Approximation, Randomization, and Combinatorial Optimization

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

17th International Workshop, APPROX 2014, and 18th International Workshop, RANDOM 2014 September 4–6, 2014, Barcelona, Spain

Edited by Klaus Jansen José D. P. Rolim Nikhil R. Devanur Cristopher Moore

LIPIcs – Vol. 28 – APPROX/RANDOM’14 www.dagstuhl.de/lipics Editors Klaus Jansen José D. P. Rolim University of Kiel University of Geneva Kiel Geneva [email protected] [email protected]

Nikhil R. Devanur Cristopher Moore Microsoft Research Santa Fe Institute Redmond New Mexico [email protected] [email protected]

ACM Classiﬁcation 1998 C.2.1 Network Architecture and Design, C.2.2 Computer-communication, E.4 Coding and Information Theory, F. Theory of Computation, F.1.0 Computation by Abstract Devices, F.1.1 Models of Computation – relations between models, F.1.2 Modes of Computation, F.1.3 Complexity Measures and Classes, F.2.0 Analysis of Algorithms and Problem Complexity, F.2.1 Numerical Algorithms and Problems, F.2.2 Nonnumerical Algorithms and Problems G.1.2 Approximation, G.1.6 Optimization, G.2 Discrete Mathematics, G.2.1 Combinatorics, G.2.2 Graph Theory, G.3 Probability and Statistics, I.1.2 Algorithms, J.4 Computer Applications – Social and Behavioral Sciences

ISBN 978-3-939897-74-3

Published online and open access by Schloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing, Saarbrücken/Wadern, Germany. Online available at http://www.dagstuhl.de/dagpub/978-3-939897-74-3.

Publication date September, 2014

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Digital Object Identiﬁer: 10.4230/LIPIcs.APPROX-RANDOM.2014.i

ISBN 978-3-939897-74-3 ISSN 1868-8969 http://www.dagstuhl.de/lipics LIPIcs – Leibniz International Proceedings in Informatics

LIPIcs is a series of high-quality conference proceedings across all ﬁelds in informatics. LIPIcs volumes are published according to the principle of Open Access, i.e., they are available online and free of charge.

Editorial Board Susanne Albers (TU München) Chris Hankin (Imperial College London) Deepak Kapur (University of New Mexico) Michael Mitzenmacher (Harvard University) Madhavan Mukund (Chennai Mathematical Institute) Catuscia Palamidessi (INRIA) Wolfgang Thomas (RWTH Aachen) Pascal Weil (Chair, CNRS and University Bordeaux) Reinhard Wilhelm (Saarland University)

ISSN 1868-8969 www.dagstuhl.de/lipics

Contents

Preface ix

Contributed Talks of APPROX

Fully Dynamic All-Pairs Shortest Paths: Breaking the O(n) Barrier Ittai Abraham, Shiri Chechik, and Kunal Talwar ...... 1 Approximation Algorithms for Minimum-Load k-Facility Location Sara Ahmadian, Babak Behsaz, Zachary Friggstad, Amin Jorati, Mohammad R. Salavatipour, and Chaitanya Swamy ...... 17 The Cover Number of a Matrix and its Algorithmic Applications Noga Alon, Troy Lee, and Adi Shraibman ...... 34 Network Design with Coverage Costs Siddharth Barman, Shuchi Chawla, and Seeun Umboh ...... 48 Online Set Cover with Set Requests Kshipra Bhawalkar, Sreenivas Gollapudi, and Debmalya Panigrahi ...... 64 Lowest Degree k-Spanner: Approximation and Hardness Eden Chlamtáč and Michael Dinitz ...... 80 Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching Michael Crouch and Daniel M. Stubbs ...... 96 Guruswami-Sinop Rounding without Higher Level Lasserre Amit Deshpande and Rakesh Venkat ...... 105 Improved Approximation Algorithm for Steiner k-Forest with Nearly Uniform Weights Michael Dinitz, Guy Kortsarz, and Zeev Nutov ...... 115 Computing Opaque Interior Barriers à la Shermer Adrian Dumitrescu, Minghui Jiang, and Csaba D. Tóth ...... 128 Hardness of Submodular Cost Allocation: Lattice Matching and a Simplex Coloring Conjecture Alina Ene and Jan Vondrák ...... 144 Constrained Monotone Function Maximization and the Supermodular Degree Moran Feldman and Rani Izsak ...... 160 On the Equivalence of the Bidirected and Hypergraphic Relaxations for Steiner Tree Andreas Emil Feldmann, Jochen Könemann, Neil Olver, and Laura Sanità ...... 176 Reaching Consensus via non-Bayesian Asynchronous Learning in Social Networks Michal Feldman, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg . . . 192 Deliver or Hold: Approximation Algorithms for the Periodic Inventory Routing Problem Takuro Fukunaga, Afshin Nikzad, and R. Ravi ...... 209 Complexity and Approximation of the Continuous Network Design Problem Martin Gairing, Tobias Harks, and Max Klimm ...... 226

