance in parallel settings. This [email protected] framework requires as black box an algorithm that com- putes the distances of several smaller strings all at once. Oren Weimann For a quantum algorithm, we reduce the black box to met- University of Haifa ric estimation and provide efficient algorithms for approx- [email protected] imating it. We further show that this framework enables us to approximate edit distance in distributed settings. To this end, we provide a MapReduce algorithm to approx- CP16 imate edit distance within a factor of 3, with sublinearly On the Difference Between Closest, Furthest, many machines and sublinear memory. Also, our algorithm and Orthogonal Pairs: Nearly-Linear Vs Barely- runs in a logarithmic number of rounds. Subquadratic Complexity in Computational Geom- etry Mahdi Boroujeni Sharif University of Technology Pair-finding problems for n points in d-dimensional Eu- [email protected] clidean space (and p spaces more generally) have typi- cally had two kinds of running-time solutions: (Nearly- Soheil Ehsani Linear) less than dpoly(d) · n logO(d) n time, or (Barely- DA18 Abstracts 61

2−1/Θ(d) Subquadratic) f(d) · n time, for various f.For studied√ by Friedman and Linial (DCG 1993). They proved example, in Euclidean space, finding a Closest Pair among an Ω( d) lower bound on the competitive ratio, and con- d n points in R is nearly-linear, while known algorithms for jectured that a competitive ratio depending only on d is finding a Furthest Pair are only barely-subquadratic. Is possible. However, despite much interest in the problem, there a barrier to obtaining nearly-linear algorithms for the conjecture remains wide open. We consider the setting problems which are currently only barely-subquadratic? in which the convex bodies are nested: F1 ⊃ ... ⊃ Fn. We give a novel exact and deterministic self-reduction for The nested setting is closely related to extending the on- d the Orthogonal Vectors problem on n vectors in {0, 1} line LP framework of Buchbinder and Naor (ESA 2005) to to n vectors in Zω(log d) that runs in 2o(d) time. As a arbitrary linear constraints. Moreover, this setting retains consequence, barely-subquadratic problems such as Eu- much of the difficulty of the general setting and captures an clidean Furthest Pair, Euclidean Bichromatic Closest Pair, essential obstacle in resolving Friedman and Linial’s con- and Incidence Detection do not have O(n2−) time algo- jecture. In this work, we give the first f(d)-competitive rithms (in Turing models of computation) for dimensional- algorithm for chasing nested convex bodies in Rd. ity d = ω(log log n)2, unless the Orthogonal Vectors Con- jecture and the Strong Exponential Time Hypothesis are Nikhil Bansal false. That is, while the poly-log-log-dimensional case of Department of Mathematics and Computer Science Closest Pair is in n1+o(1) time, the poly-log-log-dimensional Eindhoven University of Technology, Eindhoven, case of Furthest Pair can encode larger-dimensional prob- Netherlands lems conjectured to require n2−o(1) time. Other related [email protected] results are shown. Martin Bohm Ryan Williams Charles University Stanford University [email protected]ff.cuni.cz [email protected] Marek Elias CP17 Eindhoven University of Technology, Netherlands [email protected] Boolean Function Analysis Meets Stochastic Opti- mization: An Approximation Scheme for Stochas- tic Knapsack Grigorios Koumoutsos TU Eindhoven The stochastic knapsack problem is the stochastic variant [email protected] of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and Seeun W. Umboh a collection of items where each item is associated with a University of Wisconsin-Madison profit and a probability distribution on its size. The goal [email protected] is to select a subset of items with maximum profit and violate the capacity constraint with probability at most p (referred to as the overflow probability). In this paper, CP17 we design efficient approximation schemes for this problem Stochastic Load Balancing on Unrelated Machines without relaxing the capacity constraint. • Our first result is in the case when item sizes are We consider the problem of makespan minimization: i.e., Bernoulli random variables. In this case, we design a scheduling jobs on machines to minimize the maximum (nearly) fully polynomial time approximation scheme load. For the deterministic case, good approximations are (FPTAS) which only relaxes the overflow probability. known even when the machines are unrelated. However, the problem is not well-understood when there is uncer- • Our second result generalizes the first result to the tainty in the job sizes. In our setting the job sizes are case when all the item sizes are supported on a (com- stochastic, i.e., the size of a job j on machine i is a random mon) set of constant size. variable Xij , whose distribution is known. The goal is to • Our third result is in the case when item sizes are so- find a fixed assignment of jobs to machines, to minimize called hypercontractive random variables i.e., random the expected makespan. For the identical machines special variables whose second and fourth moments are within case when the size of a job is the same across all machines, constant factors of each other. In other words, the a constant-factor approximation algorithm has long been kurtosis of the random variable is upper bounded by known. However, the problem has remained open even for a constant. In this case, we design a polynomial time the related machines case. Our main result is a constant- approximation scheme which relaxes both the overflow factor approximation for the most general case of unrelated probability and maximum profit. machines. The main technical challenge we overcome is ob- taining an efficiently computable lower bound for the op- Anindya De timal solution. We give an exponential-sized LP that we Northwestern University argue gives a strong lower bound. Then we show how to [email protected] round any fractional solution to satisfy only a small subset of the constraints, which are enough to bound the expected makespan of our solution. We then consider two general- CP17 izations. The first is the budgeted makespan minimization Nested Convex Bodies Are Chaseable problem. We extend our above result to a constant-factor. The second problem is the q-norm minimization problem. In the Convex Body Chasing problem, we are given an Here we give an O(q/ log q)-approximation algorithm. d initial point v0 ∈ R and an online sequence of n convex bodies F1,...,Fn. When we receive Fi, we are required Xiangkun Shen to move inside Fi. Our goal is to minimize the total dis- University of Michigan tance travelled. This fundamental online problem was first [email protected] 62 DA18 Abstracts

Anupam Gupta machines to minimize makespan, and show a lower bound 4 Carnegie Mellon University 3 . For the special case when the jobs are infinitesimal, [email protected] we give a 1.233-robust algorithm with an asymptotic lower bound of 1.207. We also study a case of fair allocation, Amit Kumar where the objective is to minimize the difference between IIT Delhi the maximum and minimum machine load. [email protected] Clifford Stein, Mingxian Zhong Columbia University Viswanath Nagarajan cliff@ieor.columbia.edu, [email protected] University of Michigan [email protected] CP18 CP17 Steiner Point Removal — Distant Terminals Don’t (Really) Bother An Alon-Boppana Type Bound for Weighted Graphs and Lowerbounds for Spectral Sparsifica- Given a weighted graph G =(V,E,w)withasetofk tion terminals T ⊂ V , the Steiner Point Removal problem seeks for a minor of the graph with vertex set T , such that the We prove the following Alon-Boppana type theorem for distance between every pair of terminals is preserved within general (not necessarily regular) weighted graphs: if G is a small multiplicative distortion. Kamma, Krauthgamer an n-node weighted undirected graph with dn/2edgesand and Nguyen used a ball-growing algorithm to show that 1/8 5 girth g>2d +1,andifλ1 ≤ λ2 ≤ ···λn are the eigen- the distortion is at most O(log k) for general graphs. In values of the (non-normalized) Laplacian of G,then this paper, we improve the distortion bound to O(log2 k).   The improvement is achieved based on a known algorithm λ 4 1 n ≥ 1+ √ − O that constructs terminal-distance exact-preservation minor 5 4 | | λ2 d d 8 with O(k ) (which is independent of V )vertices,andalso   two tail bounds on the sums of independent exponential (The Alon-Boppana theorem gives λn ≥ 1+ √4 − O 1 in random variables, which allow us to show that it is unlikely λ2 d d unweighted d-regular graphs of diameter >d1.5.) Our re- for a non-terminal being contracted to a distant terminal. sult implies a lower bound for spectral sparsifiers. Batson, Yun Kuen Cheung Spielman and Srivastava proved that for every G there is√ an Max Planck Institute for Informatics -spectral-sparsifier H of average degree d where ≈ 4√ 2 d Saarland Informatics Campus and the edges of H are a (weighted) subset of the edges [email protected] of G. Batson, Spielman and Srivastava also show that the bound on cannot be reduced below ≈ √2 when G is a d clique; our result implies that cannot be reduced below CP18 ≈ √4 . The method of Batson, Spielman and Srivastava Fast, Deterministic and Sparse Dimensionality Re- d proves a more general result, about sparsifying sums of duction rank-one matrices, and their method applies to an “online’ We provide a deterministic construction of the sparse setting.√ √ We show that for the online matrix setting the Johnson-Lindenstrauss transform of Kane & Nelson 4 2/ d bound is tight, up to lower order terms. (J.ACM 2014) which runs, under a mild restriction, in the time necessary to apply the sparse embedding matrix to Luca Trevisan the input vectors. Specifically, given a set of n vectors UC Berkeley in Rd and target error ε, we give a deterministic algo- [email protected] rithm to compute a {−1, 0, 1} embedding matrix of rank O((log n)/ε2)withO((log n)/ε) entries per column which Nikhil Srivastava preserves the norms of the vectors to within 1 ± ε. If NNZ, U.C. Berkeley the number of non-zero entries in the input set of vectors, [email protected] is Ω(d2), our algorithm runs in time O(NNZ·log n/ ). One ingredient in our construction is an extremely simple proof of the Hanson-Wright inequality for subgaussian random CP17 variables, which is more amenable to derandomization. As Scheduling When You Don’t Know the Number of an interesting byproduct, we are able to derive the essen- Machines tially optimal form of the inequality in terms of its func- tional dependence on the parameters. Often in a scheduling problem, there is uncertainty about the jobs to be processed. The issue of uncertainty regard- Daniel Dadush ing the machines has been much less studied. In this paper, New York University we study a scheduling environment in which jobs first need [email protected] to be grouped into some sets before the number of ma- chines is known, and then the sets need to be scheduled on machines without being separated. In order to evalu- CP18 ate algorithms in such an environment, we introduce the Steiner Point Removal with Distortion O(log K) idea of an α-robust algorithm, one which is guaranteed to return a schedule on any number m of machines that is In the Steiner point removal (SPR) problem, we are given within an α factor of the optimal schedule on m machine, aweightedgraphG =(V,E) and a set of terminals K ⊂ V where the optimum is not subject to the restriction that of size k. The objective is to find a minor M of G with the sets cannot be separated. Under such environment, we only the terminals as its vertex set, such that the dis- 5 give a ( 3 + )-robust algorithm for scheduling on parallel tance between the terminals will be preserved up to a DA18 Abstracts 63

small multiplicative distortion. Kamma, Krauthgamer and tantly Dehn fillings on link complements. Nguyen [KKN15] used a ball-growing algorithm with expo- nential distributions to show that the distortion is at most Arnaud de Mesmay O(log5 k). Cheung [Cheung18] improved the analysis of the Ecole Normale Superieur same algorithm, bounding the distortion by O(log2 k). We [email protected] improve the analysis of this ball-growing algorithm even further, bounding the distortion by O(log k). Yo’av Rieck Department of Mathematical Sciences Arnold Filtser University of Arkansas Ben gurion university of the negev [email protected] [email protected] Eric Sedgwick DePaul University CP18 [email protected] Impossibility of Dimension Reduction in the Nu- clear Norm Martin Tancer IST Austria Let S1 be the Banach space of compact linear operators [email protected]ff.cuni.cz → ∞ T : 2 2 whose nuclear norm T S1 = j=1 σj (T ) ∞ is finite, where {σj (T )}j=1 are the singular values of T . ⊂ We prove that there exists arbitrarily large C S1 that CP19 √ cannot be embedded with distortion O(1) into any |C|o(1)- ATight 2-Approximation for Linear 3-Cut dimensional linear subspace of S1. C is not even a O(1)- Lipschitz quotient of any subset of any |C|o(1)-dimensional We investigate the approximability of the linear 3-cut prob- linear subspace of S1.Thus,S1 does not admit a dimension lem in directed graphs, which is the simplest unsolved case reduction result ´a la Johnson and Lindenstrauss (1984), of the linear k-cut problem. The input here is a directed which complements the work of Harrow, Montanaro and graph D =(V,E) with node weights and three specified Short (2011) on the limitations of quantum dimension re- terminal nodes s, r, t ∈ V , and the goal is to find a mini- duction under the assumption that the embedding into low mum weight subset of non-terminal nodes whose removal dimensions is a quantum channel. Such a statement was ensures that s cannot reach r and t,andr cannot reach t. previously known with S1 replaced by 1 via the work of The problem is approximation-equivalent to the problem of Brinkman and Charikar (2003). In fact, C can be taken blocking rooted in- and out-arborescences, and it also has to be the same set as the one that Brinkman and Charikar applications in network coding and security. The approx- considered, viewed as a collection of diagonal matrices in imability of linear 3-cut has been wide open until now: the S1. The challenge is to demonstrate that C cannot be best known lower bound under the Unique Games Conjec- faithfully realized in an arbitrary low-dimensional subspace ture (UGC) was 4/3, while the best known upper bound of S1, while Brinkman and Charikar obtained such an as- was 2 using a trivial algorithm.√ In this work we completely sertion only for subspaces of S1 that consist of diagonal close this gap: we present a 2-approximation algorithm operators. We establish this by proving that the Markov and show that this factor is tight assuming UGC. Our con- 2-convexity constant of any finite dimensional linear sub- tributions are twofold: (1) we analyze a natural two-step space X of S1 is O( log dim(X)). deterministic rounding scheme through the lens of a single- step randomized rounding scheme with non-trivial distri- Assaf Naor butions, and (2) we construct√ integrality gap instances Theory group that meet the upper bound of 2. Our gap instances can Microsoft Research be viewed as a weighted graph sequence converging to a [email protected] “graph limit structure’.

Gilles Pisier Vivek Madan Texas A&M University University of illinois Urbana-Champaign [email protected] [email protected]

Gideon Schechtman Kristof Berczi Weizmann Institute E¨otv¨os Lor´and University [email protected] Hungary [email protected]

CP18 Karthekeyan Chandrasekaran Department of Industrial and Enterprise Systems Embeddability in R3 is NP-hard Engineering University of Illinois, Urbana-Champaign We prove that the problem of deciding whether a 2- or [email protected] 3-dimensional simplicial complex embeds into R3 is NP- hard. This stands in contrast with the lower dimensional caseswhichcanbesolvedinlineartime,andavariety Tamas Kiraly of computational problems in R3 like unknot or 3-sphere Eotvos Lorand University, Budapest recognition which are in NP ∩ co-NP (assuming the gen- [email protected] eralized Riemann hypothesis). Our reduction encodes a satisfiability instance into the embeddability problem of a 3-manifold with boundary tori, and relies extensively CP19 on techniques from low-dimensional topology, most impor- Near-Optimal Approximation Algorithm for Simul- 64 DA18 Abstracts

taneous Max-Cut tions.

