Lecture Notes in Computer Science 5555Commenced Publication in 1973Founding and Former Series Editors:Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board

David Hutchison, UK

Josef Kittler, UK

Alfred Kobsa, USA

John C. Mitchell, USA

Oscar Nierstrasz, Switzerland

Bernhard Steffen, Germany

Demetri Terzopoulos, USA

Gerhard Weikum, Germany

Takeo Kanade, USA

Jon M. Kleinberg, USA

Friedemann Mattern, Switzerland

Moni Naor, Israel

C. Pandu Rangan, India

Madhu Sudan, USA

Doug Tygar, USA

Advanced Research in Computing and Software Science

Subline of Lectures Notes in Computer Science

Subline Series Editors

Giorgio Ausiello, University of Rome ‘La Sapienza’, Italy

Vladimiro Sassone, University of Southampton, UK

Subline Advisory Board

Susanne Albers, University of Freiburg, Germany

Benjamin C. Pierce, University of Pennsylvania, USA

Bernhard Steffen, University of Dortmund, Germany

Madhu Sudan, Microsoft Research, Cambridge, MA, USA

Deng Xiaotie, City University of Hong Kong

Jeannette M. Wing, Carnegie Mellon University, Pittsburgh, PA, USA

Susanne AlbersAlberto Marchetti-SpaccamelaYossi MatiasSotiris NikoletseasWolfgang Thomas (Eds.)

Automata, Languagesand Programming36th International Colloquium, ICALP 2009Rhodes, Greece, July 5-12, 2009Proceedings, Part I

13

Volume Editors

Susanne AlbersUniversity of Freiburg, Department of Computer ScienceGeorges Köhler Allee 79, 79110, Freiburg, GermanyE-mail: salbers@informatik.uni-freiburg.de

Alberto Marchetti-SpaccamelaSapienza University of RomeDepartment of Computer and Systems SciencesVia Ariosto 25, 00184 Roma, ItalyE-mail: alberto@dis.uniroma1.it

Yossi MatiasTel Aviv University, School of Computer ScienceGoogle R&D Center, Tel Aviv 69978, IsraelE-mail: matias@cs.tau.ac.il

Sotiris NikoletseasUniversity of Patras and CTIN. Kazantzaki Street 1, 26504 Rion, Patras, GreeceE-mail: nikole@cti.gr

Wolfgang ThomasRWTH Aachen, Lehrstuhl Informatik 7Ahornstraße 55, 52074 Aachen, GermanyE-mail: thomas@informatik.rwth-aachen.de

Library of Congress Control Number: 2009929832

CR Subject Classification (1998): F.2, F.3, I.2.1, G.1, G.2, I.1

LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues

ISSN 0302-9743ISBN-10 3-642-02926-4 Springer Berlin Heidelberg New YorkISBN-13 978-3-642-02926-4 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting,reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publicationor parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,in its current version, and permission for use must always be obtained from Springer. Violations are liableto prosecution under the German Copyright Law.

springer.com

© Springer-Verlag Berlin Heidelberg 2009Printed in Germany

Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, IndiaPrinted on acid-free paper SPIN: 12715473 06/3180 5 4 3 2 1 0

Preface

ICALP 2009, the 36th edition of the International Colloquium on Automata,Languages and Programming, was held on the island of Rhodes, July 6–10,2009. ICALP is a series of annual conferences of the European Association forTheoretical Computer Science (EATCS) which first took place in 1972. Thisyear, the ICALP program consisted of the established track A (focusing onalgorithms, complexity and games) and track B (focusing on logic, automata,semantics and theory of programming), and of the recently introduced track C(in 2009 focusing on foundations of networked computation).

In response to the call for papers, the Program Committee received 370 sub-missions: 223 for track A, 84 for track B and 63 for track C. Out of these, 108papers were selected for inclusion in the scientific program: 62 papers for trackA, 24 for track B and 22 for track C. The selection was made by the ProgramCommittees based on originality, quality, and relevance to theoretical computerscience. The quality of the manuscripts was very high indeed, and many deserv-ing papers could not be selected.

ICALP 2009 consisted of five invited lectures and the contributed papers.This volume of the proceedings contains all contributed papers presented in trackA together with the papers by the invited speakers Kurt Mehlhorn (Max-Planck-Institut fur Informatik, Saarbrucken) and Christos Papadimitriou (University ofCalifornia at Berkeley). A companion volume contains all contributed paperspresented at the conference in track B and track C, together with the papersby the invited speakers Georg Gottlob (University of Oxford), Tom Henzinger(Ecole Polytechnique Federale de Lausanne), and Noam Nisan (Google, Tel Aviv,and Hebrew University).