17th Int’l Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX’14) / 18th Int’l Workshop on Randomization and Computation (RANDOM’14). Editors: Klaus Jansen, José Rolim, Nikhil Devanur, and Cristopher Moore Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany vi Contents

Approximate Pure Nash Equilibria in Weighted Congestion Games Christoph Hansknecht, Max Klimm, and Alexander Skopalik ...... 242 Discrepancy Without Partial Colorings Nicholas J. A. Harvey, Roy Schwartz, and Mohit Singh ...... 258 Universal Factor Graphs for Every NP-Hard Boolean CSP Shlomo Jozeph ...... 274 A 9/7-Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs Jeremy A. Karp and R. Ravi ...... 284 Sherali-Adams Gaps, Flow-Cover Inequalities and Generalized Conﬁgurations for Capacity-Constrained Facility Location Stavros G. Kolliopoulos and Yannis Moysoglou ...... 297 Lower Bounds on Expansion of Graph Powers Tsz Chiu Kwok and Lap Chi Lau ...... 313 An Improved Approximation Algorithm for the Hard Uniform Capacitated k-median Problem Shanfei Li ...... 325 Approximation Algorithms for Hypergraph Small Set Expansion and Small Set Vertex Expansion Anand Louis and Yury Makarychev ...... 339 Robust Appointment Scheduling Shashi Mittal, Andreas S. Schulz, and Sebastian Stiller ...... 356 Computational Complexity of Certifying Restricted Isometry Property Abhiram Natarajan and Yi Wu ...... 371 Gap Ampliﬁcation for Small-Set Expansion via Random Walks Prasad Raghavendra and Tselil Schramm ...... 381 Power of Preemption on Uniform Parallel Machines Alan J. Soper and Vitaly A. Strusevich ...... 392 Improved Approximation Algorithms for Matroid and Knapsack Median Problems and Applications Chaitanya Swamy ...... 403 Robust Approximation of Temporal CSP Suguru Tamaki and Yuichi Yoshida ...... 419 Parity is Positively Useless Cenny Wenner ...... 433

Contributed Talks of RANDOM

The Condensation Phase Transition in Random Graph Coloring Victor Bapst, Amin Coja-Oghlan, Samuel Hetterich, Felicia Raßmann, and Dan Vilenchik ...... 449 Contents vii

The Information Complexity of Hamming Distance Eric Blais, Joshua Brody, and Badih Ghazi ...... 465 An Approximate Version of the Tree Packing Conjecture via Random Embeddings Julia Böcher, Jan Hladký, Diana Piguet, and Anusch Taraz ...... 490 On Sharp Thresholds in Random Geometric Graphs Milan Bradonjić and Will Perkins ...... 500 Average Case Polyhedral Complexity of the Maximum Stable Set Problem Gábor Braun, Samuel Fiorini, and Sebastian Pokutta ...... 515 An Optimal Algorithm for Large Frequency Moments Using O(n1−2/k) Bits Vladimir Braverman, Jonathan Katzman, Charles Seidell, and Gregory Vorsanger 531 Certifying Equality With Limited Interaction Joshua Brody, Amit Chakrabarti, Ranganath Kondapally, David P. Woodruﬀ, and Grigory Yaroslavtsev ...... 545 #BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Non-uniqueness Region Jin-Yi Cai, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, Mark Jerrum, Daniel Štefankovič, and Eric Vigoda ...... 582 The Power of Super-logarithmic Number of Players Arkadev Chattopadhyay and Michael E. Saks ...... 596 On Reconstructing a Hidden Permutation Flavio Chierichetti, Anirban Dasgupta, Ravi Kumar, and Silvio Lattanzi ...... 604 Two Sides of the Coin Problem Gil Cohen, Anat Ganor, and Ran Raz ...... 618 Absorption Time of the Moran Process Josep Díaz, Leslie Ann Goldberg, David Richerby, and Maria Serna ...... 630 Sampling a Uniform Solution of a Quadratic Equation Modulo a Prime Power Chandan Dubey and Thomas Holenstein ...... 643 Unidirectional Input/Output Streaming Complexity of Reversal and Sorting Nathanaël François, Rahul Jain, and Frédéric Magniez ...... 654 Improved Lower Bounds for Testing Triangle-freeness in Boolean Functions via Fast Matrix Multiplication Hu Fu and Robert Kleinberg ...... 669 Ferromagnetic Potts Model: Reﬁned #BIS-hardness and Related Results Andreas Galanis, Daniel Štefankovič, Eric Vigoda, and Linji Yang ...... 677 Space Pseudorandom Generators by Communication Complexity Lower Bounds Anat Ganor and Ran Raz ...... 692 On Multiple Input Problems in Property Testing Oded Goldreich ...... 704 Communication Complexity of Set-Disjointness for All Probabilities Mika Göös and Thomas Watson ...... 721