In the simultaneous Max-Cut problem, we are given k Jakub Pachocki weighted graphs on the same set of n vertices, and the goal OpenAI is to find a cut of the vertex set so that the minimum, over [email protected] the k graphs, of the cut value is as large as possible. Pre- vious work of Bhangale et.al. [BKS15] gave a polynomial Liam Roditty time algorithm which achieved an approximation factor of Bar Ilan University 1/2 − o(1) for this problem (and an approximation factor [email protected] of 1/2+ k in the unweighted case, where k goesto0ask goes to infinity). In this work, we give an approximation Aaron Sidford algorithm for simultaneous Max-Cut with an approxima- Stanford University tion factor of 0.878 (for all constant k). The natural SDP [email protected] formulation for simultaneous Max-Cut was shown to have an integrality gap of 1/2+ k in Bhangale et.al. [BKS15]. Roe Tov In achieving the better approximation guarantee, we use a Bar Ilan University stronger Sum-of-Squares hierarchy SDP relaxation and a [email protected] rounding algorithm based on Raghavendra-Tan [RT12], in addition to techniques from [BKS15]. Virginia Vassilevska Williams Amey Bhangale MIT Weizmann Institute [email protected] [email protected] CP19 Subhash Khot Hypergraph k-Cut in Randomized Polynomial New York University Time [email protected] In the hypergraph k-cut problem, the input is a hyper- Swastik Kopparty graph, and the goal is to find a smallest subset of hy- Rutgers University peredges whose removal ensures that the remaining hyper- [email protected] graph has at least k connected components. This problem is known to be at least as hard as the densest k-subgraph Sushant Sachdeva problem when k is part of the input (Chekuri-Li, 2015). We Google, Mountain View CA present a randomized polynomial time algorithm to solve [email protected] the hypergraph k-cut problem for constant k. Our algo- rithm solves the more general hedge k-cut problem when Devanathan Thiruvenkatachari the subgraph induced by every hedge has a constant num- New York University ber of connected components. In the hedge k-cut prob- [email protected] lem, the input is a hedgegraph specified by a vertex set and a disjoint set of hedges,whereeachhedge is a subset of edges defined over the vertices. The goal is to find a CP19 smallest subset of hedges whose removal ensures that the number of connected components in the remaining under- Approximating Cycles in Directed Graphs lying (multi-)graph is at least k. Our algorithm is based on random contractions akin to Karger’s min cut algorithm. The girth of a graph is a fundamental graph parame- Our main technical contribution is a distribution over the ter. Unfortunately all known algorithms for computing, hedges (hyperedges) so that random contraction of hedges even approximately, the girth and girth-related structures (hyperedges) chosen from the distribution succeeds in re- in directed weighted m-edge and n-node graphs require turning an optimum solution with large probability. Ω(minnω ,mn)time(for2≤ ω<2.373). In this pa- per, we drastically improve these runtimes as follows: * Karthekeyan Chandrasekaran Multiplicative Approximations in Nearly Linear Time: We Department of Industrial and Enterprise Systems give an algorithm that in O(m) time computes an O(1)- Engineering multiplicative approximation of the girth as well as an University of Illinois, Urbana-Champaign O(1)-multiplicative roundtrip spanner with O(n)edges [email protected] with high probability * Nearly Tight Additive Approxima- tions: For unweighted graphs and any α ∈ (0, 1) we give Chao Xu an algorithm that in O(mn1−α) time computes an O(na)- Department of Computer Science additive approximation of the girth, w.h.p. We show that University of Illinois, Urbana-Champaign the runtime of our algorithm cannot be significantly im- [email protected] proved without a breakthrough in combinatorial boolean matrix multiplication. If the girth is O(na), then the al- Xilin Yu gorithm is deterministic. Our main technical contribution Department of Computer Science to achieve these results is the first nearly linear time al- University of Illinois at UrbanaChampaign gorithm for computing roundtrip covers, a directed graph [email protected] decomposition concept key to previous roundtrip spanner constructions. Previously it was not known how to com- pute these significantly faster than Ω(mn)time.Given CP19 the traditional difficulty in efficiently processing directed A Near-Linear Approximation Scheme for Multi- graphs, we hope our techniques may find further applica- cuts of Embedded Graphs with a Fixed Number of DA18 Abstracts 65

Terminals University of Warsaw [email protected], [email protected] For an undirected edge-weighted graph G and a set R of pairs of vertices called pairs of terminals, a multicut is a JakubL¸ acki set of edges such that removing these edges from G discon- Google Research, New York nects each pair in R. We provide an algorithm computing a [email protected] (1 + ε)-approximation of the minimum multicut of a graph (O(g+t)3) · O(g+t) · G in time (g + t) (1/ε) n log n,whereg is Piotr Sankowski the genus of G and t is the number of terminals. This is University of Warsaw tight in several aspects, as the minimum multicut problem [email protected] is both APX-hard and W[1]-hard (parameterized by the number of terminals), even on planar graphs (equivalently, when g = 0). Our result, in the field of fixed-parameter CP20 approximation algorithms, mostly relies on concepts bor- Lempel-Ziv: A ”One-Bit Catastrophe” But Not a rowed from computational topology of graphs on surfaces. Tragedy In particular, we use and extend various recent techniques concerning homotopy, homology, and covering spaces (even The so-called “one-bit catastrophe” for the compression in the planar case). We also exploit classical ideas stem- algorithm LZ’78 asks whether the compression ratio of an ming from approximation schemes for planar graphs and infinite word can change when a single bit is added in front low-dimensional geometric inputs. A key insight towards of it. We answer positively this open question raised by our result is a novel characterization of a minimum mul- Lutz and others: we show that there exists an infinite word ticut as the union of some Steiner trees in the universal w such that ρsup(w) = 0 but ρinf(0w) > 0, where ρsup cover of the surface in which G is embedded. and ρinf are respectively the lim sup and the lim inf of the compression ratios ρ of the prefixes. To that purpose we Vincent Cohen-Addad explore the behaviour of LZ’78 on finite words and show CNRS, LIP6, Universit´e Pierre et Marie Curie the following results: Paris, France [email protected] • There is a constant C>0 such that, for any finite word w and any letter a, ρ(aw) ≤ C ρ(w)log|w|. Eric´ Colin De Verdi`ere Thus, sufficiently compressible words (ρ(w)= CNRS, LIGM o(1/ log |w|)) remain compressible with a letter in Universit´e Paris-Est Marne-la-Vall´ee front; [email protected] • The previous result is tight up to a multiplicative con- stant for any compression ratio ρ(w)=O(1/ log |w|). Arnaud de Mesmay In particular, there are infinitely many words w sat- Ecole Normale Superieur isfying ρ(w)=O(1/ log |w|) but ρ(0w)=Ω(1). [email protected] Guillaume Lagarde,SylvainPerifel CP20 IRIF, Univ. Paris Diderot [email protected], [email protected] Optimal Dynamic Strings In this paper, we study the fundamental problem of main- CP20 taining a dynamic collection of strings under the following operations: Optimal-Time Text Indexing in BWT-runs Bounded Space • make string – add a string of constant length, • concat – concatenate two strings, Indexing highly repetitive texts has become an important • split – split a string into two at a given position, problem since the turn of the millennium. A relevant com- pressibility measure for repetitive texts is r,thenumber • compare – find the lexicographical order (less, equal, of runs in their Burrows-Wheeler Transform (BWT). One greater) between two strings, of the earliest indexes for repetitive collections, the Run- • LCP – calculate the longest common prefix of two Length FM-index, used O(r) space and was able to effi- strings. ciently count the number of occurrences of a pattern in We develop a generic framework for dynamizing the re- the text. However, it was unable to locate the positions compression method recently introduced by Je˙z[J.ACM, of those occurrences efficiently within a space bounded in 2016]. It allows us to present an efficient data structure for terms of r. Since then, a number of other indexes with the above problem, where an update requires only O(log n) space bounded by other measures of repetitiveness — the worst-case time with high probability, with n being the number of phrases in the Lempel-Ziv parse, the size of the total length of all strings in the collection, and a query smallest grammar generating the text, the size of the small- takes constant worst-case time. On the lower bound side, est automaton recognizing the text factors — have been we prove that even if the only possible query is checking proposed for efficiently locating, but not directly counting, equality of two strings, either updates or queries must take the occurrences of a pattern. In this paper we close this amortized Ω(log n) time; hence our implementation is op- long-standing problem, showing how to extend the Run- timal. Length FM-index so that it can locate the occurrences ef- ficiently within O(r) space (in loglogarithmic time each), Pawel Gawrychowski and reaching optimal time within O(r log(n/r)) space. We University of Wroclaw also describe a structure using O(r log(n/r)) space that re- [email protected] places the text and efficiently extracts any text substring, with an O(log(n/r)) additive time penalty over the opti- Adam Karczmarz, Tomasz Kociumaka mum. Preliminary experiments show that our new struc- 66 DA18 Abstracts

ture outperforms the alternatives by orders of magnitude we improve the power of n in both bounds. For the up- in the space/time tradeoff map. per bound, we introduce a recursion technique, that pro- vides a test for any power of n larger than 2/5. For the Nicola Prezza lower bound, we introduce a new problem called Truestring Technical University of Denmark Equivalence, which is easily reducible to the 2-type Dyck [email protected] language property testing problem. For this new problem, we show a lower bound of n to the power of 1/5. Gonzalo Navarro University of Chile Tatiana Starikovskaya [email protected] University of Bristol, UK [email protected] Travis Gagie EIT, Diego Portales University, Chile Eldar Fischer [email protected] Technion Israel Institute of Technology, Haifa, Israel [email protected] CP20 In-Place Sparse Suffix Sorting Fr´ed´eric Magniez CNRS, IRIF, Univ Paris Diderot Suffix arrays encode the lexicographical order of all suffixes France of a text and are often combined with the Longest Common [email protected] Prefix array (LCP) to simulate navigational queries on the suffix tree in reduced space. In space-critical applications such as sparse and compressed text indexing, only informa- CP21 tion regarding the lexicographical order of a size-b subset Computing the Independence Polynomial: from of all n text suffixes is often needed. Such information can the Tree Threshold Down to the Roots be stored space-efficiently (in b words) in the sparse suffix array (SSA). The SSA and its relative sparse LCP array Abstract not available at time of publication (SLCP) can be used as a space-efficient substitute of the sparse suffix tree. Very recently, Gawrychowski and Ko- Nicholas Harvey ciumaka showed that the sparse suffix tree (and therefore University of British Columbia SSA and SLCP) can be built in asymptotically optimal [email protected] O(b) space with a Monte Carlo algorithm running in O(n) time. The main reason for using the SSA and SLCP arrays Piyush Srivastava in place of the sparse suffix tree is, however, their reduced Tata Institute of Fundamental Research space of b words each. This leads naturally to the quest [email protected] for in-place algorithms building these arrays. Franceschini and Muthukrishnan showed that the full suffix array can be Jan Vondrak built in-place and in optimal running time. On the other hand, finding sub-quadratic in-place algorithms for build- Stanford University ing the SSA and SLCP for general subsets of suffixes has n/a been an elusive task for decades. In this paper, we give the first solution to this problem. CP21 Nicola Prezza Probabilistic Existence of Large Sets of Designs Technical University of Denmark [email protected] A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been re- cently introduced by Kuperberg, Lovett, and Peled (STOC CP20 2012). Using this technique, it can be shown that under Improved Bounds for Testing Dyck Languages certain conditions, a randomly chosen structure has the re- quired properties of a t-(n, k, λ) combinatorial design with We consider the problem of deciding membership in Dyck tiny, yet positive,probability. Herein, we strengthen both languages, a fundamental family of context-free languages, the method and the result of Kuperberg, Lovett, and Peled comprised of well-balanced strings of parentheses. In this as follows. We modify the random choice and the analy- problem we are given a string of length n in the alphabet sis to show that, under the same conditions, not only does of parentheses of m types and must decide if it is well- a t-(n, k, λ) design exist but, in fact, with positive prob- balanced. We consider this problem in the property testing ability there exists a large set of such designs — that is, setting, where one would like to make the decision while a partition of the set of k-subsets of [n]intot-(n, k, λ)de- querying as few characters of the input as possible. Prop- signs. Specifically, using the probabilistic approach derived erty testing of strings for Dyck language membership for herein, we prove that for all sufficiently large n,large sets m = 1, with a number of queries independent of the in- of t-(n, k, λ) designs exist whenever k>9t and the neces- put size n, was provided in [Alon, Krivelevich, Newman sary divisibility conditions are satisfied. This resolves the and Szegedy, SICOMP 2001]. Property testing of strings existence conjecture for large sets of designs for all k>9t. for Dyck language membership for m ≥ 2 was first inves- tigated in [Parnas, Ron and Rubinfeld, RSA 2003]. They Sankeerth Rao Karingula showed an upper bound and a lower bound for distinguish- PhD Student UCSD ing strings belonging to the language from strings that are [email protected] far (in terms of the Hamming distance) from the language, which are respectively (up to polylogarithmic factors) the Shachar Lovett, Alexander Vardy 2/3 power and the 1/11 power of the input size n. Here University of California San Diego DA18 Abstracts 67

[email protected], [email protected] obtained by dropping the odd set constraints of size larger than (1 + )/ from the description of the matching poly- tope. Previously, a tight lower bound of 2Ω(n) was only CP21 1 known for = O n [Rothvoss, STOC ’14; Braun and Stability of the Lanczos Method for Matrix Func- Pokutta, IEEE Trans. Information Theory ’15] whereas tion Approximation 2 ≤ ≤ Ω(1/) for n 1, the best lower bound was 2 [Rothvoss, STOC ’14]. The key new ingredient in our proof is a close The ubiquitous Lanczos method can approximate f(A)x connection to the non-negative rank of a lopsided version for any symmetric matrix A,vectorx, and function f.In of the unique disjointness matrix. exact arithmetic, the method’s error after k iterations is bounded by the error of the best degree-k polynomial ap- Makrand Sinha proximating f(x) on the range [λmin(A),λmax(A)]. How- ever, despite decades of work, it has been unclear if this Paul G. Allen School of Computer Science & Engineering powerful guarantee holds in finite precision. We resolve this University of Washington, Seattle | |≤ [email protected] problem, proving that when maxx∈[λmin,λmax] f(x) C, Lanczos essentially matches the exact arithmetic guaran- tee if computations use roughly log(C A )bitsofprecision. Our proof leverages stability of the Chebyshev recurrence CP22 to bound the stability of any polynomial approximating f. Thin Graph Classes and Polynomial-Time Approx- − We further study the special case of f(A)=A 1,where imation Schemes exact arithmetic Lanczos matches the best polynomial ap- proximating f at each of A’s eigenvalues, rather than on Baker (1994) devised a powerful technique to obtain ap- the full range. In seminal work, Greenbaum extends this proximation schemes for various problems restricted to pla- bound to finite precision: Lanczos matches any polynomial nar graphs. Her technique can be directly extended to approximating 1/x in a tiny range around each eigenvalue. various other graph classes, among the most general ones While this bound is stronger than ours, we exhibit matrices the graphs avoiding a fixed apex graph as a minor. Fur- with condition number κ where exact arithmetic Lanczos ther generalizations (e.g., to all proper minor closed graph converges in polylog(κ) iterations, but Greenbaum’s bound classes) are known, but they use a combination of tech- predicts Ω(κ1/5). Our analysis raises the question of if less niques and usually focus on somewhat restricted classes of than poly(κ) iterations can be expected in finite precision, problems. We present a new type of graph decompositions even for favorable eigenvalue distributions. (thin systems of overlays) generalizing Baker’s technique and leading to straightforward polynomial-time approxi- Christopher Musco, Cameron Musco mation schemes. We also show that many graph classes Massachusetts Institute of Technology (all proper minor-closed classes, and all subgraph-closed [email protected], [email protected] classes with bounded maximum degree and strongly sub- linear separators) admit such decompositions. Aaron Sidford Stanford University Zdenek Dvorak [email protected] Computer Science Institute Charles University, Prague [email protected]ff.cuni.cz CP21 Localization of Electrical Flows CP22 We show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a ran- Ramsey Spanning Trees and Their Applications dom edge is O(log2 n). This is a consequence of a more general result which shows that the spectral norm of the The metric Ramsey problem asks for the largest subset entrywise absolute value of the transfer impedance matrix S of a metric space that can be embedded into an ultra- of a graph is O(log2 n). This result implies a simple obliv- metric (more generally into a Hilbert space) with a given ious routing scheme based on electrical flows in the case of distortion. Mendel and Naor devised the so called Ramsey transitive graphs. Partitions to address this problem, and showed the algo- rithmic applications to approximate distance oracles. We Nikhil Srivastava study the natural extension of the metric Ramsey problem Microsoft Research India to graphs, and introduce the notion of Ramsey Spanning [email protected] Trees. We ask for the largest subset S ⊆ V of a given graph G =(V,E), such that there exists a spanning tree of G that Aaron Schild, Satish Rao has small stretch for S. Applied iteratively, this provides University of California, Berkeley a small collection of spanning trees, such that each vertex [email protected], [email protected] has a tree providing low stretch paths to all other vertices. We use this collection to devise the first compact stateless routing scheme with O(1) routing decision time, and la- CP21 bels which are much shorter than in all previous schemes. Lower Bounds for Approximating the Matching We first revisit the metric Ramsey problem, and provide Polytope a new deterministic construction. We prove that for every k,anyn-point metric space has a subset S of size at least We prove that any linear program that approximates the n1−1/k which embeds into an ultrametric with distortion matching polytope on n-vertex graphs up to a factor of 8k, providing the state-of-the-art deterministic construc- 2 ≤ ≤ n (1 + ) for any n 1musthaveatleast α/ inequali- tion of distance oracles. Next, we prove that for every k, ties where 0 <α<1 is an absolute constant. This is tight any n-vertex graph G =(V,E) has a subset S of size at as exhibited by the (1 + ) approximating linear program least n1−1/k, and a spanning tree of G,thathasstretch 68 DA18 Abstracts