The following workshops were held as satellite events of ICALP 2009:

ALGOSENSORS 2009—5th International Workshop on Algorithmic Aspects ofWireless Sensor Networks

DCM 2009—5th International Workshop on Developments in ComputationalModels

FOCLASA 2009—8th International Workshop on Foundations of CoordinationLanguages and Software Architectures

QUANTLOG 2009—Workshop on Quantitative Logics 2009

We wish to thank all authors who submitted extended abstracts for consid-eration, the Program Committees for their scholarly effort, and all referees whoassisted the Program Committees in the evaluation process.

Thanks are due to the sponsors (Ministry of National Education and Re-ligious Affairs of Greece, Research Academic Computer Technology Institute(CTI), Piraeus Bank) for their support, and to the Research Academic

VI Preface

Computer Technology Institute (CTI) for the local organization. We are alsograteful to all members of the Organizing Committee.

Thanks also to Andrei Voronkov for his help with the conference managementsystem EasyChair, which was used in handling the submissions and the electronicPC meeting as well as in assisting in the assembly of the proceedings.

April 2009 Susanne AlbersAlberto Marchetti Spaccamela

Yossi MatiasPaul G. Spirakis

Wolfgang Thomas

Organization

Program Committee

Track A

Susanne Albers University of Freiburg, Germany (Chair)Gerth Brodal University of Aarhus, DenmarkMartin Dyer University of Leeds, UKIrene Finocchi University of Rome “La Sapienza”, ItalyAnna Gal University of Texas at Austin, USANaveen Garg IIT Delhi, IndiaRaffaele Giancarlo University of Palermo, ItalyAndrew Goldberg Microsoft Research, Silicon Valley, USAMordecai Golin Hong Kong UniversityMichel Habib LIAFA, Paris 7, FranceThore Husfeldt Lund University, SwedenKazuo Iwama University of Kyoto, JapanHoward Karloff AT&T Labs, USAYishay Mansour Tel Aviv University and Google, IsraelJiri Matousek Charles University, Prague, Czech RepublicMarios Mavronicolas University of Cyprus, CyprusPiotr Sankowski University of Warsaw and ETH Zurich,

SwitzerlandRaimund Seidel University of Saarbrucken, GermanyPaul Spirakis CTI and University of Patras, GreeceDorothea Wagner University of Karlsruhe, GermanyPeter Widmayer ETH Zurich, SwitzerlandRonald de Wolf CWI Amsterdam, The Netherlands

Track B

Albert Atserias Universitat Politecnica de Catalunya,Barcelona, Spain

Jos Baeten Eindhoven University of Technology,The Netherlands

Gilles Barthe IMDEA Software, Madrid, SpainMikolaj Bojanczyk Warsaw University, PolandChristian Choffrut University Denis Diderot, Paris, FranceThierry Coquand Goteborg University, SwedenRoberto di Cosmo University Denis Diderot, Paris, FranceKousha Etessami University of Edinburgh, Scotland, UKDexter Kozen Cornell University, USA

VIII Organization

Stephan Kreutzer Oxford University, UKOrna Kupferman Hebrew University, IsraelKim Guldstrand Larsen Aalborg University, DenmarkDale Miller Ecole Polytechnique, Palaiseau, FranceMarkus Muller-Olm University of Munster, GermanyAnca Muscholl University Bordeaux 1, FranceR. Ramanujam Institute of Mathematical Sciences,

Chennai, IndiaSimona Ronchi

Della Rocca University of Turin, ItalyJan Rutten CWI, Amsterdam, The NetherlandsVladimiro Sassone University of Southampton, UKPeter Sewell University of Cambridge, UKHoward Straubing Boston College, USAWolfgang Thomas RWTH Aachen University, Germany (Chair)

Track C

Hagit Attiya Technion, IsraelAndrei Broder Yahoo, USAXiaotie Deng City University of Hong KongDanny Dolev Hebrew University, IsraelMichele Flammini University of L’Aquila, ItalyPierre Fraigniaud CNRS, Paris, FranceAshish Goel University of Stanford, USAMatthew Hennessy Trinity College Dublin, IrelandKohei Honda University of London, UKRobert Kleinberg Cornell University, USAElias Koutsoupias University of Athens, GreeceAlberto

Marchetti Spaccamela University of Rome “La Sapienza”, Italy(Co-chair)

Yossi Matias Google and Tel Aviv University, Israel(Co-chair)

Silvio Micali MIT, USAMuthu Muthukrishnan Google, NY, USAMoni Naor Weizmann Institute, IsraelMogens Nielsen University of Aarhus, DenmarkHarald Raecke University of Warwick, UKJose Rolim University of Geneva, SwitzerlandChristian Schindelhauer University of Freiburg, GermanyRoger Wattenhofer ETH Zurich, SwitzerlandMartin Wirsing University of Munich, Germany