APPROX/RANDOM’14 viii Contents

List Decoding Group Homomorphisms between Supersolvable Groups Alan Guo and Madhu Sudan ...... 737 Evading Subspaces over Large Fields and Explicit List-Decodable Rank-Metric Codes Venkatesan Guruswami and Carol Wang ...... 748 Exchangeability and Realizability: De Finetti Theorems on Graphs T.S. Jayram and Jan Vondrák ...... 762 Global and Local Information in Clustering Labeled Block Models Varun Kanade, Elchanan Mossel, and Tselil Schramm ...... 779 Embedding Hard Learning Problems into Gaussian Space Adam Klivans and Pravesh Kothari ...... 793 Smoothed Analysis on Connected Graphs Michael Krivelevich, Daniel Reichman, and Wojciech Samotij ...... 810 Local Algorithms for Sparse Spanning Graphs Reut Levi, Dana Ron, and Ronitt Rubinfeld ...... 826 The Complexity of Ferromagnetic Two-spin Systems with External Fields Jingcheng Liu, Pinyan Lu, and Chihao Zhang ...... 843 It’s a Small World for Random Surfers Abbas Mehrabian and Nick Wormald ...... 857 Deterministic Coupon Collection and Better Strong Dispersers Raghu Meka, Omer Reingold, and Yuan Zhou ...... 872 Pseudorandomness and Fourier Growth Bounds for Width 3 Branching Programs Thomas Steinke, Salil Vadhan, and Andrew Wan ...... 885 Preface

This volume contains the papers presented at the 17th International Workshop on Approx- imation Algorithms for Combinatorial Optimization Problems (APPROX 2014) and the 18th International Workshop on Randomization and Computation (RANDOM 2014), which took place concurrently in Universitat Politècnica de Catalunya Barcelona, Spain, during September 4–6, 2014. APPROX focuses on algorithmic and complexity issues surrounding the development of eﬃcient approximate solutions to computationally diﬃcult problems, and was the 17th in the series after Aalborg (1998), Berkeley (1999), Saarbrücken (2000), Berkeley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), Boston (2008), Berkeley (2009), Barcelona (2010), and Princeton (2011), Berkeley (2013). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 18th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley (1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), Boston (2008), Berkeley (2009), Barcelona (2010), Princeton (2011), Boston (2012), Berkeley (2013).

Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space algorithms, sub-linear time algorithms, streaming algorithms, embeddings and metric geometry, mathematical programming meth- ods, combinatorial problems in graphs and networks, game theory, markets and economic applications, geometric problems, packing, covering, scheduling, approximate learning, design and analysis of online algorithms, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, phase transitions, computational learning theory, and other applications of approximation and randomness.

The volume contains 31 contributed papers, selected by the APPROX Program Committee out of 64 submissions, and 30 contributed papers, selected by the RANDOM Program Committee out of 62 submissions.

We would like to thank all of the authors who submitted papers, the invited speakers, the members of the Program Committees, and the external reviewers. We gratefully acknowledge the support from the Microsoft Research, USA, the Institute of Computer Science of the Christian-Albrechts-Universität zu Kiel, the Santa Fe Institute, USA, and the Department of Computer Science of the University of Geneva.

September 2014 Nikhil R. Devanur Klaus Jansen Cristopher Moore José D. P. Rolim

Organization

Program Committees APPROX 2014

Niv Buchbinder Tel Aviv University, Israel Deeparnab Chakrabarty Microsoft Research, India Siu On Chan Microsoft Research UC, Berkeley, USA Shuchi Chawla University of Washington, USA Eden Chlamtac Princeton University, USA Nikhil R. Devanur (chair) Microsoft Research, Redmond, USA Alina Ene Princeton University, USA Konstantinos Georgiu University of Waterloo, Canada Telikepalli Kavitha Indian Institute of Science, Bangalore, India Ken Ichi Kawarabayashi National Institute of Informatics, Tokyo, Japan Jochen Koenemann University of Waterloo, Canada Amit Kumar Indian Institute of Technology, New Delhi, India Konstantin Makarychev Microsoft Research, Redmond, USA Debmalya Panigrahi Duke University, USA Thomas Rothvoss Massachusetts Institute of Technology, USA Barna Saha AT&T Shannon Research Laboratory, New Jersey, USA Bruce Shepherd McGill University Montreal, Canada Aravind Srinvasan University of Maryland, USA David Williamson Cornell University, USA