O(k log log n) between any point in S and any point in V . Applications

Ittai Abraham A chordless cycle in a graph G is an induced subgraph of Vmware Research G which is a cycle of length at least four. We prove that [email protected] the Erd˝os-P´osa property holds for chordless cycles, which resolves the major open question concerning the Erd˝os- Shiri Chechik P´osa property. Our proof for chordless cycles is construc- Tel-Aviv University, Israel tive: in polynomial time, one can either find k +1vertex- 2 [email protected] disjoint chordless cycles, or ck log k vertices hitting every chordless cycle for some constant c. It immediately im- plies an approximation algorithm of factor O(opt log opt) Michael Elkin Chordal Vertex Deletion Ben-Gurion University for . We complement our [email protected] main result by showing that the class of all chordless cycles of length at least  for any fixed  ≥ 5doesnothavethe Erd˝os-P´osa property. As a corollary, for a non-negative in- Arnold Filtser tegral function w defined on the vertex set of a graph G, Ben gurion university of the negev the minimum value w(x) over all vertex sets S where [email protected] x∈S G − S isaforestisatmostO(k2 log k)wherek is the max- imum number of cycles (not necessarily vertex-disjoint) in Ofer Neiman G such that each vertex v is used at most w(v)times. Ben-Gurion University of the Negev [email protected] O-Joung Kwon Technische Universit¨at Berlin [email protected] CP22 Quasi-Regular Sequences and Optimal Schedules Eun Jung Kim for Security Games CNRS, LAMSADE-Universite Paris Dauphine [email protected] We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of differ- ent values. An attacker, knowing the defender’s strategy, CP22 chooses which target to attack and for how long. If the A Hamiltonian Cycle in the Square of a 2- attacker spends time t at a target i of value ai without Connected Graph in Linear Time interruption by the defender, his utility is tai;ifinter- rupted, his utility is 0. The defender aims to minimize the attacker’s utility. The defender’s strategy consists of a Fleischner’s theorem says that the square of every 2- schedule for visiting the targets; it takes her unit time to connected graph contains a Hamiltonian cycle. We present switch between targets. Optimal defender play, although a proof resulting in an O(|E|) algorithm for producing a 2 occurring in continuous time, reduces to a combinatorial Hamiltonian cycle in the square G of a 2-connected graph 2 question regarding the existence of infinite sequences over G =(V,E). The previous best was O(|V | )byLauin a finite alphabet, with the following properties for each 1980. More generally, we get an O(|E|) algorithm for pro- symbol i:(1)i constitutes a prescribed fraction p of the ducing a Hamiltonian path between any two prescribed ver- i 2 sequence. (2) The occurrences of i are spread apart close tices, and we get an O(|V | ) algorithm for producing cycles 2 | | to evenly: the ratio of the longest to shortest interval be- C3,C4,...,C|V | in G of lengths 3, 4,..., V ,respectively. tween consecutive occurrences is bounded by a parameter K. We call such sequences K-quasi-regular. A 1-quasi- Stephen Alstrup regular sequence ensures defender optimality. However, for Department of Computer Science, University of K<2, K-quasi-regular sequences may not exist. Surpris- Copenhagen ingly, randomized 2-quasi-regular sequences also suffice for Denmark defender optimality. We show that such sequences always [email protected] exist, and can be calculated efficiently. We provide several additional results on the existence of K-quasi regular and Agelos Georgakopoulos approximately optimal sequences. Mathematics Institute, University of Warwick UK David Kempe [email protected] University of Southern California [email protected] Eva Rotenberg University of Copenhagen Leonard Schulman [email protected] Caltech [email protected] Carsten Thomassen Department of Applied Mathematics and Computer Omer Tamuz Science California Institute of Technology Technical University of Denmark [email protected] [email protected]

CP22 CP23 Erd˝os-P´osa Property of Chordless Cycles and Its Sampling Random Colorings of Sparse Random DA18 Abstracts 69

Graphs [email protected]

We study the mixing properties of the Glauber dynamics for sampling k-colorings of a random graph G(n, d/n)for CP23 constant d. The best known rapid mixing results for gen- Tight Bounds for Coalescing-Branching Random eral graphs are in terms of the maximum degree Δ of the Walks on Regular Graphs input graph G and hold when k>11Δ/6. Improved results hold when k>αΔ for graphs with girth ≥ 5 and Δ suf- A Coalescing-Branching Random Walk (COBRA) is a nat- ficiently large where α =1.7632 ...; further improvements ural extension to the standard random walk on a graph. on the constant α hold with stronger assumptions. For The process starts with one pebble at an arbitrary node. G(n, d/n) the maximum degree is a function of n and the In each round every pebble splits into k pebbles, which are goal is to obtain results in terms of the expected degree d. sent to k random neighbors. At the end of the round all The following rapid mixing results for G(n, d/n)holdwith pebbles at the same node coalesce into a single pebble. Be- high probability over the instances of G(n, d/n)forlarged. sides its mathematical interest, this process is relevant as Mossel and Sly (2009) proved rapid mixing for constant k, an information dissemination primitive and a basic model and Efthymiou (2014) improved this to k linear in d.The for the spread of epidemics. We study the cover time of condition was improved to k>3d by Yin and Zhang (2016) COBRA, which is the time until each node has seen at least − using non-MCMC methods. Here we prove rapid mixing one pebble. Our main result is a bound of O(φ 1 log n) when k>αdwhere α =1.7632 ... is the same constant rounds with high probability on the cover time of CO- as above. Moreover we obtain O(n3) mixing time of the BRA with k = 2, on any regular graph with n nodes and Glauber dynamics, while in previous rapid mixing results conductance φ. This improves upon all previous bounds the exponent was an increasing function in d. Our proof for the problem in term of graph expansion parameters analyzes an appropriately defined block dynamics to “hide’ (Dutta et al. 2015, Mitzenmacher et al. 2016, Cooper et high-degree vertices. One new aspect in our improved ap- al. 2016/17). We also show that for any connected regular proach is utilizing so-called local uniformity properties for graph, the cover time is O(n log n) with high probability. the analysis of block dynamics. Both bounds are asymptotically tight. Since our bounds coincide with the worst-case time bounds for push rumor Charilaos Efthymiou spreading on regular graphs until all nodes are informed, Goethe University Frankfurt this raises the question whether COBRA and push rumor [email protected] spreading perform similarly in general. We answer this negatively by separating the cover time of COBRA and the rumor spreading time of push by a super-polylogarithmic Thomas Hayes factor on a family of tree-like regular graphs. University of New Mexico, USA [email protected] Petra Berenbrink University of Hamburg Daniel Stefankovic [email protected] Department of Computer Science University of Rochester George Giakkoupis [email protected] INRIA Rennes, France [email protected] Eric Vigoda Georgia Institute of Technology Peter Kling [email protected] Universit¨at Hamburg [email protected]

CP23 CP23 Uniform Generation of Random Graphs with Power-Law Degree Sequences Estimating Graph Parameters Via Random Walks with Restarts

We give a linear-time algorithm that approximately uni- In this paper we discuss the problem of estimating graph formly generates a random simple graph with a power-law parameters from a random walk with restarts. An algo- degree sequence whose exponent is at least 2.8811. While rithm observes the trajectory of a random walk over an sampling graphs with power-law degree sequence of expo- unknown graph G, starting from a vertex x. The algo- nent at least 3 is fairly easy, and many samplers work ef- rithm also sees the degrees along the trajectory. The only ficiently in this case, the problem becomes dramatically other power that the algorithm has is to request that the more difficult when the exponent drops below 3; ours is random walk be reset to its initial state at any given time, the first provably practicable sampler for this case. We based on what it has seen so far. Our main results are as also show that with an appropriate rejection scheme, our follows. For regular graphs G, one can estimate the num- algorithm can be tuned into an exact uniform sampler. The 2 ber of vertices nG and the  mixing time of G from x running time of the exact sampler is O(n2.107 ) with high √ in O( n (tG )3/4) steps, where tG is the uniform mix- probability, and O(n4.081 ) in expectation. G unif unif ing time of the random walk. The algorithm is based on the number of intersections of random walk paths and im- Pu Gao proves on previous methods which only consider collisions. University of Toronto We also show that the time complexity of our algorithm is [email protected] optimal (up to log factors) for 3-regular graphs with pre- scribed mixing times. For general graphs, we adapt the Nick Wormald intersections algorithm to compute the number of edges 2 Monash University mG and the  mixing time from the starting vertex x in 70 DA18 Abstracts

√  G 3/4 O( mG (tunif) ) steps. Under mild additional assump- PCSPs exhibits a dichotomy (it is either polynomial-time tions, the number of vertices can also be estimated by this tractable or NP-hard) when the clauses are symmetric and time. We complement these results by showing that if ei- allow for negations of variables. In particular, we show ther mG or the mixing time is known, the other parameter that every such polynomial-time tractable instance can be can be estimated with few steps via a self-stopping algo- solved via either Gaussian elimination over F2 or a linear rithm. programming relaxation. We achieve our dichotomy the- orem by extending the weak polymorphism framework of Anna Ben-Hamou AGH which itself is a generalization of the algebraic ap- Universit´e Pierre et Marie Curie proach used by polymorphisms to study CSPs. In both [email protected] the algorithm and hardness portions of our proof, we in- corporate new ideas and techniques not utilized in the CSP Roberto I. Oliveira case. IMPA [email protected] Joshua Brakensiek, Venkatesan Guruswami Carnegie Mellon University Yuval Peres [email protected], [email protected] Microsoft Research, Redmond [email protected] CP24 The Complexity of Counting Surjective Homomor- CP23 phisms and Compactions Comparing Mixing Times on Sparse Random A homomorphism from a graph G to a graph H is a func- Graphs tion from the vertices of G to the vertices of H that pre- serves edges. A homomorphism is surjective if it uses all It is natural to expect that nonbacktracking random walk of the vertices of H and it is a compaction if it uses all of will mix faster than simple random walks, but so far this the vertices of H and all of the non-loop edges of H.Hell has only been proved in regular graphs. To analyze typ- and Neˇsetˇril gave a complete characterisation of the com- ical irregular graphs, let G be a random graph on n ver- plexity of deciding whether there is a homomorphism from tices with minimum degree 3 and a degree distribution that an input graph G to a fixed graph H.Acompletechar- has exponential tails. We determine the precise worst-case acterisation is not known for surjective homomorphisms mixing time for simple random walk on G,andshowthat, − or for compactions, though there are many interesting re- with high probability, it exhibits cutoff at time h 1 log n, sults. Dyer and Greenhill gave a complete characterisa- where h is the asymptotic entropy for simple random tion of the complexity of counting homomorphisms from walk on a Galton–Watson tree that approximates G lo- an input graph G to a fixed graph H.Inthispaper,we cally. (Previously this was only known for typical start- give a complete characterisation of the complexity of count- ing points.) Furthermore, we show this asymptotic mixing ing surjective homomorphisms from an input graph G to a time is strictly larger than the mixing time of nonback- fixed graph H and we also give a complete characterisation tracking walk, via a delicate comparison of entropies on of the complexity of counting compactions from an input the Galton–Watson tree. graph G to a fixed graph H. Anna Ben-Hamou Jacob Focke, Leslie Ann Goldberg, Standa Zivn´ˇ y Universit´e Pierre et Marie Curie University of Oxford [email protected] [email protected], [email protected], [email protected] Eyal Lubetzky Courant Institute New York University CP24 [email protected] Resource-Efficient Common Randomness and Secret-Key Schemes Yuval Peres Microsoft Research, Redmond We study common randomness where two parties have ac- [email protected] cess to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability CP24 of agreement. This problem is at the core of secret key Promise Constraint Satisfaction: Structure Theory generation in cryptography, with connections to commu- and a Symmetric Boolean Dichotomy nication under uncertainty and locality sensitive hashing. We take the approach of treating correlated sources as a A classic result of Schaefer [STOC, 1978] classifies all con- critical resource, and ask whether common randomness can straint satisfaction problems (CSPs) over the Boolean do- be generated resource-efficiently. We consider two notable main to be either in P or NP-hard. This paper con- sources in this setup arising from correlated bits and cor- siders a promise-problem variant of CSPs called PCSPs. related Gaussians. We design the first explicit schemes Many problems such as approximate graph and hypergraph that use only a polynomial number of samples (in the key coloring, the (2 + )-SAT problem due to Austrin, Gu- length) so that the players can generate shared keys that ruswami, and H˚astad [SIAM Journal on Computing, 2017], agree with constant probability using optimal communica- and the digraph homomorphism problem can be placed in tion. The best previously known schemes were both non- this framework. This paper is motivated by the pursuit of constructive and used an exponential number of samples. understanding the computational complexity of Boolean In the amortized setting, we characterize the largest achiev- PCSPs, determining which PCSPs are polynomial-time able ratio of key length to communication in terms of the tractable or NP-hard. As our main result, we show that external and internal information costs, two well-studied DA18 Abstracts 71

quantities in theoretical computer science. Our schemes [email protected] reveal a new connection between common randomness and unbiased error-correcting codes, e.g., dual-BCH codes and Jiapeng Zhang their analogues in Euclidean space. University of California, San Diego [email protected] Badih Ghazi MIT [email protected] CP25 Reachability Preservers: New Extremal Bounds T.S. Jayram and Approximation Algorithms IBM Research - Almaden [email protected] Say we are given a directed graph G =(V,E)onn nodes, asetofsourcesS ⊆ V of size |S| = n1/3, and a subset ⊆ × ∈ 2/3 CP24 P S V of pairs (s, t)wheres S,ofsizeO(n ), such that for all pairs (s, t) ∈ P , there is a path from s to t. Dichotomy for Real Holantc Problems Our goal is to remove as many edges from G as possible Holant problems capture a class of Sum-of-Product compu- while maintaining the reachability of all pairs in P .How tations such as counting matchings. It is inspired by holo- many edges will we have to keep? In this paper, we make graphic algorithms and is equivalent to tensor networks, polynomial progress in both the upper and lower bounds with counting CSP being a special case. A classification for for these Reachability Preservers over bounds that were Holant problems is more difficult to prove, not only because implicit in the literature. We show that in the above sce- it logically implies a classification for counting CSP, but nario, O(n) edges will always be sufficient, and in general also due to the deeper reason that there exist more intricate one is even guaranteed a subgraph on O(n + n ·|P |·|S|) polynomial time tractable problems in the broader frame- edges that preserves the reachability of all pairs in P .We work. We discover a new family of constraint functions L complement this with a lower bound graph construction, which define polynomial time computable counting prob- establishing that the above result fully characterizes the lems. These do not appear in counting CSP, and no newly settings in which we are guaranteed a preserver of size discovered tractable constraints can be symmetric. It has a O(n). We also design an efficient algorithm that can always delicate support structure related to error-correcting codes. compute a preserver of existentially optimal size. The sec- Local holographic transformations is fundamental in its ond contribution of this paper is a new connection between tractability. We prove a complexity dichotomy theorem extremal graph sparsification results and classical Steiner for all Holant problems defined by any real valued con- Network Design problems. We improve the state of the art straint function set on Boolean variables and contains two approximation algorithms for the most basic Steiner-type 0.6+ 0-1 pinning functions. Previously, dichotomy for the same problem in directed graphs from the O(n )ofChla- framework was only known for symmetric constraint func- matac, Dinitz, Kortsarz, and Laekhanukit (SODA’17) to 0.577+ tions. The set L supplies the last piece of tractability. We O(n ). also prove a dichotomy for a variant of counting CSP as a technical component toward this Holant dichotomy. Amir Abboud Stanford University Pinyan Lu [email protected] Shanghai University of Finance and Economics [email protected] Greg Bodwin MIT Jin-Yi Cai [email protected] University of Wisconsin, Madison [email protected] CP25 Mingji Xia Optimal Vertex Fault Tolerant Spanners (for fixed Institute of Software, Chinese Academy of Sciences. stretch) University of Chinese Academy of Sciences [email protected] A k-spanner of a graph G is a sparse subgraph H whose shortest path distances match those of G up to a multi- plicative error k. In this paper we study spanners that are CP24 resistant to faults. A subgraph H ⊆ G is an f vertex fault \ \ The Robust Sensitivity of Boolean Functions tolerant (VFT) k-spanner if H F is a k-spanner of G F for any small set F of f vertices that might “fail.’ One of The sensitivity conjecture is one of the central open prob- the main questions in the area is: what is the minimum size lems in Boolean complexity. A recent work of Gopalan et of an f fault tolerant k-spanner that holds for all n node al. [CCC 2016] conjectured a robust analog of the sensitiv- graphs (as a function of f, k and n)? This question was ity conjecture, which relates the decay of the Fourier mass first studied in the context of geometric graphs [Levcopou- of a Boolean function to moments of its sensitivity. We los et al. STOC ’98, Czumaj and Zhao SoCG ’03] and has prove the robust sensitivity conjecture in this work with more recently been considered in general undirected graphs near optimal parameters. [Chechik et al. STOC ’09, Dinitz and Krauthgamer PODC ’11]. In this paper, we settle the question of the optimal Shachar Lovett size of a VFT spanner, in the setting where the stretch fac- University of California, San Diego tor k is fixed. Specifically, we prove that every (undirected, [email protected] possibly weighted) n-node graph G has a (2k − 1)-spanner 1−1/k 1+1/k resilient to f vertex faults with Ok(f n )edges, Avishay Tal and this is fully optimal (unless the famous Erd¨os Girth Stanford University Conjecture is false). Our lower bound even generalizes 72 DA18 Abstracts