Organization IX

Organizing Committee

- Paul G. Spirakis, Research Academic Computer Technology Institute andUniversity of Patras, Greece (Conference Chair)

- Elias Koutsoupias, Department of Informatics and Telecommunications,University of Athens, Greece (Conference Chair)

- Christos Kaklamanis, Research Academic Computer Technology Institute andUniversity of Patras, Greece (Conference Chair)

- Christos D. Zaroliagis, Research Academic Computer Technology Institute andUniversity of Patras, Greece (Workshops Chair)

- Sotiris Nikoletseas, Research Academic Computer Technology Institute andUniversity of Patras, Greece (Proceedings Chair)

- Ioannis Chatzigiannakis, Research Academic Computer TechnologyInstitute and University of Patras, Greece (Publicity Chair)

- Rozina Efstathiadou, Research Academic Computer Technology Institute,Greece (Finance Chair)

- Lena Gourdoupi, Research Academic Computer Technology Institute, Greece(Conference Secretariat)

Referees (Track A)

Scott AaronsonPeyman AfshaniNoga AlonCarme AlvarezKazuyuki AmanoAndris AmbainisYossi AzarMaxim BabenkoEric BachMichael BackesNikhil BansalJeremy BarbayReinhard BauerMichael BaurAmos BeimelBoaz BenmosheStephane BessyPhilip BilleDavide BiloAndreas BjorklundMarkus BlaserLiad BlumrosenHans BodlaenderAndrej Bogdanov

Jan BoudaTomas BrazdilMark BravermanHajo BroersmaNiv BuchbinderLeizhen CaiAlberto CapraraGiusi CastiglioneHo-Leung ChanPierre CharbitHong-Bin ChenJianer ChenZhi-Zhong ChenFlavio ChierichettiMarek ChrobakAmin Coja-OghlanColin CooperJoshua CooperGraham CormodeArtur CzumajPooya DaboodiIvan DamgardStefan DantchevShantanu Das

Daniel DellingErik DemaineJosep DiazFlorian DiedrichYann DisserHristo DjidjevFeodor DraganKlaus DragerArnaud DurandStefan DziembowskiKhaled ElbassioniMichael ElkinDavid EppsteinLeah EpsteinRolf FagerbergAndreas Emil FeldmannAmos FiatEldar FischerJohannes FischerAbie FlaxmanLisa FleischerRudolf FleischerHolger FlierFedor Fomin

X Organization

Dimitris FotakisAlan FriezeKeith FrikkenSaturo FujishigeToshihiro FujitoEmanuele Guido FuscoPeter GacsMarco GaertlerFrancois Le GallMichael GattoCyril GavoileBeat GfellerPaun GheorgheRodolphe GiroudeauPaul GoldbergNavin GoyalFabrizio GrandoniMark GreveMichelangelo GrigniElena GrigorescuMartin GroheSudipto GuhaAnupam GuptaRobert GorkeInge Li GørtzMohammadTaghi

HajiaghayiMagnus HalldorssonXin HanKristoffer

Arnsfelt HansenNick HarveyAndreas HinzMartin HolzerFlorian HornTomas HruzJohn IaconoGabor IvanyosMaurice JansenMark JerrumDavid JohnsonNatasha JonoskaStasys JuknaAllan

Grønlund Jørgensen

Christos KaklamanisMing-Yang KaoHaim KaplanAnna KarlinPetteri KaskiBastian KatzTelikepalli KavithaRohit KhandekarLefteris KirousisBjorn Kjos-HanssenRolf KleinMikko KoivistoJean-Claude KonigSpyros KontogiannisTakeshi KoshibaLukasz KowalikMark KrentelMarcus KrugAntonın KuceraAmit KumarStefan LangermanJames LeeTroy LeeStefano LeonardiLeonid LevinMinming LiMathieu LiedloffVincent LimouzyAndrzej LingasZhenming LiuBruno LoffZvi LotkerMark ManasseBodo MantheyConrado MartinezClaire MathieuArie MatsliahTomomi MatsuiJens MaueFrederic MazoitAndrew McGregorColin McDiarmidSteffen MeckeSascha MeinertMark Mercer