RANDOM 2014

Louigi Addario-Berry McGill University, Montreal, Canada Nayantara Bhatnagar University of Delaware, Newark, USA Amin Coja-Oghlan Goethe University, Frankfurt, Germany David Galvin University of Notre Dame, South Bend, USA Valentine Kabanets Simon Fraser University, Burnaby, Canada Michael Molloy University of Toronto, Canada Cristopher Moore (chair) Santa Fe Institute, New Mexico, USA Assaf Naor New York University, USA Krzysztof Onak IBM T.J. Watson Research Center, USA Dana Ron Tel-Aviv University, Israel Alex Russell University of Connecticut, USA Dominik Scheder Tsinghua University, Beijing, China Devavrat Shah Laboratory for Information and Decision Systems, Cambridge, USA Perla Sousi University of Cambridge, USA Mario Szegedy University of New Jersey, Piscataway, USA Amnon Ta-Shma Tel-Aviv University, Israel Thomas Vidick California Institute of Technology, USA

External Reviewers

Dimitris Achlioptas Klim Efremenko Susanne Albers Charilaos Efthymiou Ammar Ammar Leah Epstein Alexandr Andoni Omid Etesami Per Austrin Uriel Feige Yossi Azar Sándor Fekete Eric Bach Moran Feldman Paul Balister Andreas Feldmann Victor Bapst Nikolaos Fountoulakis Alexander Barg Ariel Gabizon Surender Baswana Shirshendu Ganguly Mohammad Bavarian Ankit Garg Shankar Bhamidi Naveen Garg Umang Bhaskar Efraim Gelman Arnab Bhattacharyya Balázs Gerencsér Pritam Bhattacharya George Giakkoupis Eric Blais Oded Goldreich Milan Bradonjic Simon Griﬃths Fernando Brandao Elena Grigorescu Mark Braverman Tom Gur Guy Bresler Ori Gurel-Gurevich Joshua Brody Pooya Hatami Nicolas Broutin Thomas Hayes Jaroslaw Byrka Timon Hertli Clément Canonne Samuel Hetterich Amit Chakrabarti Martin Hildebrand Siu On Chan Chien-Chung Huang Sourav Chatterjee Sungjin Im Arkadev Chattopadhyay Yoichi Iwata Po-An Chen Ragesh Jaiswal Shahar Chen Sune Jakobsen Sixia Chen Mark Jerrum Mahdi Cheraghchi Volker Kaibel Flavio Chierichetti Sagar Kale George Christodoulou Satyen Kale Marek Chrobak Matthew Katz Fabian Chudak Tali Kaufman Ilan Cohen Muhammad Khan Gil Cohen Julia Komjathy Colin Cooper Swastik Kopparty Artur Czumaj Ravishankar Krishnaswamy Olivier Durand de Gevigney Florent Krzakala Ronald de Wolf Janardhan Kulkarni Dean Doron Nirman Kumar Martin Dyer Ravi Kumar

Oded Lachish Tomasz Radzik Kevin Leckey Harry Raecke Marc Lelarge Felicia Rassmann Virginie Lerays Ran Raz Vahid Liaghat Alexander Razborov Ricardo Restrepo Lopez Daniel Reichman Shachar Lovett Omer Reingold Pinyan Lu Sebastien Roch Eyal Lubetzky Noga Ron-Zewi Gabor Lugosi Andrzej Rucinski Takanori Maehara Sivan Sabato Yury Makarychev Sushant Sachdeva Arie Matsliah Rishi Saket Kevin Matulef Thomas Sauerwald Andrew McGregor Saket Saurabh Or Meir Rahul Savani Julian Mestre Roy Schwartz Ankur Moitra Rocco Servedio Sonoko Moriyama Ronen Shaltiel Ben Morris Asaf Shapira Elchanan Mossel Alexander Sherstov Dhruv Mubayi Igor Shparlinski Viswanath Nagarajan Vittoria Silvestri Meghana Nasre Arno Siri-Jégousse Joe Neeman Allan Sly Ralph Neininger Hao Song Jelani Nelson Christian Sommer Huy Nguyen Dan Spielman Ryan O’Donnell Joachim Spoerhase Sewoong Oh Piyush Srivastava Roberto Oliveira Alexandre Stauﬀer Yota Otachi Mike Steele Jiangwei Pan Daniel Štefankovič Konstantinos Panagiotou John Steinberger Periklis Papakonstantinou David Steurer Michal Parnas Benny Sudakov Farzad Parvaresh Nike Sun Chris Peikert Jukka Suomela Ron Peled Kenjiro Takazawa Tommy Pensyl Li-Yang Tan Guillem Perarnau Prasad Tetali Yury Person Justin Thaler Gábor Pete Nicolas Trotignon Michał Pilipczuk Madhur Tulsiani Yury Polyanskiy Christopher Umans Pawel Pralat Seeun Umboh Michal Przykucki Andrew Uzzell Richard Pymar Salil Vadhan Reviewers xv