to imply that no data structure capable of approximat- linear time whether a graph is k vertices away from being ing distG\F (s, t) similarly can beat the space usage of our planar [FOCS 2009, SODA 2014] or bipartite [SODA 2014, spanner in the worst case. SICOMP 2016], the best known algorithms in the case of directed acyclicity are the algorithm of Garey and Tarjan Greg Bodwin [IPL 78] which runs in time O(nk−1m) and the algorithm of MIT Chen, Liu, Lu, O’Sullivan and Razgon [JACM 2008] which [email protected] runs in time O(k!4k k4nm). We settle this question by giv- ing an algorithm that decides whether a given graph is k Michael Dinitz vertices away from being acyclic, in time O(k!4k k5(n+m)). Johns Hopkins University Our algorithm is designed via a general methodology that [email protected] shaves off a factor of n from some algorithms that use the powerful technique of iterative compression. The two main Merav Parter features of our methodology are: (i) This is the first generic The Weizmann Institute of Science, Rehovot, Israel. technique for designing linear time algorithms for directed [email protected] cut-problems and(ii)itcanbeusedincombinationwith future improvements in algorithms for the compression ver- Multicut Virginia Vassilevska Williams sion of other well-studied cut-problems such as Directed Subset Feedback Vertex Set MIT and . [email protected] Ramanujan M. Sridharan TU Wien CP25 [email protected] Approximate Single Source Fault Tolerant Shortest Path Daniel Lokshtanov University of Bergen Let G =(V,E)beann-vertices m-edges directed graph [email protected] with edge weights in the range [1,W]andL =log(W ). Let s ∈ V be a designated source. In this paper we address Saket Saurabh several variants of the problem of maintaining the (1 + )- IMSc +UiB approximate shortest path from s to each v ∈ V \{s} in [email protected] the presence of a failure of an edge or a vertex. We show that G has a subgraph H with O(nL/ )edgessuchthat for any x, v ∈ V , the graph H \ x contains a path whose CP25 length is a (1+ )-approximation of the length of the short- Approaching 3 for the s-t-path TSP est path from s to v in G \ x. We show that the size of the 2 subgraph H is optimal (up to logarithmic factors) by prov- We show that there is a polynomial-time algorithm with ingalowerboundofΩ(nL/ ) edges. We show that there 3 approximation guarantee 2 + for the s-t-path TSP, for exists an O(nL/ )sizeoraclethatforanyv ∈ V reports a any fixed >0. It is well known that Wolsey’s analysis (1+ )-approximate distance of v from s on a failure of any of Christofides’ algorithm also works for the s-t-path TSP ∈ x V in O(log log1+(nW )) time. We show that the size with its natural LP relaxation except for the narrow cuts of the oracle is optimal (up to logarithmic factors) by prov- (in which the LP solution has value less than two). A fixed ingalowerboundofΩ(nL/ log n). We also present two optimum tour has either a single edge in a narrow cut (then distributed algorithms, namely single source routing scheme call the edge and the cut lonely) or at least three (then and single source labeling scheme. call the cut busy). Our algorithm “guesses’ (by dynamic programming) lonely cuts and edges. Then we partition Keerti Choudhary, Surender Baswana the instance into smaller instances and strengthen the LP, IIT Kanpur requiring value at least three for busy cuts. By setting up [email protected], [email protected] a k-stage recursive dynamic program, we can compute a 1 spanning tree (V,S) and an LP solution y such that ( 2 + Moazzam Hussain O(2−k))y is in the T -join polyhedron, where T is the set WorldQuant Research, India of vertices whose degree in S has the wrong parity. [email protected] Vera Traub, Jens Vygen Liam Roditty University of Bonn Bar Ilan University [email protected], [email protected] [email protected] CP26 CP25 Spatial Mixing and Non-Local Markov Chains When Recursion Is Better Than Iteration: A Linear-Time Algorithm for Acyclicity with Few Er- We consider spin systems with nearest-neighbor interac- ror Vertices tions on an n-vertex d-dimensional cube of the integer lat- tice graph Zd. We study the effects that the strong spatial Planarity, bipartiteness and (directed) acyclicity are basic mixing condition (SSM) has on the rate of convergence to graph properties with classic linear time recognition algo- equilibrium distribution of non-local Markov chains. We rithms. However, the problems of testing whether a given prove that SSM implies O(log n) mixing of a block dynam- (di)graph has k vertices whose deletion makes it planar, ics whose steps can be implemented efficiently. We then bipartite or a directed acyclic graph (DAG) are all funda- develop a comparison methodology that allows us to extend mental NP-complete problems when k is part of the input. this result to other non-local dynamics. As a first applica- While we now know that for any fixed k,wecantestin tion of our method we prove that, if SSM holds, then the DA18 Abstracts 73

relaxation time (i.e., the inverse spectral gap) of general bath dynamics, in which global updates allow this MCMC block dynamics is O(r), where r is the number of blocks. sampler to switch between metastable states and ideally As a second application of our technology we show that mix faster. Gore and Jerrum (1997) found that this dy- SSM implies an O(1) bound for the relaxation time of the namics may in fact exhibit slow mixing: they showed that, Swendsen-Wang dynamics for the ferromagnetic Ising and for the Potts model with q ≥ 3 colors on the complete Potts models. We also prove that for monotone spin sys- graph on n vertices at the critical√ point βc(q), Swendsen– tems SSM implies that the mixing time of systematic scan Wang dynamics has tmix ≥ exp(c n). Galanis et al. (2015) 2 1/3 dynamics is O(log n(log log n) ). Our proofs use a variety showed that tmix ≥ exp(cn ) throughout the critical win- of techniques for the analysis of Markov chains including dow (βs,βS ) around βc, and√ Blanca and Sinclair (2015) coupling, functional analysis and linear algebra. established that tmix ≥ exp(c n) in the critical window for corresponding mean-field FK model, which implied the Antonio Blanca same bound for Swendsen–Wang via known comparison es- U.C. Berkeley  timates. In both cases, an upper bound of tmix ≤ exp(c n) [email protected] was known. Here we show that the mixing time is truly exponential in n:namely,tmix ≥ exp(cn) for Swendsen– Pietro Caputo Wang dynamics when q ≥ 3andβ ∈ (βs,βS), and the University of Rome Tre same bound holds for the related MCMC samplers for the [email protected] mean-field FK model when q>2.

Alistair Sinclair Reza Gheissari, Eyal Lubetzky University of California, Berkeley Courant Institute [email protected] New York University [email protected], [email protected] Eric Vigoda Georgia Institute of Technology Yuval Peres [email protected] Microsoft Research, Redmond [email protected]

CP26 Testing Ising Models CP26 The Diameter of Dense Random Regular Graphs Given samples from an unknown multivariate distribution p, is it possible to distinguish whether p is the product of There is a tight upper bound on the order (the number its marginals versus p being far from every product distri- of vertices) of d-regular graphs of diameter D,knownas bution? Similarly, is it possible to distinguish whether p the Moore bound in graph theory. This bound yields the equals a given distribution q versus p and q being far from lower bound D0(n, d) of the diameter of d-regular graphs each other? These problems of testing independence and of order n. Actually, the diameter diam(Gn,d) of a random goodness-of-fit have received enormous attention in statis- d-regular graph Gn,d of order n is known to be the same as tics, information theory, and theoretical computer science, D0(n, d)uptoafactor1+o(1) for 3 ≤ d = O(1), whereas with sample-optimal algorithms known in several interest- there exists a gap diam(Gn,d)−D0(n, d)=Ω(loglogn). In ing regimes of parameters. Unfortunately, it has also been this paper, we investigate the gap diam(Gn,d) − D0(n, d) understood that these problems become intractable in large for d =(β + o(1))nα where α ∈ (0, 1) and β>0are dimensions, necessitating exponential samples. Motivated any constants. We show that for such a d,diam(Gn,d)= − by the exponential lower bounds for general distributions α 1 + 1 with high probability. Our result yields that − as well as the ubiquity of Markov Random Fields (MRFs) the gap is 1 if α 1 is an integer and d ≥ nα,andis0 in the modeling of high-dimensional distributions, we ini- otherwise. The upper bound of diam(Gn,d) follows from tiate the study of distribution testing on structured mul- the embedding theorem due to Dudek et al. We obtain the tivariate distributions, and in particular the prototypical lower bound of diam(Gn,d) by the careful analysis of the example of MRFs: the Ising Model. We demonstrate that, shortest path lengths between fixed vertex pairs. in this structured setting, we can avoid the curse of di- mensionality, obtaining sample and time efficient testers Nobutaka Shimizu for independence and goodness-of-fit. Along the way, we The University of Tokyo develop new tools for bounding the variance of functions of nobutaka [email protected] the Ising model, using and improving upon the exchange- able pairs framework developed by Chatterjee. In particu- CP26 lar, we prove variance bounds for multi-linear functions of the Ising model in the high-temperature regime. Consensus of Interacting Particle Systems on Erd¨os-R´enyi Graphs Constantinos Daskalakis, Nishanth Dikkala,Gautam Kamath Interacting Particle Systems—exemplified by the voter MIT model, iterative majority, and iterative k−majority [email protected], [email protected], processes—have found use in many disciplines including [email protected] distributed systems, statistical physics, social networks, and Markov chain theory. In these processes, nodes up- date their “opinion’ according to the frequency of opinions CP26 amongst their neighbors. We propose a family of models Exponentially Slow Mixing in the Mean-Field parameterized by an update function that we call Node Dy- Swendsen-Wang Dynamics namics: every node initially has a binary opinion. At each round a node is uniformly chosen and randomly updates its Swendsen–Wang dynamics for the Potts model was pro- opinion with the probability distribution specified by the posed in the late 1980’s as an alternative to single-site heat- value of the update function applied to the frequencies of its 74 DA18 Abstracts

neighbors’ opinions. In this work, we prove that the Node most3nandatleastlinearinn,evenwhenthebuyers’val- Dynamics converge to consensus in time Θ(n log n)incom- ues are correlated across stages, under a monotone hazard plete graphs and dense Erd¨os-R´enyi random graphs when rate assumption on the stage distributions. We also prove the update function is from a large family of “majority-like’ results on the number of additional buyers necessary for functions. Our technical contribution is a general frame- VCG at every stage to be an α-approximation of the opti- work that upper bounds the consensus time. In contrast mal revenue. As a corollary we provide the first results on to previous work that relies on handcrafted potential func- prior-independent dynamic auctions. This is, to the best of tions, our framework systematically constructs a potential our knowledge, the first non-trivial positive guarantees for function based the state space structure. simple ex-post IR dynamic auctions for correlated stages.

Grant Schoenebeck, Fang-Yi Yu Siqi Liu University of Michigan UC Berkeley [email protected], [email protected] [email protected]

Alexandros Psomas CP27 Carnegie Mellon University Separation in Correlation-Robust Monopolist [email protected] Problem with Budget

We consider a monopolist seller that has n heterogeneous CP27 items to sell to a single buyer. The seller’s goal is to maxi- mize her revenue. We study this problem in the correlation- Revenue Maximization with an Uncertainty- robust framework recently proposed by Carroll [Econo- Averse Buyer metrica 2017]. In this framework, the seller only knows marginal distributions for each separate item but has no Most work in mechanism design assumes that buyers are information about correlation across different items in the risk neutral; some considers risk aversion arising due to a joint distribution. Any mechanism is then evaluated ac- non-linear utility for money. Yet behavioral studies have cording to its expected profit in the worst-case, over all pos- established that real agents exhibit risk attitudes which sible joint distributions with given marginal distributions. cannot be captured by any expected utility model. We ini- Carroll’s main result states that in multi-item monopoly tiate the study of revenue-optimal mechanisms under be- problem with buyer, whose value for a set of items is ad- havioral models beyond expected utility theory. We adopt ditive, the optimal correlation-robust mechanism should a model from prospect theory which arose to explain these sell items separately. We use alternative dual Linear Pro- discrepancies and incorporates agents under-weighting un- gramming formulation for the optimal correlation-robust certain outcomes. In our model, an event occurring with mechanism design problem. This LP can be used to com- probability x<1 is worth strictly less to the agent than pute optimal mechanisms in general settings. We give an x times the value of the event when it occurs with cer- alternative proof for the additive monopoly problem with- tainty. We present three main results. First, we charac- out constructing worst-case distribution. As a surprising terize optimal mechanisms as menus of two-outcome lot- byproduct of our approach we get that separation result teries. Second, we show that under a reasonable bounded- continues to hold even when buyer has a budget constraint risk-aversion assumption, posted pricing obtains a constant on her total payment. Namely, the optimal robust mecha- approximation to the optimal revenue. Notably, this result nism splits the total budget in a fixed way across different is “risk-robust’ in that it does not depend on the details items independent of the bids, and then sells each item of the buyer’s risk attitude. Third, we consider dynamic separately with a respective per item budget constraint. settings in which the buyers uncertainty about his future value may allow the seller to extract more revenue. In Pinyan Lu, Nick Gravin contrasttothepositiveresultabove,hereweshowitis Shanghai University of Finance and Economics not possible to achieve any constant-factor approximation [email protected], [email protected] to revenue using deterministic mechanisms in a risk-robust manner.

CP27 Shuchi Chawla On the Competition Complexity of Dynamic Mech- Department of Computer Sciences anism Design University of Wisconsin-Madison [email protected] The Competition Complexity of an auction measures how much competition is needed for the revenue of a simple Kira Goldner auction to surpass the optimal revenue. A classic result by Oberlin College Bulow and Klemperer, states that the Competition Com- [email protected] plexity of VCG, in the case of n i.i.d. buyers and one item, is 1. In other words, it is better to invest in recruiting J. Benjamin Miller one extra buyer and run VCG than to invest in learning University of Wisconsin-Madison the buyers’ underlying distribution and run the revenue [email protected] maximizing auction tailored to this distribution. In this paper we study the Competition Complexity of dynamic Emmanouil Pountourakis auctions. Consider the following problem: a monopolist University of Texas at Austin is selling m items in m consecutive stages to n interested [email protected] buyers. A buyer realizes her value for item k in the begin- ning of stage k. How many additional buyers are necessary and sufficient for VCG at each stage to extract revenue at least that of the optimal dynamic auction? We prove CP27 that the Competition Complexity of dynamic auctions is at On the Complexity of Simple and Optimal Deter- DA18 Abstracts 75

ministic Mechanisms for An Additive Buyer Princeton University [email protected], [email protected], We show that the problem of implementing a Revenue- [email protected] Optimal Deterministic Mechanism Design problem for a single additive buyer is #P-hard, even when the distribu- tions have support size 2 for each item and, more impor- CP28 tantly, even when the optimal solution is guaranteed to be Improved Bounds for Testing Forbidden Order Pat- of a very simple kind: the seller picks a price for each in- terns dividual item and a price for the grand bundle of all the items; the buyer can purchase either the grand bundle at A sequence f : {1,...,n}→R contains a permutation π of its given price or any subset of items at their total individ- length k if there exist i < ... < i such that, for all x, y, ual prices. The following problems are also #P-hard, as 1 k f(ix)

CP27 Omri Ben-Eliezer The Menu Complexity of ’One-and-a-Half- Tel Aviv University Dimensional’ Mechanism Design [email protected]

We study the menu complexity of optimal and Cl´ement Canonne approximately-optimal auctions in the context of the Columbia University “FedEx’ problem, a so-called “one-and-a-half-dimensional’ [email protected] setting where a single bidder has both a value and a dead- line for receiving an item[Fiat:2016]. The menu complex- ity[HartN13] of an auction is equal to the number of dis- CP28 tinct (allocation, price) pairs that a bidder might receive. A o(d) · polylog n Monotonicity Tester for Boolean We show the following when the bidder has n possible dead- d lines: Functions over the Hypergrid [n] • Exponential menu complexity is necessary to We study monotonicity testing of Boolean functions over be exactly optimal: There exist instances where d ≥ n − the hypergrid [n] and design a non-adaptive tester with 1- the optimal mechanism has menu complexity 2 1. ˜ 5/6 · This matches exactly the upper bound provided by sided error whose query complexity is O(d ) polylog n. Fiat et al.’s algorithm, and resolves one of their open Previous to our work, the best known testers had query complexity linear in d but independent of n.Weimprove questions. o d (1) • Fully polynomial menu complexity is neces- upon these testers as long as n =2 . To obtain our re- sary and sufficient for approximation: For sults, we work with what we call the augmented hypergrid, all instances, there exists a mechanism guar- which adds extra edges to the hypergrid. Our main tech- anteeing a multiplicative (1 − )-approximation nical contribution is a Margulis-style isoperimetric result for the augmented hypergrid, and our tester (like previ- to the optimal revenue with menu complexity ous testers for the hypercube domain) performs directed 3/2 min{n/,ln(vmax)} 2 O(n  )=O(n / ), where vmax de- random walks on this structure. notes the largest value in the support of integral dis- tributions. Hadley Black • There exist instances where any mechanism guaran- University of California, Santa Cruz teeing a multiplicative (1−O(1/n2))-approximation to [email protected] the optimal revenue requires menu complexity Ω(n2). Our main technique is the polygon approximation of con- Deeparnab Chakrabarty cave functions[Rote91], and our results here should be of Dartmouth College independent interest. [email protected] Raghuvansh R. Saxena, Ariel Schvartzman, Matt C. Seshadhri Weinberg University of California, Santa Cruz 76 DA18 Abstracts

  ˜ √n · log(1/) n·α · 1 O(log(1/)) [email protected] are O m  + m  where n denotes the number of vertices and m denotes the number of edges. In terms of the dependence on n and m this bound is opti- CP28 mal up to poly-logarithmic factors. We leave it as an open Tolerant Junta Testing and the Connection to Sub- question whether the dependence on 1/ can be improved modular Optimization and Function Isomorphism from quasi-polynomial to polynomial. Our techniques in- clude an efficient local simulation for approximating the A function f : {0, 1}n →{0, 1} is a k-junta if it depends outcome of a global (almost) forest-decomposition algo- on at most k of its variables. We consider the problem rithm as well as a tailored procedure of edge sampling. of tolerant testing of k-juntas, where the testing algorithm must accept any function that is -close to some k-junta and reject any function that is -far from every k-junta Reut Levi for some  = O( )andk = O(k). Our first result is an Weizmann Institute algorithm that solves this problem with query complexity [email protected] polynomial in k and 1/ . This result is obtained via a new polynomial-time approximation algorithm for submodular Talya Eden function minimization under large cardinality constraints, Tel-Aviv University which holds even when only given an approximate oracle [email protected]. access to the function. Our second result considers the case  where k = k. We show how to obtain a smooth tradeoff Dana Ron between the amount of tolerance and the query complexity Tel-Aviv Univeristy in this setting. Specifically, we design an algorithm that [email protected]. given ρ ∈ (0, 1/2) accepts any function that is ρ/8-close to some k-junta and rejects any function that is -far from every k-junta. The query complexity of the algorithm is CP28 k log k O ρ(1−ρ)k . Finally, we show how to apply the second Cache-Oblivious and Data-Oblivious Sorting and result to the problem of tolerant isomorphism testing be- Applications tween two unknown Boolean functions f and g.Wegive an algorithm for this problem whose query complexity only Although external-memory sorting has been a classical depends on the (unknown) smallest k such that either f or algorithms abstraction and has been heavily studied in g is close to being a k-junta. the literature, perhaps somewhat surprisingly, when data- obliviousness is a requirement, even very rudimentary ques- Eric Blais tions remain open. Prior to our work, it is not even University of Waterloo known how to construct a comparison-based,external- [email protected] memory oblivious sorting algorithm that is optimal in IO- cost. We make a significant step forward in our under- Cl´ement Cannone standing of external-memory, oblivious sorting algorithms. Columbia University Not only do we construct a comparison-based,external- [email protected] memory oblivious sorting algorithm that is optimal in IO- cost, our algorithm is also cache-agnostic in that the algo- rithm need not know the storage hierarchy’s internal pa- Talya Eden rameters such as the cache and cache-line sizes. Our result Tel Aviv University immediately implies a cache-agnostic ORAM construction [email protected] whose asymptotic IO-cost matches the best known cache- aware scheme. Last but not the least, we propose and Amit Levi adopt a new and stronger security notion for external- University of Waterloo memory, oblivious algorithms and argue that this new no- [email protected] tion is desirable for resisting possible cache-timing attacks. Thus our work also lays a foundation for the study of obliv- Dana Ron ious algorithms in the cache-agnostic model. Tel-Aviv University [email protected] T-H. Hubert Chan The University of Hong Kong [email protected] CP28 Testing Bounded Arboricity Yue Guo, Wei-Kai Lin, Elaine Shi Cornell University In this paper we consider the problem of testing whether [email protected], [email protected], runt- a graph has bounded arboricity. Graphs with bounded [email protected] arboricity have been studied extensively in the past, in particular since for many problems they allow for much CP29 more efficient algorithms and/or better approximation ra- tios. We present a tolerant tester in the sparse-graphs Tight Analysis of Parallel Randomized Greedy Mis model. The sparse-graphs model allows access to degree We provide a tight analysis which settles the round com- queries and neighbor queries, and the distance is defined plexity of the well-studied parallel randomized greedy MIS with respect to the actual number of edges. More specifi- algorithm, thus answering the main open question of cally, our algorithm distinguishes between graphs that are Blelloch, Fineman, and Shun [SPAA’12]. The paral- -close to having arboricity α and graphs that c · -far from having arboricity 3α,wherec is an absolute small constant. lel/distributed randomized greedy Maximal Independent The query complexity and running time of the algorithm Set (MIS) algorithm works as follows. An order of the DA18 Abstracts 77

vertices is chosen uniformly at random. Then, in each in hypergraphs has been a long-standing algorithmic chal- round, all vertices that appear before their neighbors in lenge, dating back nearly 30 years to a survey of Karp the order are added to the independent set and removed & Ramachandran (1990). Despite its apparent simplicity, from the graph along with their neighbors. The main there have been no general sub-polynomial-time algorithms question of interest is the number of rounds it takes un- or hardness reductions. The best randomized parallel al- til the graph is empty. This algorithm has been stud- gorithm for hypergraphs of fixed rank r was developed ied since 1987, initiated by Coppersmith, Raghavan, and by Beame & Luby (1990) and Kelsen (1992), running in Tompa [FOCS’87], and the previously best known bounds time roughly (log n)r!. The key probabilistic tool of this were O(log n) rounds in expectation for Erd˝os-R´enyi ran- algorithm is a concentration bound for low-degree poly- dom graphs by Calkin and Frieze [Random Struc. & Alg. nomials applied to independent input variables; this is a ’90] and O(log2 n) rounds with high probability for general natural generalization of concentration bounds for sums graphs by Blelloch, Fineman, and Shun [SPAA’12]. We of independent random variables, which are ubiquitous in combinatorics and computer science. The algorithm of prove a high probability upper bound of O(log n)onthe Kelsen cannot be derandomized in a standard way, and round complexity of this algorithm in general graphs, and there are no deterministic parallel algorithms for hyper- that this bound is tight. This also shows that parallel ran- graph MIS known for any fixed rank r>3. We improve domized greedy MIS is as fast as the celebrated algorithm the randomized algorithm of Kelsen to obtain a running of Luby [STOC’85, JALG’86] r time of (log n)2 . We also give a method for derandomiz- ing concentration bounds for polynomials, thus obtaining Manuela Fischer, Andreas Noever r+3 ETH Zurich a deterministic algorithm running in (log n)2 time and manuela.fi[email protected], [email protected] (mn)O(1) processors. Our analysis can also apply when r is slowly growing; using this in conjunction with a strategy of Bercea et al. (2015) gives a deterministic MIS algorithm CP29 log m running in time exp(O( log log m +loglogn). Space-Optimal Majority in Population Protocols

Population protocols are a model of distributed computing, David G. Harris in which n agents with limited local state interact ran- University of Maryland domly, and cooperate to collectively compute global pred- [email protected] icates. Majority is a central task, in which agents need to collectively reach a decision as to which one of two states A or B had a higher initial count. Two important complex- ity metrics are the time that a protocol requires to stabi- CP29 lize to an output decision, and the state space size that each agent requires. It is known that majority requires Community Detection on Euclidean Random Ω(log log n) states per agent to allow for poly-logarithmic Graphs time stabilization, and that O(log2 n) states are sufficient. Thus, there is an exponential gap between the upper and We study Community Detection (CD) on a class of sparse lower bounds. We provide a new lower bound of Ω(log n) 1−c spatial random graphs embedded in the Euclidean space. states for any protocol which stabilizes in O(n )time, Our graph is the planted-partition version of the random for any c>0. This result is conditional on basic mono- connection model studied in Stochastic Geometry. Each tonicity and output assumptions, satisfied by all known node has two labels - an i.i.d. uniform {−1, +1} valued protocols. Technically, it represents a significant depar- community label and a Rd valued location label which form ture from previous lower bounds. We give an algorithm the support of a Poisson Point Process of intensity λ on for majority which uses O(log n) states, and stabilizes in Rd 2 . Conditional on the labels, edges are drawn indepen- O(log n) time. Central to the algorithm is a new leaderless dently at random depending on both the community and phase clock, which allows nodes to synchronize in phases location labels of nodes. The CD problem then consists in of Θ(n log n) consecutive interactions using O(log n) states estimating the partition of nodes into communities better per node. We also employ our phase clock to build a leader than at random, based on an observation of the random election algorithm with O(log n) states, which stabilizes in 2 graph and the spatial location labels on nodes. We es- O(log n)time. tablish a non-trivial phase-transition for this problem in Rati Gelashvili terms of λ. We show that for small λ, there exists no algo- MIT rithm for CD. For large λ, we propose an algorithm which [email protected] solves CD efficiently. In certain special cases, we estab- lish the exact threshold on λ which separates the existence of an algorithm which solves CD from the impossibility of Dan Alistarh such an algorithm. We also establish a distinguishability ETH Zurich result which says that one can always efficiently infer the [email protected] existence of a partition given the graph and the spatial lo- cations even when one cannot identify the partition better James Aspnes than at random. This is a new phenomenon not observed Yale thus far in any Erd˝os-R´enyi based models. [email protected] Abishek Sankararaman CP29 The University of Texas at Austin Derandomized Concentration Bounds for Polyno- [email protected] mials, and Hypergraph Maximal Independent Set Fran¸cois Baccelli A parallel algorithm for maximal independent set (MIS) The University of Texas At Austin 78 DA18 Abstracts

[email protected] goal of the players is to win a race rather than maximizing the expected payoff.

CP29 Soheil Behnezhad Approximate Positive Correlated Distributions University of Maryland and Approximation Algorithms for D-Optimal De- [email protected] sign Avrim Blum Experimental design is a classical area in statistics. In Carnegie Mellon University the combinatorial experimental design problem, the aim is [email protected] to estimate an unknown m-dimensional vector x from lin- ear measurements where a Gaussian noise is introduced in Mahsa Derakhshan each measurement. The goal is to pick k out of the given University of Maryland n experiments so as to make the most accurate estimate [email protected] of the unknown parameter x. Given a set S of chosen ex- periments, the most likelihood estimate x can be obtained by a least squares computation. One of the robust mea- MohammadTaghi Hajiaghayi sures of error estimation is the D-optimality criterion which University of Maryland, College Park aims to minimize the generalized variance of the estimator. [email protected] The problem gives rise to two natural variants depending on whether repetitions of experiments is allowed or not. Mohammad Mahdian We show a close connection between approximation algo- Google Research rithms for the D-optimal design problem and constructions [email protected] of approximately m-wise positively correlated distributions. 1 This connection allows us to obtain a e -approximation for Christos H. Papadimitriou the D-optimal design problem with and without repetitions ?University of California at Berkeley giving the first constant factor approximation for the prob- [email protected] lem. We then consider the case when the number of ex- periments chosen is much larger than the dimension m and Ronald L. Rivest − k ≥ 2m show one can obtain (1 )-approximation if  when Massachusetts Institute of Technology m 1 · 1 repetitions are allowed and if k = O  + 2 log  when [email protected] no repetitions are allowed improving on previous work.

Weijun Xie Saeed Seddighin Virginia Tech University of Maryland, College Park [email protected] [email protected]

Mohit Singh Philip B. Stark H. Milton Stewart School of Industrial & Systems University of California at Berkeley Engineering [email protected] Georgia Institute of Technology [email protected] CP30 Approximating the Nash Social Welfare with CP30 Budget-Additive Valuations From Battlefields to Elections: Winning Strategies of Blotto and Auditing Games We present the first constant-factor approximation algo- rithm for maximizing the Nash social welfare when allo- Mixedstrategiesareoftenevaluatedbasedontheexpected cating indivisible items to agents with budget-additive val- payoff that they guarantee. This is not always desirable. uation functions. Budget-additive valuations represent an In this paper, we consider games for which maximizing important class of submodular functions. They have at- the expected payoff deviates from the actual goal of the tracted a lot of research interest in recent years due to many players. To address this issue, we introduce the notion of interesting applications. For every >0, our algorithm a(u, p)-maxmin strategy which ensures receiving a min- obtains a (2.404 + )-approximation in time polynomial in imum utility of u with probability at least p.Wethen the input size and 1/ . Our algorithm relies on rounding an give approximation algorithms for the problem of finding approximate equilibrium in a linear Fisher market where a(u, p)-maxmin strategy for these games. We consider sellers have earning limits (upper bounds on the amount the classic Colonel Blotto game. Two colonels divide their of money they want to earn) and buyers have utility lim- troops among a set of battlefields. Each battlefield is won its (upper bounds on the amount of utility they want to by the colonel that puts more troops in it. The payoff of achieve). In contrast to markets with either earning or each colonel is the weighted number of battlefields that she utility limits, these markets have not been studied before. wins. The Colonel Blotto game has found applications in They turn out to have fundamentally different properties. the analysis of many different forms of competition: from Although the existence of equilibria is not guaranteed, we sports to advertisement, to politics. We show that if we show that the market instances arising from the Nash so- maximize the expected payoff of a player, it does not nec- cial welfare problem always have an equilibrium. Further, essarily maximize the winning probability of that player for we show that the set of equilibria is not convex, answering certain applications of Colonel Blotto. We give an exact a question of Cole et al. (EC 2017). We design an FPTAS algorithm for a natural variant of the continuous version to compute an approximate equilibrium, a result that may of this game. More generally, we provide constant and log- be of independent interest. arithmic approximation algorithms that approximate the optimal strategies of the players in this game when the Jugal Garg DA18 Abstracts 79

UNIV OF ILLINOIS AT URBANA CHAMPAIGN our protocol for the allocation problem implies a new style [email protected] of truthful mechanisms.

Martin Hoefer Mark Braverman, Jieming Mao, S. Matthew Weinberg Goethe-Universitat Frankfurt am Main Princeton University [email protected] [email protected], jiem- [email protected], [email protected] Kurt Mehlhorn MPI for Informatics CP30 Saarbruecken, Germany [email protected] A New Class of Combinatorial Markets with Cov- ering Constraints: Algorithms and Applications

CP30 We introduce a new class of combinatorial markets in which agents have covering constraints over resources required Nash Social Welfare for Indivisible Items under and are interested in delay minimization. Our market Separable, Piecewise-Linear Concave Utilities model is applicable to several settings including schedul- Recently Cole and Gkatzelis gave the first constant factor ing and communicating over a network. This model is approximation algorithm for the problem of allocating in- quite different from the traditional models, to the extent divisible items to agents, under additive valuations, so as that neither do the classical equilibrium existence results to maximize the Nash Social Welfare (NSW). We give con- seem to apply to it nor do any of the efficient algorithmic stant factor algorithms for a substantial generalization of techniques developed to compute equilibria. In particular, their problem – to the case of separable, piecewise-linear our model does not satisfy the condition of non-satiation, concave utility functions. We give two such algorithms, which is used critically to show the existence of equilibria the first using market equilibria and the second using the in traditional market models and we observe that our set theory of real stable polynomials. Both approaches require of equilibrium prices could be a connected, non-convex set. new algorithmic ideas. We give a proof of the existence of equilibria and a poly- nomial time algorithm for finding one, drawing heavily on Tung Mai techniques from LP duality and submodular minimization. Georgia Institute of Technology Finally, we show that our model inherits many of the fair- [email protected] ness properties of traditional equilibrium models as well as new models, such as CEEI. Nima Anari Sadra Yazdanbod Stanford University Georgia Institute of Technology [email protected] [email protected] Shayan Oveis Gharan Nikhil R. Devanur University of Washington Microsoft Research, Redmond [email protected] [email protected] Vijay Vazirani Jugal Garg University of California, Irvine UNIV OF ILLINOIS AT URBANA CHAMPAIGN [email protected]. [email protected]

CP30 Ruta Mehta On Simultaneous Two-Player Combinatorial Auc- University of Illinois at Urbana-Champaign tions [email protected]

We consider the following communication problem: Al- Vijay V. Vazirani ice and Bob each have some valuation functions v1(·)and Georgia Institute of Technology v2(·) over subsets of m items, and their goal is to parti- [email protected] tion the items into S, S¯ in a way that maximizes the wel- fare, v1(S)+v2(S¯). We study both the allocation problem, which asks for a welfare-maximizing partition and the de- CP31 cision problem, which asks whether or not there exists a Tight Bounds on the Round Complexity of the Dis- partition guaranteeing certain welfare, for binary XOS val- tributed Maximum Coverage Problem uations. For interactive protocols with poly(m) communi- cation, a tight 3/4-approximation is known. For interactive We study the distributed maximum coverage problem in protocols, the allocation problem is provably harder than which the input sets S1,...,Sm over universe [n] are par- the decision problem: any solution to the allocation prob- titioned across p machines and the goal is to find k sets lem implies a solution to the decision problem with one whose union covers the most number of elements. The additional round and log m additional bits of communica- computation proceeds in rounds. In each round, all ma- tion via a trivial reduction. Surprisingly, the allocation chines simultaneously send a message to a central coor- problem is provably easier for simultaneous protocols. In dinator who then communicates back to the machines a other words, this trivial reduction from decision to alloca- summary to guide the computation for the next round. tion problems provably requires the extra round of commu- At the end, the coordinator outputs the answer. The main nication. We further discuss the implications of our results measures of efficiency in this setting are the approximation for the design of truthful combinatorial auctions in general, ratio of the returned solution, the communication cost of and extensions to general XOS valuations. In particular, each machine, and the number of rounds of computation. 80 DA18 Abstracts