Nithin Mahendra Varma Juan Vera Aravindan Vijayaraghavan Dan Vilenchik Antonia Wachter-Zeh Stephan Wagner Zizhuo Wang Justin Ward Lutz Warnke Thomas Watson Omri Weinstein Andreas Wiese David Woodruﬀ John Wright Bang Ye Wu Patrick Xia Ning Xie Chaoping Xing Guang Yang Grigory Yaroslavtsev Yuichi Yoshida Raphael Yuster Lenka Zdeborova Peng Zhang Yufei Zhao David Zuckerman

APPROX/RANDOM’14

List of Authors

Ittai Abraham Martin Gairing Sara Ahmadian Anat Ganor Noga Alon Andreas Galanis Badih Ghazi Mika Göös Eric Blais Leslie Ann Goldberg Victor Bapst Oded Goldreich Siddharth Barman Sreenivas Gollapudi Babak Behsaz Alan Guo Kshipra Bhawalkar Heng Guo Julia Böttcher Venkatesan Guruswami Milan Bradonjić Gábor Braun Vladimir Braverman Christoph Hansknecht Joshua Brody Tobias Harks Nicholas J. A. Harvey Samuel Hetterich Jin-Yi Cai Jan Hladký Amit Chakrabarti Thomas Holenstein Arkadev Chattopadhyay Shuchi Chawla Shiri Chechik Nicole Immorlica Flavio Chierichetti Rani Izsak Eden Chlamtáč Gil Cohen Amin Coja-Oghlan Rahul Jain Michael Crouch T.S. Jayram Mark Jerrum Minghui Jiang Anirban Dasgupta Amin Jorati Amit Deshpande Shlomo Jozeph Josep Díaz Michael Dinitz Chandan Dubey Varun Kanade Adrian Dumitrescu Jeremy A. Karp Jonathan Katzman Robert Kleinberg Alina Ene Max Klimm Adam Klivans Michal Feldman Jochen Könemann Moran Feldman Stavros G. Kolliopoulos Andreas Emil Feldmann Ranganath Kondapally Samuel Fiorini Guy Kortsarz Nathanaël François Pravesh Kothari Zachary Friggstad Michael Krivelevich Hu Fu Ravi Kumar Takuro Fukunaga Tsz Chiu Kwok

Silvio Lattanzi Michael E. Saks Lap Chi Lau Mohammad R. Salavatipour Troy Lee Wojciech Samotij Reut Levi Laura Sanità Shanfei Li Tselil Schramm Anand Louis Andreas S. Schulz Jingcheng Liu Roy Schwartz Pinyan Lu Charles Seidell Brendan Lucier Maria Serna Adi Shraibman Mohit Singh Alexander Skopalik Frédéric Magniez Alan J. Soper Yury Makarychev Daniel Štefankovič Abbas Mehrabian Thomas Steinke Raghu Meka Sebastian Stiller Shashi Mittal Vitaly A. Strusevich Elchanan Mossel Daniel M. Stubbs Yannis Moysoglou Madhu Sudan Chaitanya Swamy

Suguru Tamaki Abhiram Natarajan Kunal Talwar Afshin Nikzad Anusch Taraz Zeev Nutov Csaba D. Tóth Seeun Umboh Salil Vadhan Neil Olver Rakesh Venkat Eric Vigoda Dan Vilenchik Jan Vondrák Debmalya Panigrahi Gregory Vorsanger Will Perkins Andrew Wan Diana Piguet Carol Wang Sebastian Pokutta Thomas Watson S. Matthew Weinberg Cenny Wenner David P. Woodruﬀ Prasad Raghavendra Nick Wormald Felicia Raßmann Yi Wu R. Ravi Linji Yang Ran Raz Grigory Yaroslavtsev Daniel Reichman Yuichi Yoshida Omer Reingold David Richerby Chihao Zhang Dana Ron Yuan Zhou Ronitt Rubinfeld