Our main result is an asymptotically tight bound on the ing power than commonly used measures, based on local tradeoff between these measures for the maximum cover- or partial structural information of networks. Despite the age problem. We show that any r-round protocol for this strong advantages of Kirchhoff index as a centrality mea- problem either incurs a communication cost of k·mΩ(1/r) or sure, computing the exact value of Kirchhoff edge centrality only achieves an approximation factor of kΩ(1/r).Wethen for each edge in a graph is computationally demanding. To complement our lower bound by showing that there exist solve this problem, for each of the θ-Kirchhoff edge central- e ity metrics, we present an efficient algorithm to compute an r-round protocol that achieves an − -approximation e 1 its -approximation for all the m edges in nearly linear time with a communication cost of k · mO(1/r) as well as an r- in m. The proposed θ-Kirchhoff edge centrality is the first round protocol that achieves a kO(1/r)-approximation with ˜ global metric of edge importance that can be provably ap- only O(n) communication per machine. We further use proximated in nearly-linear time. Moreover, according to our results in this setting to obtain new bounds for the the θ-Kirchhoff edge centrality, we present a θ-Kirchhoff maximum coverage problem in other main models of com- vertex centrality measure, as well as a fast algorithm to putation for massive datasets such as dynamic streams and compute -approximate Kirchhoff vertex centrality for all the MapReduce model. the n vertices in nearly linear time in m. Sepehr Assadi, Sanjeev Khanna University of Pennsylvania Huan Li, Zhongzhi Zhang [email protected], [email protected] Fudan University, China [email protected], [email protected] CP31 Conflict-Free Coloring of Intersection Graphs of Geometric Objects CP31

In FOCS’2002, Even et al. introduced the notion of Lower Bounds for Symbolic Computation on conflict-free (CF) colorings of geometrically defined hyper- Graphs: Strongly Connected Components, Live- graphs. They motivated it by frequency assignment prob- ness, Safety, and Diameter lems in cellular networks. This notion has been extensively studied since then. A CF coloring of a graph is a coloring of its vertices such that the neighborhood (pointed or closed) A model of computation that is widely used in the formal of each vertex contains a vertex whose color differs from analysis of reactive systems is symbolic algorithms. In this the colors of all other vertices in that neighborhood. In model the access to the input graph is restricted to sym- this paper we study CF colorings of intersection graphs of bolic operations, which are expensive in comparison to the geometric objects. We show that any intersection graph standard RAM operations. We give lower bounds on the of n pseudo-discs in the plane admits a CF coloring with number of symbolic operations for basic graph problems O(log n) colors, with respect to both closed and pointed such as the computation of the strongly connected compo- neighborhoods, and that the latter bound is asymptoti- nents (SCCs) and of the approximate diameter as well as cally sharp. Using our methods, we obtain a strengthening for fundamental problems in model checking such as safety, of the two main results of Even et al.: Any family F of liveness, and co-liveness. Our lower bounds are linear in the n discs in the plane can be colored with O(log n) colors number of vertices of the graph, even for constant-diameter in such a way that for any disc B in the plane, the set graphs. For none of these problems lower bounds on the of discs in F that intersect B contains a uniquely-colored number of symbolic operations were known before. The element. Moreover, such a coloring can be computed deter- lower bounds show an interesting separation of these prob- ministically in polynomial time. In view of the motivation lems from the reachability problem, which can be solved to study such colorings, this suggests further applications with O(D) symbolic operations, where D is the diameter to frequency assignment in wireless networks. Finally, we of the graph. Additionally we present an approximation√ ˜ present bounds on the number of colors needed for CF algorithm for the graph diameter which requires O(n D) colorings of other classes of intersection graphs, including symbolic steps to achieve a (1 + )-approximation for any intersection graphs of axis-parallel rectangles and of ρ-fat constant >0. This compares to O(n · D) symbolic steps objects in the plane. for the (naive) exact algorithm and O(D) symbolic steps for a 2-approximation. Finally we also give a refined analy- Chaya Keller, Shakhar Smorodinsky sis of the SCC algorithm of [Gentilini et al. 2008], showing BenGurionUniversity that it uses an optimal number of symbolic steps that is [email protected], [email protected] proportional to the sum of the diameters of the SCCs.

CP31 Veronika Loitzenbauer University of Vienna Kirchhoff Index As a Measure of Edge Centrality [email protected] in Weighted Networks: Nearly Linear Time Algo- rithms Krishnendu Chatterjee We propose to use the well-known Kirchhoff index as the IST Austria measure of edge centrality in weighted networks, called θ- [email protected] Kirchhoff edge centrality. The Kirchhoff index of a network is defined as the sum of effective resistances over all vertex Wolfgang Dvor´ak pairs. The centrality of an edge e is reflected in the in- TU Wien crease of Kirchhoff index of the network when the edge e is [email protected] partially deactivated, characterized by a parameter θ.We define two equivalent measures for θ-Kirchhoff edge central- Monika Henzinger ity. Both are global metrics and have a better discriminat- Univeristy of Vienna, Austria DA18 Abstracts 81

− O log log n+log δ 1 [email protected] variant can be solved using ( ε2 +logn)bits of space, which we show to be optimal.

CP31 Jaroslaw Blasiok Algorithms Based on *-Algebras, and Their Appli- Harvard Unibersity cations to Isomorphism of Polynomials with One [email protected] Secret, Group Isomorphism, and Polynomial Iden- tity Testing CP32 We consider two basic algorithmic problems concerning Efficient O(n/ ) Spectral Sketches for the Laplacian (skew-)symmetric matrix tuples. The first problem asks and Its Pseudoinverse to decide, given two tuples of (skew-)symmetric matrices (B1,...,Bm)and(C1,...,Cm), whether there exists an In this paper we consider the problem of efficiently com- invertible matrix A such that for every i ∈{1,...,m}, puting -sketches for the Laplacian and its pseudoinverse. t A BiA = Ci. We show that this problem can be solved For a given matrix A and an error tolerance , we seek to in randomized polynomial time over finite fields of odd construct a function f such that for any vector x (chosen size, the real field, and the complex field. The second obliviously from f), with high probability (1 − )xAx ≤ problem asks to decide, given a tuple of square matrices f(x) ≤ (1+ )xAx. Our goal is to construct such a sketch (B1,...,Bm), whether there exist invertible matrices A f efficiently and to store it in the least space possible. ∈{ } and D, such that for every i 1,...,m , ABiD is (skew- We provide nearly-linear time algorithms that, when given )symmetric. We show that this problem can be solved in a Laplacian matrix L∈Rn×n and an error tolerance deterministic polynomial time over fields of characteristic , produces O˜(n/ )-size sketches of both L and its pseu- not 2. For both problems we exploit the structure of the ˜ underlying ∗-algebras (algebras with an involutive anti- doinverse’s quadratic form, where the O() notation hides automorphism). Applications of our results range from polylogarithmic factors in n and . Our algorithms im- ˜ 1.6 multivariate cryptography, group isomorphism, to polyno- prove upon the previous best sketch size of O(n/ )for sketching Laplacians by Andoni et al [ITCS 2016] and the mial identity testing: (1) Test isomorphism of quadratic 2 forms with one secret over a finite field of odd size. (2) previous best sketch size of O(n/ ) for sketching Lapla- Test isomorphism of p-groups of class 2 and exponent p (p cian pseudoinverses by Batson, Spielman, and Srivastava k [STOC 2009]. odd) with order p in time polynomial in the group√ order, O( k) Furthermore, we show how to compute all-pairs effective when the commutator subgroup is of order p .(3)De- resistances from our O˜(n/ )-size sketch in O˜(n2/ )time. terministically reveal two families of singularity witnesses This improves upon the previous best running time of for the symbolic determinant identity testing problem. O˜(n2/ 2) by Spielman and Teng, [STOC 2004]. Youming Qiao Centre for Quantum Software and Information Arun Jambulapati, Aaron Sidford University of Technology Sydney Stanford University [email protected] [email protected], [email protected]

G´abor Ivanyos CP32 Institute for Computer Science and Control Hungarian Academy of Sciences A Nearly Instance Optimal Algorithm for Top-K [email protected] Ranking under the Multinomial Logit Model We study the active learning problem of top-k ranking CP32 from multi-wise comparisons under the popular multino- mial logit model. Our goal is to identify the top-k items Optimal Streaming and Tracking Distinct Elements with high probability by adaptively querying sets for com- with High Probability parisons and observing the noisy output of the most pre- ferred item from each comparison. To achieve this goal, we The distinct elements problem is one of the fundamen- design a new active ranking algorithm without using any tal problems in streaming algorithms — given a stream information about the underlying items’ preference scores. of integers in the range {1,...,n},wewishtoprovidea We also establish a matching lower bound on the sample (1 + ε) approximation of the number of distinct elements complexity even when the set of preference scores is given in the input. After a long line of research optimal solu- to the algorithm. These two results together show that tion for this problem with constant probability of success, the proposed algorithm is nearly instance optimal (simi- using O( 1 +logn) bits of space, was given by Kane, Nel- ε2 lar to instance optimal [Ronald Fagin, Amnon Lotem, and son and Woodruff in 2010. The standard approach used Moni Naor, Optimal aggregation algorithms for middle- in order to achieve low failure probability δ,istotakea − ware, J. Comput. Syst. Sci., 66(4):614-656, 2003], but up median of log δ 1 parallel repetitions of the original algo- to polylog factors). Our work extends the existing litera- rithm. We show that such a multiplicative space blow- ture on rank aggregation in three directions. First, instead up is unnecessary: we provide an optimal algorithm using −1 of studying a static problem with fixed data, we investigate O log δ ( ε2 +logn) bits of space — matching known lower the top-k ranking problem in an active learning setting. − bounds for this problem. That is, the log δ 1 factor does Second, we show our algorithm is nearly instance optimal, not multiply the log n term. This settles completely the which is a much stronger theoretical guarantee. Finally, we space complexity of the distinct elements problem with re- extend the pairwise comparison to the multi-wise compari- spect to all standard parameters. We consider also strong son, which has not been fully explored in ranking literature. tracking (or continuous monitoring) variant of the distinct elements problem, where we want an algorithm which pro- vides an approximation of the number of distinct elements Xi Chen seen so far, at all times of the stream. We show that this New York Unviersity 82 DA18 Abstracts

[email protected] MIT [email protected] Yuanzhi Li,JiemingMao Princeton University Ronitt Rubinfeld [email protected], [email protected] CSAIL, MIT and Tel Aviv University [email protected]

CP32 Ali Vakilian Estimating Graph Parameters from Random Order MIT Streams CSAIL [email protected] We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. Anak Yodpinyanee We illustrate our technique by proving that in random or- MIT der streams with probability at least 2/3, [email protected] • the number of connected components of G can be approximated up to an additive error of εn using CP33 1 O(1/ε3) ( ε ) space, Envy-Free Chore Division for An Arbitrary Num- • the weight of a minimum spanning tree of an input ber of Agents graph with integer edges weights from {1,...,W} can be approximated within a multiplicative factor of 1+ε Chore division, introduced by Gardner in 1970s, is the   O˜(W 3/ε3) problem of fairly dividing a chore among n different agents. using 1 space, ε In particular, in an envy-free chore division, we would like • the size of a maximum independent set in planar to divide a negatively valued heterogeneous object among graphs can be approximated within a multiplicative a number of agents who have different valuations for differ- O(1) /ε (1/ε)log (1 ) ent parts of the object, such that no agent envies another factor of 1 + ε using space 2(1/ε) . agent. It is the dual variant of the celebrated cake cutting problem, in which we would like to divide a desirable object Pan Peng among agents. In this paper, we provide the first discrete Faculty of Computer Science, University of Vienna and bounded envy-free protocol for chore division for an [email protected] arbitrary number of agents. We produce major and pow- erful tools for designing protocols for the fair division of Christian Sohler negatively valued objects. These tools are based on struc- Department of Computer Science tural results and important observations. In general, we Technische Universitat Dortmund believe these structures and techniques may be useful not [email protected] only in chore division but also in other fairness problems.

Hadi Yami, Sina Dehghani, Alireza Farhadi, CP32 MohammadTaghi Hajiaghayi Set Cover in Sub-Linear Time University of Maryland [email protected], [email protected], We study the classic set cover problem from the perspec- [email protected], [email protected] tive of sub-linear algorithms. Given access to a collection of m sets over n elements in the query model, we show that sub-linear algorithms derived from existing techniques CP33 have almost tight query complexities. On one hand, first we show an adaptation of the streaming algorithm of Har- Almost Envy-Freeness with General Valuations Peled et al. to the sub-linear query model, that returns an ˜ 1/(α−1) The goal of fair division is to distribute resources among α-approximate cover using O(m(n/k) + nk)queries competing players in a “fair” way. Envy-freeness is the to the input, where k denotes the value of a minimum set most extensively studied fairness notion in fair division. cover. We then complement this upper bound by proving Envy-free allocations do not always exist with indivisible that for lower values of k, the required number of queries goods, motivating the study of relaxed versions of envy- ˜ 1/(2α) is Ω(m(n/k) ), even for estimating the optimal cover freeness. We study the envy-freeness up to any good (EFX) size. Moreover, we prove that even checking whether a property, which states that no player prefers the bundle of given collection of sets covers all the elements would require another player following the removal of any single good, Ω(nk) queries. These two lower bounds provide strong evi- and prove the first general results about this property. We dence that the upper bound is almost tight for certain val- use the leximin solution to show existence of EFX allo- ues of the parameter k. On the other hand, we show that cations in several contexts, sometimes in conjunction with this bound is not optimal for larger values of the parameter Pareto optimality. For two players with valuations obeying k,asthereexistsa(1+ε)-approximation algorithm with a mild assumption, one of these results provides stronger O˜(mn/kε2) queries. We show that this bound is essen- guarantees than the currently deployed algorithm on Splid- tially tight for sufficiently small constant ε, by establishing dit, a popular fair division website. Unfortunately, find- a lower bound of Ω(˜ mn/k)querycomplexity. ing the leximin solution can require exponential time. We show that this is necessary by proving an exponential lower Piotr Indyk bound on the number of value queries needed to identify an Massachusetts Institute of Technology EFX allocation, even for two players with identical valua- [email protected] tions. We consider both additive and more general valua- tions, and our work suggests that there is a rich landscape Sepideh Mahabadi of problems to explore in the fair division of indivisible DA18 Abstracts 83

goods with different classes of player valuations. Hu Fu, Chris Liaw University of British Columbia Benjamin Plaut [email protected], [email protected] Stanford University [email protected] Pinyan Lu Shanghai University of Finance and Economics Tim Roughgarden [email protected] Stanford University Computer Science Department [email protected] CP33 Targeting and Signaling in Ad Auctions

CP33 Modern ad auctions allow advertisers to target more spe- cific segments of the user population. Unfortunately, this is The Price of Information in Combinatorial Opti- not always in the best interest of the ad platform – partially mization hiding some information could improve the platform’s rev- enue. In this paper, we examine how to optimally reveal Consider a network design application where we wish to information about the ad opportunity to the advertisers lay down a minimum-cost spanning tree in a given graph; in order to maximize revenue in a second-price ad auc- however, we only have stochastic information about the tion. We consider a model in which bidders’ valuations edge costs. To learn the precise cost of any edge, we have depend on a random state of the ad opportunity drawn to conduct a study that incurs a price. Our goal is to find a from an extremely large support, and focus on developing spanning tree while minimizing the disutility, which is the algorithms whose running time is independent of the num- sum of the tree cost and the total price that we spend on the ber of ad opportunity realizations. When the auctioneer is studies. Situations such as the above often arise in practice restricted to send a public signal to all bidders, we study when we wish to find a good solution to an optimization a well-motivated Bayesian valuation setting in which the problem, but we start with only some partial knowledge auctioneer and bidders both have private information, and about the input parameters. The missing information can present two results: (1) an exponential lower bound on be found only after paying a probing price, which we call the minimum number of signals required in any constant- the price of information. What strategy should we adopt approximate signaling scheme; (2) a “simple” signaling to optimize our expected utility/disutility? A classical ex- scheme that serves as a constant approximation under mild ample of the above setting is Weitzman’s “Pandora’s box’ assumptions. We also initiate an exploration on the power problem where we are given probability distributions on of being able to send private signals to different bidders. values of n independent random variables. The goal is to In a basic setting where the auctioneer knows bidders’ val- choose a single variable with a large value, but we find uations, we exhibit a polynomial-time private scheme that the actual outcomes only after paying a price. Our work extracts almost full surplus even in the worst Bayes Nash is a generalization of this model to other combinatorial equilibrium. This illustrates the surprising power of private optimization problems such as matching, set cover, facil- signaling schemes in extracting revenue. ity location, and prize-collecting Steiner tree. We give a technique that reduces such problems to their non-price Ashwinkumar Badanidiyuru, Kshipra Bhawalkar counterparts, and use it to design exact/approximation al- Google Research gorithms to optimize our utility/disutility. [email protected], [email protected] Sahil Singla Haifeng Xu CMU University of Southern California [email protected] [email protected]

CP33 CP34 The Value of Information Concealment The Complexity of Distributed Edge Coloring with Small Palettes We consider a revenue optimizing seller selling a single item to a buyer, on whose private value the seller has a noisy The complexity of distributed edge coloring depends heav- signal. We show that, when the signal is kept private, arbi- ily on the palette size as a function of the maximum degree trarily more revenue could potentially be extracted than if Δ. In this paper we explore the complexity of edge coloring the signal is leaked or revealed. We then show that, if the in the LOCAL model in different palette size regimes. seller is not allowed to make payments to the buyer, the • We simplify the round elimination technique of gap between the two is bounded by a multiplicative factor Brandt et al. and prove that (2Δ − 2)-edge color- of 3, subject to fairly mild conditions on the joint distribu- ing requires Ω(logΔ log n) time w.h.p. and Ω(logΔ n) tion of the value and signal. Our examples show that both time deterministically, even on trees. conditions are necessary for a constant bound to hold. We • connect this scenario to multi-bidder single-item auctions We give a randomized edge coloring√ algorithm using ˜ where bidders’ values are correlated. Results similar to palette sizes as small as Δ+O( Δ), which is a natural the above are shown for the gap between the revenue of barrier for randomized approaches. The running time · a Bayesian incentive compatible, ex post individually ra- of the algorithm is at most O(log Δ TLLL), where tional auction and that of a dominant strategy incentive TLLL is the complexity of a permissive version of the compatible auction. constructive Lovasz local lemma. • We develop a new distributed Lovasz local lemma al- Zhihao Gavin Tang gorithm for tree-structured dependency graphs, which The University of Hong Kong leads to a (1 + )Δ-edge coloring algorithm for trees [email protected] running in O(log log n)time. 84 DA18 Abstracts

• A natural approach to computing (Δ + 1)-edge color- Konstantinos Panagiotou ings (Vizing’s theorem) is to extend partial colorings University of Munich by re-coloring parts of the graph. We prove that this [email protected] approach may be viable, but in the worst case requires recoloring subgraphs of diameter Ω(Δ log n). This is Pascal Su in contrast to distributed algorithms for Brooks’ the- ETH Zurich orem, which exploit the existence of O(logΔ n)-length [email protected] augmenting paths.

CP34 Yi-Jun Chang University of Michigan Mst in O(1) Rounds of Congested Clique [email protected] We present a distributed randomized algorithm finding Minimum Spanning Tree (MST) of a given graph in O(1) Qizheng He, Wenzheng Li rounds, with high probability, in the congested clique IIIS, Tsinghua University model. The input graph in the congested clique model is a [email protected], graph of n nodes, where each node initially knows only its [email protected] incident edges. The communication graph is a clique with limited edge bandwidth: each two nodes (not necessarily Seth Pettie neighbours in the input graph) can exchange O(log n)bits. University of Michigan As in previous works, the key part of the MST algorithm is [email protected] an efficient Connected Components (CC) algorithm. How- ever, unlike the former approaches, we do not aim at simu- Jara Uitto lating the standard Boruvka’s algorithm, at least at initial ETH Zurich stages of the CC algorithm. Instead, we develop a new [email protected] technique which combines connected components of sam- ple sparse subgraphs of the input graph in order to accel- erate the process of uncovering connected components of CP34 the original input graph. Our result addresses a problem proposed by Lotker et al. [SPAA 2003; SICOMP 2005] Labeling Schemes for Nearest Common Ancestors ∗ Through Minor-Universal Trees and improves over previous O(log n) algorithm of Ghaf- fari et al. [PODC 2016], and O(log log log n) algorithm of A labeling scheme for nearest common ancestors assigns a Hegeman et al. [PODC 2015]. It also determines Θ(1) distinct binary string, called the label, to every node of a round complexity in the congested clique for MST, as well tree. Given the labels of two nodes (and no further infor- as other graph problems, including bipartiteness, cut veri- mation about the topology of the tree), we can compute fication, s-t connectivity, and cycle containment. the label of their nearest common ancestor. The goal is to make the labels short. Alstrup, Gavoille, Kaplan, and Tomasz Jurdzinski Rauhe [Theor. Comput. Syst. 37(3):441-456 2004] showed University of Wroclaw that O(log n)-bit labels are enough. More recently, Al- [email protected] strup, Halvorsen, and Larsen [SODA 2014] refined this to only 2.772 log n, and provided a lower bound of 1.008 log n. Krzysztof Nowicki We connect the question of designing such a scheme to the University of Wroclaw existence of a tree, called a minor-universal tree, that con- University of Wroclaw tains every tree on n nodes as a topological minor. Even [email protected] though it is not clear if a labeling scheme must be based on such a notion, we argue that all existing schemes can be reformulated as such. We show that this notion allows CP34 us to easily obtain good bounds on the length of the la- Fast Space Optimal Leader Election in Population bels. As the main upper bound, we show that 2.318 log n- Protocols bit labels are enough. On the lower bound side, we show that any minor-universal tree for trees on n nodes must The model of population protocols refers to the growing 2.174 contain Ω(n ) nodes. We complement the existential in popularity theoretical framework suitable for studying results with a generic transformation that allows us, for pairwise interactions within a large collection of simple in- any labeling scheme for nearest common ancestors based distinguishable entities, frequently called agents.Inthis on a minor-universal tree, to decrease the query time to paper the emphasis is on the space complexity in fast leader constant, while increasing the length of the labels by lower election via population protocols governed by the random order terms. scheduler, which uniformly at random selects pairwise in- teractions from the population of n agents. The main re- Pawel Gawrychowski sult of this paper is a new fast and space optimal leader University of Wroclaw election protocol. The new protocol operates in parallel [email protected] time O(log2 n)equivalenttoO(n log2 n)sequentialpair- wise interactions, in which each agent utilises O(log log n) Fabian Kuhn states. This double logarithmic space utilisation matches 1 University of Freiburg, Germany asymptotically the existing lower bound 2 log log n on the [email protected] number of states utilised by agents in any leader election n algorithm with the running time o( polylog n ). Our solu- Jakub Lopuszanski tion takes an advantage of the concept of phase clocks, a University of Wroclaw fundamental synchronisation and coordination tool in Dis- [email protected] tributed Computing. We propose a new fast and robust DA18 Abstracts 85

population protocol for initialisation of phase clocks to be for Q supported on {0, 1}×{0, 1}. We extend their result run simultaneously in multiple modes and intertwined with to Q supported on any finite alphabet. Moreover, we show the leader election process. We also provide the reader with that If can be simulated, our algorithm also provides a the relevant formal argumentation indicating that our so- (non-interactive) simulation protocol. We rely on recent lution is always correct and fast with high probability. results in Gaussian geometry (by the authors) as well as a new smoothing argument inspired by the method of boost- Leszek A. Gasieniec ing from learning theory and potential function arguments University of Liverpool from complexity theory and additive combinatorics. [email protected] Anindya De Grzegorz Stachowiak Northwestern University Uniwersytet Wroclawski [email protected] [email protected] Elchanan Mossel MIT CP34 n/a Ergodic Effects in Token Circulation Joe Neeman We consider a dynamical process in a network which dis- UT Austin tributes all particles (tokens) located at a node among its na/ neighbors, in a round-robin manner. We show that in the recurrent state of this dynamics (i.e., disregarding a polynomially-long initialization phase of the system), the CP35 number of particles located on a given edge, averaged over Which Distribution Distances Are Sublinearly an interval of time, is tightly concentrated around the av- Testable? erage particle density in the system. Formally, for a system of k particles in a graph of m edges, during any interval of Given samples from an unknown distribution p and a de- length T , this time-averaged value is k/m±O(1/T ), when- scription of a distribution q, are p and q close or far? This ever gcd(m, k)=O(1) (and so, e.g., whenever m is a prime question of ”identity testing” has received significant at- number). To achieve these bounds, we link the behavior tention in the case of testing whether p and q are equal or of the studied dynamics to ergodic properties of traversals far in total variation distance. However, in recent work, the based on Eulerian circuits on a symmetric directed graph. following questions have been been critical to solving prob- Our results are proved through sum set methods. As a lems at the frontiers of distribution testing: -Alternative corollary, we obtain bounds on the idleness of the stud- Distances: Can we test whether p and q are far in other ied dynamics, i.e., on the longest possible time between distances? -Robustness: Can we test when p and q are two consecutive appearances of a token on an edge, taken close, rather than equal? And if so, close in which dis- over all edges. Minimizing idleness is fundamental to the tances? Motivated by these questions, we characterize the study of the patrolling problem in networks. Our results complexity of distribution testing under a variety of dis- tances, including L1, L2, Hellinger, KL, and χ2.Foreach immediately imply a bound of O(m/k) on the idleness of  pair of distances d1 and d2, we study the complexity of the studied process, showing that it is a distributed O(1)- testing if p and q are close in d1 versus far in d2, with a competitive solution to the patrolling task, for all of the focus on identifying which problems allow strongly sublin- covered cases. Our work provides further insights which ear testers. We provide matching upper and lower bounds may be interesting in load-balancing applications. for each case. We also study these questions in the case where we only have samples from q, showing qualitative Adrian Kosowski differences from identity testing in terms of when robust- Inria Paris ness can be achieved. Our algorithms fall into the classi- [email protected] cal paradigm of chi-squared statistics, but require crucial changes to handle the challenges introduced by each dis- Przemyslaw Uznanski tance we consider. Finally, we survey other recent results ETH Zurich in an attempt to serve as a reference for the complexity of [email protected] various distribution testing problems.

Constantinos Daskalakis, Gautam Kamath, John Wright CP35 MIT Non Interactive Simulation of Correlated Distribu- [email protected], [email protected], [email protected] tionsIsDecidable

A basic problem in information theory is the following: CP35 Let P =(X, Y) be an arbitrary distribution where the Robustly Learning a Gaussian: Getting Optimal marginals X and Y are (potentially) correlated. Let Alice Error, Efficiently and Bob be two players where Alice gets samples {xi}i≥1 and Bob gets samples {yi}i≥1 and for all i,(xi,yi) ∼ P. We study the fundamental problem of learning the parame- What joint distributions Q can be simulated by Alice and ters of a high-dimensional Gaussian in the presence of noise Bob without any interaction? Classical works in informa- –whereanε-fraction of our samples were chosen by an ad- tion theory by G´acs-K¨orner and Wyner answer this ques- versary. We give robust estimators that achieve estimation tion when at least one of P or Q is the distribution Eq error O(ε) in the total variation distance, which is optimal (Eq is defined as uniform over the points (0, 0) and (1, 1)). up to a universal constant that is independent of the di- However, other than this special case, the answer to this mension. In the case where just the mean is unknown,√ our question is understood in very few cases. Recently, Ghazi, robustness guarantee is optimal up to a factor of 2and Kamath and Sudan showed that this problem is decidable the running time is polynomial in d and 1/ε.Whenboth 86 DA18 Abstracts

the mean and covariance are unknown, the running time kernel density estimates within error , with coreset size is polynomial in d and quasipolynomial in 1/ε.Moreover 2/ 2, but no other aspects of the data, including the di- all of our algorithms require only a polynomial number mension, the diameter of the point set, or the bandwidth of samples. Our work shows that the same sorts of error of the kernel common to other approximations. When the guarantees that were established over fifty years ago in the dimension is unrestricted, we show this bound is tight for one-dimensional setting can also be achieved by efficient these kernels as well as a much broader set. This work algorithms in high-dimensional settings. provides a careful analysis of the iterative Frank-Wolfe al- gorithm adapted to this context, an algorithm called ker- Ilias Diakonikolas nel herding. This analysis unites a broad line of work that USC spans statistics, machine learning, and geometry. When [email protected] the dimension d is constant, we demonstrate much tighter bounds on the size of the coreset specifically for Gaussian Gautam Kamath kernels, showing that it is bounded by the size of the core- MIT set for axis-aligned rectangles. Currently the best known 1 d 1 [email protected] constructive bound is O(  log  ), and non-constructively, thiscanbeimprovedby log 1 . Thisimprovesthebest Daniel Kane  constant dimension bounds polynomially for d ≥ 3. UC San Diego [email protected] Wai Ming Tai, Jeff Phillips University of Utah Jerry Li, Ankur Moitra [email protected], jeff[email protected] MIT [email protected], [email protected] CP36 Alistair Stewart Covering a Tree with Rooted Subtrees – Parame- USC terized and Approximation Algorithms [email protected] We consider the multiple traveling salesman problem on a weighted tree. In this problem there are m salesmen lo- CP35 cated at the root initially. Each of them will visit a subset Cycles in Adversarial Regularized Learning of vertices and return to the root. The goal is to assign a tour to every salesman such that every vertex is visited and Regularized learning is a fundamental technique in on- longest tour among all salesmen is minimized. The prob- line optimization, machine learning and many other fields lem is equivalent to the subtree cover problem, in which we of computer science. A natural question that arises in cover a tree with rooted subtrees such that the weight of these settings is how regularized learning algorithms be- the maximum weighted subtree is minimized. The classi- have when faced against each other. We study a natural cal machine scheduling problem can be viewed as a special formulation of this problem by coupling regularized learn- case of our problem when the given tree is a star. We pro- ing dynamics in zero-sum games. We show that the sys- vide approximation and parameterized algorithms for this tem’s behavior is Poincar´e recurrent, implying that almost problem. We first present a PTAS (Polynomial Time Ap- every trajectory revisits any (arbitrarily small) neighbor- proximation Scheme). We then observe that, the problem hood of its starting point infinitely often. This cycling remains NP-hard even if tree height and edge weight are behavior is robust to the agents’ choice of regularization constant, and present an FPT algorithm for this problem mechanism (each agent could be using a different regu- parameterized by the largest tour length. To achieve the larizer), to positive-affine transformations of the agents’ FPT algorithm, we show a more general result. We prove utilities, and it also persists in the case of networked com- that, integer linear programming that has a tree-fold struc- petition, i.e., for zero-sum polymatrix games. ture is in FPT, which extends the FPT result for the n-fold integer programming by Hemmecke, Onn and Romanchuk Panayotis Mertikopoulos (Math. Programming, 2013). Univ. Grenoble Alpes, CNRS [email protected] Lin Chen Zhejiang University Christos Papadimitriou [email protected] Columbia University [email protected] D´aniel Marx Hungarian Academy of Sciences (MTA SZTAKI), Georgios Piliouras Budapest,Hungary Singapore University of Technology and Design [email protected] [email protected] CP36 CP35 Fully Polynomial Fpt Algorithms for Some Classes Improved Coresets for Kernel Density Estimates of Bounded Clique-Width Graphs

We study the construction of coresets for kernel density Recently, hardness results for problems in P were achieved estimates. That is we show how to approximate the kernel using reasonable complexity theoretic assumptions such as density estimate described by a large point set with another the Strong Exponential Time Hypothesis. According to kernel density estimate with a much smaller point set. For these assumptions, many graph theoretic problems do not characteristic kernels (including Gaussian and Laplace ker- admit truly subquadratic algorithms. A central technique nels), our approximation preserves the L∞ error between used to tackle the difficulty of the above mentioned prob- DA18 Abstracts 87

lems is fixed-parameter algorithms with polynomial depen- UiB+SDU dency in the fixed parameter (P-FPT). Applying this tech- [email protected] nique to clique-width, an important graph parameter, re- mained to be done. In this paper we study several graph Pranabendu Misra theoretic problems for which hardness results exist such UiB as cycle problems, distance problems and maximum match- [email protected] ing. We give hardness results and P-FPT algorithms, us- ing clique-width and some of its upper-bounds as param- Ramanujan M. S. eters. We believe that our most important result is an O 4 · University of Warwick (k n + m)-time algorithm for computing a maximum [email protected] matching where k is either the modular-width or the P4- sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such Saket Saurabh as cographs. Our algorithms are based on preprocessing IMSc +UiB methods using modular decomposition and split decompo- [email protected] sition. Thus they can also be generalized to some graph classes with unbounded clique-width. Meirav Zehavi Ben-Gurion University David Coudert [email protected] Universit´eCˆote dAzur, Inria, CNRS, I3S, France [email protected] CP36 Guillaume Ducoffe An Fpt Algorithm Beating 2-Approximation for K- ICI National Institute for Research and Development in Cut Informatics In the k-cut problem, we are given an edge-weighted graph guillaume.ducoff[email protected] G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k con- Alexandru Popa nected components. Prior work on this problem gives, for ICI National Institute for Research and Development in all h ∈ [2,k], a (2 − h/k)-approximation algorithm for Informatics, Romania k-cut that runs in time nO(h). Hence to get a (2 − )- [email protected] approximation algorithm for some absolute constant ,the best runtime using prior techniques is nO(k).Moreover,it − CP36 was recently shown that getting a (2 )-approximation for general k is NP-hard, assuming the Small Set Expansion Parameterized Algorithms for Survivable Network Hypothesis. If we use the size of the cut as the parame- Design with Uniform Demands ter, an FPT algorithm to find the exact k-cut is known, but Survivable Network Design Problem solving the k-cut problem exactly is W [1]-hard if we param- In the (SNDP), eterize only by the natural parameter of k. An immediate the input is an edge-weighted (di)graph G andaninteger ∈ question is: can we approximate k-cut better in FPT-time, ruv for every pair of vertices u, v V (G). The objective using k as the parameter? We answer this question pos- is to construct a subgraph H of minimum weight which itively. We show that for some absolute constant >0, contains ruv edge-disjoint (or node-disjoint) u-v paths. An there exists a (2 − )-approximation algorithm that runs important restriction of this problem is one where the con- O(k6) ·  4 nectivity demands are the same for every pair of vertices. in time 2 O(n ). This is the first FPT algorithm In this paper, we first consider the edge-connectivity ver- that is parameterized only by k and strictly improves the sion of this problem which we call λ-Edge Connected 2-approximation. Subgraph (λ-ECS). In this problem, the input is a λ-edge Jason M. Li, Anupam Gupta, Euiwoong Lee connected (di)graph G andanintegerk and the objective Carnegie Mellon University is to check whether G contains a spanning subgraph H that [email protected], [email protected], eui- is also λ-edge connected and H excludes at least k edges of [email protected] G.Ifwereplaceλ-edge connectivity with λ-vertex connec- tivity we get the λ-Veretx Connected Subgraph (λ- VCS -ECS ) problem. We show that λ is fixed-parameter CP36 tractable (FPT) for both graphs and digraphs even if the (di)graph has non-negative real weights on the edges and Covering Small Independent Sets and Separators the objective is to exclude from H, some edges of G whose with Applications to Parameterized Algorithms total weight exceeds a prescribed value. We also show that -VCS We present two new combinatorial tools for the design of λ is FPT on digraphs; however the problem on undi- parameterized algorithms. The first is a simple linear time rected graphs remains open. randomized algorithm that given as input a d-degenerate graph G and an integer k, outputs an independent set Joergen Bang-Jensen Y , such that for every independent set X in G of size at Department of Mathematics and Computer Science most k, the probability that X is a subset of Y is at least University of Southern Denmark   −1 (d+1)k · [email protected] k k(d +1) . The second is a new (determin- istic) polynomial time graph sparsification procedure that Manu Basavaraju given a graph G,asetT = {{s1,t1}, {s2,t2},...,{s,t}} NIT Suratkal of terminal pairs and an integer k, returns an induced sub- [email protected] graph G of G that maintains all the inclusion minimal multicuts of G of size at most k, and does not contain any Kristine Vittin Klinkby (k +2)-vertex connected set of size 2O(k).Inparticular,G 88 DA18 Abstracts

excludes a clique of size 2O(k) as a topological minor. Put together, our new tools yield new randomized fixed param- eter tractable (FPT) algorithms for Stable s-t Separator, Stable Odd Cycle Transversal and Stable Multicut on gen- eral graphs, and for Stable Directed Feedback Vertex Set on d-degenerate graphs, resolving two problems left open by Marx et al. [ACM Transactions on Algorithms, 2013]. All of our algorithms can be derandomized at the cost of a small overhead in the running time.

Daniel Lokshtanov University of Bergen [email protected]

Fahad Panolan University of Bergen, Norway [email protected]

Saket Saurabh IMSc +UiB [email protected]

Roohani Sharma Institute of Mathematical Sciences, HBNI, Chennai, India [email protected]

Meirav Zehavi Ben-Gurion University [email protected] ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 89

Speaker Index 90 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

A D Gravin, Nick, CP27, 6:10 Tue Abboud, Amir, CP7, 6:10 Sun Dadush, Daniel, CP18, 4:55 Mon Groß, Martin, CP11, 9:50 Mon Akitaya, Hugo A., CP4, 3:40 Sun De, Anindya, CP17, 5:45 Mon Gu, Albert, CP14, 3:15 Mon Anari, Nima, CP14, 2:00 Mon De, Anindya, CP35, 5:45 Wed Gupta, Anupam, IP3, 11:30 Tue Andersen, Jakob L., 9:00 Mon, ALENEX de Mesmay, Arnaud, CP19, 10:40 Tue H Angriman, Eugenio, 9:50 Sun, ALENEX De Oliveira Oliveira, Mateus, CP2, 10:15 Harris, David G., CP29, 9:25 Wed Sun Assadi, Sepehr, CP31, 3:40 Wed Hartung, Lisa, 9:00 Tue, ANALCO Dikkala, Nishanth, CP26, 6:10 Tue Harvey, Nicholas, CP21, 9:25 Tue B Driemel, Anne, CP12, 9:50 Mon Behnezhad, Soheil, CP30, 9:50 Wed Hatami, Pooya, CP9, 5:20 Sun Ducoffe, Guillaume, CP36, 4:30 Wed Bendkowski, Maciej, 10:15 Tue, Hespe, Demian, 2:50 Mon, ALENEX Dvorak, Zdenek, CP22, 3:40 Tue ANALCO Holm, Jacob, CP1, 9:50 Sun Dwork, Cynthia, IP1, 11:30 Sun Ben-Eliezer, Omri, CP28, 9:25 Wed Bergamini, Elisabetta, 2:25 Mon, I E Isenmann, Lucas, CP3, 9:25 Sun ALENEX Efthymiou, Charilaos, CP23, 3:40 Tue Bernstein, Aaron, CP1, 9:25 Sun Ehsani, Soheil, CP10, 9:00 Mon J Bernstein, Aaron, CP13, 2:00 Mon Eisenbrand, Friedrich, CP11, 9:25 Mon Jambulapati, Arun, CP32, 3:15 Wed Besa Vial, Juan Jose, 3:15 Sun, ALENEX Elias, Marek, CP13, 3:15 Mon Jones, Mitchell F., CP12, 10:15 Mon Bhattacharya, Sayan, CP1, 9:00 Sun Emamjomeh-Zadeh, Ehsan, CP6, 2:50 Black, Hadley, CP28, 10:40 Wed Sun K Kamath, Gautam, CP35, 6:10 Wed Blanca, Antonio, CP26, 5:20 Tue Karanasiou, Aikaterini, 9:50 Mon, Blasiok, Jaroslaw, CP32, 2:00 Wed F Fahrbach, Matthew, CP8, 6:10 Sun ALENEX Bodwin, Greg, CP25, 4:55 Tue Fahrbach, Matthew, CP0, 10:40 Tue Karczmarz, Adam, CP1, 10:40 Sun Bodwin, Greg, CP25, 5:20 Tue Fan, Chenglin, CP3, 10:15 Sun Karingula, Sankeerth Rao, CP21, 9:00 Brakensiek, Joshua, CP24, 2:25 Tue Tue Farhadi, Alireza, CP33, 3:15 Wed Kaski, Petteri, 10:15 Mon, ALENEX Feldman, Moran, CP10, 9:50 Mon C Katzmann, Maximilian, 2:00 Mon, Ferrada, Hector, 9:00 Sun, ALENEX Cevallos, Alfonso, CP11, 9:00 Mon ALENEX Filtser, Arnold, CP18, 6:10 Mon Chan, Timothy M., CP12, 9:25 Mon Kawarabayashi, Ken-ichi, CP4, 2:25 Sun Filtser, Arnold, CP22, 2:50 Tue Chang, Hsien-Chih, CP2, 9:50 Sun Keller, Chaya, CP31, 3:15 Wed Fineman, Jeremy, CP3, 9:00 Sun Chang, Yi-Jun, CP34, 5:20 Wed Kempe, David, CP22, 2:00 Tue Fischer, Manuela, CP29, 9:00 Wed Chapman, Brynmor, CP9, 6:10 Sun Khan, Shahbaz, CP1, 10:15 Sun Focke, Jacob, CP24, 2:00 Tue Chapuy, Guillaume, CP12, 10:40 Mon Khodamoradi, Kamyar, CP6, 2:25 Sun Chen, Lin, CP36, 5:20 Wed Kling, Peter, CP23, 2:25 Tue Cheung, Yun Kuen, CP18, 5:45 Mon G Gao, Pu, CP23, 3:15 Tue Klinkby, Kristine Vittin, CP36, 6:10 Wed Chierichetti, Flavio, CP8, 5:20 Sun Garg, Jugal, CP30, 10:40 Wed Kociumaka, Tomasz, CP20, 10:15 Tue Choudhary, Keerti, CP25, 5:45 Tue Gawrychowski, Pawel, CP7, 5:45 Sun Koumoutsos, Grigorios, CP17, 4:30 Mon Chowdhury, Samir, CP15, 3:40 Mon Gawrychowski, Pawel, CP34, 4:30 Wed Kumar, Nirman, 2:25 Sun, ALENEX Clifford, Raphael, CP2, 10:40 Sun Gelashvili, Rati, CP29, 10:15 Wed Künnemann, Marvin, CP16, 5:45 Mon Cohen, Ilan R., CP13, 2:50 Mon Ghazi, Badih, CP24, 3:40 Tue Kurpicz, Florian, 9:25 Sun,, ALENEX Cohen-Addad, Vincent, CP6, 2:00 Sun Kwon, O-Joung, CP22, 3:15 Tue Cohen-Addad, Vincent, CP6, 3:15 Sun ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 91

Nayyeri, Amir, CP15, 2:25 Mon Sharma, Roohani, CP36, 4:55 Wed L Nivasch, Gabriel, 4:55 Sun, ALENEX Sheehy, Donald, CP15, 2:00 Mon Lagarde, Guillaume, CP20, 9:25 Tue Noe, Alexander, 2:00 Sun, ALENEX Shen, Xiangkun, CP17, 5:20 Mon Lahn, Nathaniel, CP7, 4:30 Sun Nøjgaard, Nikolai, 9:25 Mon, ALENEX Shi, Jessica, 2:00 Tue, ANALCO Lang, Harry, CP13, 3:40 Mon Nowicki, Krzysztof, CP34, 4:55 Wed Shimizu, Nobutaka, CP26, 4:30 Tue Le, Tien-Nam, CP5, 2:50 Sun Shin, Yujin, 4:30 Sun, ALENEX Le Gall, François, CP14, 2:25 Mon O Singla, Sahil, CP33, 2:00 Wed Levi, Amit, CP28, 9:50 Wed Ophelders, Tim, CP15, 2:50 Mon Sinha, Makrand, CP21, 10:15 Tue Levi, Reut, CP28, 9:00 Wed Sinnamon, Corwin, CP8, 4:30 Sun Li, Huan, CP31, 2:50 Wed P Paparas, Dimitris, CP27, 5:20 Tue Sportiello, Andrea, 6:10 Mon, ANALCO Li, Jason M., CP36, 5:45 Wed Paturi, Ramamohan, CP4, 2:50 Sun Stachowiak, Grzegorz, CP34, 5:45 Wed Li, Jerry, CP35, 4:30 Wed Peng, Pan, CP32, 2:25 Wed Starikovskaya, Tatiana, CP20, 10:40 Tue Li, Ray, CP9, 4:30 Sun Peres, Yuval, CP23, 2:00 Tue Straub, Jasmin, 4:30 Mon, ANALCO Li, Yuanzhi, CP32, 3:40 Wed Peres, Yuval, CP23, 2:50 Tue Subramanian, C R., 3:40 Tue, ANALCO Lin, Wei-Kai, CP28, 10:15 Wed Peres, Yuval, CP26, 5:45 Tue Sullivan, Blair, 2:50 Sun, ALENEX Lincoln, Andrea, CP16, 6:10 Mon Petti, Samantha N., 3:15 Tue, ANALCO Syrgkanis, Vasilis, CP10, 10:15 Mon Lindzey, Nathan, CP14, 3:40 Mon Piliouras, Georgios, CP35, 4:55 Wed Liu, Siqi, CP27, 4:30 Tue Plaut, Benjamin, CP33, 3:40 Wed T Löffler, Maarten, 9:25 Tue, ANALCO Tai, Wai Ming, CP35, 5:20 Wed Potukuchi, Aditya, CP9, 5:45 Sun Loitzenbauer, Veronika, CP31, 2:00 Wed Tal, Avishay, CP24, 3:15 Tue Prezza, Nicola, CP20, 9:00 Tue Lu, Pinyan, CP24, 2:50 Tue Tancer, Martin, CP18, 4:30 Mon Prezza, Nicola, CP20, 9:50 Tue Lumbroso, Jérémie, 2:50 Tue, ANALCO Tang, Zhihao Gavin, CP33, 2:25 Wed Q Thiruvenkatachari, Devanathan, CP19, M Qiao, Youming, CP31, 2:25 Wed 9:50 Tue Madan, Vivek, CP19, 9:25 Tue Quanrud, Kent, CP5, 3:40 Sun Thorup, Mikkel, IP2, 11:30 Mon Maehara, Takanori, CP5, 2:00 Sun Thorup, Mikkel, CP8, 5:45 Sun Mai, Tung, CP30, 9:25 Wed R Thorup, Mikkel, CP12, 9:00 Mon Mao, Jieming, CP30, 9:00 Wed Radermacher, Marcel, 5:45 Sun, ALENEX Tov, Roe, CP19, 9:00 Tue Martínez, Conrado, 5:20 Mon, ANALCO Ramzews, Leon, 2:25 Tue, ANALCO Traub, Vera, CP25, 4:30 Tue Mendel, Thomas, 5:20 Sun, ALENEX Rotenberg, Eva, CP22, 2:25 Tue Trevisan, Luca, CP17, 6:10 Mon Miller, J. Benjamin, CP27, 5:45 Tue Roytman, Alan, CP6, 3:40 Sun Mitzenmacher, Michael, 10:15 Sun, U ALENEX S Umans, Chris, CP14, 2:50 Mon Mohar, Bojan, CP3, 10:40 Sun Sankararaman, Abishek, CP29, 9:50 Wed Uznanski, Przemyslaw, CP34, 6:10 Wed Mouawad, Amer, CP3, 9:50 Sun Sankararaman, Karthik Abinav, CP5, 2:25 Mozes, Shay, CP7, 5:20 Sun Sun V Vakilian, Ali, CP32, 2:50 Wed Musco, Christopher, CP21, 10:40 Tue Saurabh, Saket, CP25, 6:10 Tue Vassilevska Williams, Virginia, IP4, 11:30 Saxena, Raghuvansh R., CP27, 4:55 Tue Wed N Schild, Aaron, CP21, 9:50 Tue Nägele, Martin, CP11, 10:40 Mon Verdugo, Victor, CP10, 9:25 Mon Seddighin, Saeed, CP16, 4:30 Mon Naor, Assaf, CP18, 5:20 Mon 92 ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO

W Wajc, David, CP13, 2:25 Mon Weimann, Oren, CP7, 4:55 Sun Weimann, Oren, CP16, 4:55 Mon Wessels, Mariette, CP2, 9:25 Sun Whidden, Chris, 9:50 Tue, ANALCO Wild, Sebastian, 4:55 Mon, ANALCO Williams, Aaron, CP8, 4:55 Sun Williams, Ryan, CP16, 5:20 Mon Wootters, Mary, CP9, 4:55 Sun Wu, Xian, CP10, 10:40 Mon X Xie, Weijun, CP29, 10:40 Wed Xu, Chao, CP19, 10:15 Tue Xu, Haifeng, CP33, 2:50 Wed Xu, Yinzhan, 5:45 Mon, ANALCO Y Yazdanbod, Sadra, CP30, 10:15 Wed Yolov, Nikola G., CP4, 2:00 Sun Yu, Fang-Yi, CP26, 4:55 Tue Z Zambelli, Giacomo, CP11, 10:15 Mon Zehavi, Meirav, CP4, 3:15 Sun Zhechev, Stephan, CP15, 3:15 Mon Zheng, Yufei, CP2, 9:00 Sun Zhong, Mingxian, CP17, 4:55 Mon Zhu, Xue, CP5, 3:15 Sun ACM-SIAM Symposium on Discrete Algorithms, ALENEX & ANALCO 93

Notes Astor Crowne Plaza Floor Plan