Wolfgang MerkleOthon MichailMatus MihalakShuichi MiyazakiBojan MoharBurkhard MonienFabien de MontgolfierCris MoorePat MorinHiroki MorizumiAnthony MorphettMarcin MuchaHaiko MullerFilip MurlakMuthu MuthukrishnanMasaki NakanishiSatyadev NandakumarGonzalo NavarroPhuong NguyenRolf NiedermeierJesper Buus NielsenSotiris NikoletseasEvdokia NikolovaHarumichi NishimuraMartin NollenburgMitsunori OgoharaYoshio OkamotoAlexander OkhotinAlessio OrlandiRasmus PaghPanagiota PanagopoulouRina PanigrahyChristophe PaulAndrzej PelcFernando PereiraSeth PettieWojciech PlandowskiKirk PruhsMaurice QueyranneYuval RabaniMichael RaoChristoforos

RaptopoulosSaurabh RayRudy Raymond

Organization XI

Andrea RibichiniDavid RicherbyDana RonPeter RossmanithAaron RothTim RoughgardenBjarke

Hammersholt RouneIgnaz RutterMilan RuzicHeiko RoglinAnand S.Srinivasa Rao SattiChristian SchaffnerMarcel SchongensFlorian SchoppmannRobert SchwellerMarinella SciortinoAllan ScottRobert SedgewickJean-Sebastien SereniOlivier SerreHadas ShachnaiNatalia ShakhlevichDavid ShmoysAnastasios SidiropoulosRiccardo SilvestriStephen Simpson

Man-Cho SoDavid Garcia SorianoRobert SpalekRastislav SramekJuraj StachoRob van SteeVitaly StrusevichMaxim SviridenkoMario SzegedyTadao TakaokaEiji TakimotoSuguru TamakiSeiichiro TaniJun TaruiPascal TessonDimitrios ThilikosMikkel ThorupTakeshi TokuyamaSzymon TorunczykGeza TothJakob TruelsenRyuhei UeharaUgo VaccaroMoshe VardiElad VerbinCristian VersariJan VondrakTomasz Walen

John WatrousMichael WeissEmo WelzlCenny WennerRenato WerneckUdi WiederRyan WilliamsKarl WimmerAndreas WinterPrudence WongDavid WoodruffJian XiaBinh-Minh Bui-XuaMasaki YamamotoShigeru YamashitaMihalis YannakakisKe YiMartin ZachariasenChristos ZaroliagisGuochuan ZhangShengyu ZhangQin ZhangMichal Ziv-UkelsonUri ZwickAnna Zych

Sponsoring Organizations

- Ministry of National Education and Religious Affairs of Greece- Research Academic Computer Technology Institute (CTI)- Piraeus Bank- Rigorous Mathematical Connections between the Theory of Computation and

Statistical Physics (RIMACO), European Research Council (ERC)Starting Grant

- Algorithmic Principles for Building Efficient Overlay Computers (AEOLUS)Project, EU/FET/Global Computing

- Papasotiriou Books and more- Google

Table of Contents – Part I

Invited Lectures

Assigning Papers to Referees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Kurt Mehlhorn

Algorithmic Game Theory: A Snapshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Christos H. Papadimitriou

Contributed Papers

SDP-Based Algorithms for Maximum Independent Set Problems onHypergraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Geir Agnarsson, Magnus M. Halldorsson, and Elena Losievskaja

Correlation Clustering Revisited: The“True”Cost of Error MinimizationProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Nir Ailon and Edo Liberty

Sorting and Selection with Imprecise Comparisons . . . . . . . . . . . . . . . . . . . 37Miklos Ajtai, Vitaly Feldman, Avinatan Hassidim, and Jelani Nelson

Fast FAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Noga Alon, Daniel Lokshtanov, and Saket Saurabh

Bounds on the Size of Small Depth Circuits for ApproximatingMajority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Kazuyuki Amano

Counting Subgraphs via Homomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Omid Amini, Fedor V. Fomin, and Saket Saurabh

External Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Alexandr Andoni, Piotr Indyk, Krzysztof Onak, and Ronitt Rubinfeld

Functional Monitoring without Monotonicity . . . . . . . . . . . . . . . . . . . . . . . 95Chrisil Arackaparambil, Joshua Brody, and Amit Chakrabarti

De-amortized Cuckoo Hashing: Provable Worst-Case Performance andExperimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Yuriy Arbitman, Moni Naor, and Gil Segev

Towards a Study of Low-Complexity Graphs . . . . . . . . . . . . . . . . . . . . . . . . 119Sanjeev Arora, David Steurer, and Avi Wigderson

XIV Table of Contents – Part I

Decidability of Conjugacy of Tree-Shifts of Finite Type . . . . . . . . . . . . . . . 132Nathalie Aubrun and Marie-Pierre Beal

Improved Bounds for Speed Scaling in Devices Obeying the Cube-RootRule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Nikhil Bansal, Ho-Leung Chan, Kirk Pruhs, and Dmitriy Katz

Competitive Analysis of Aggregate Max in Windowed Streaming . . . . . . . 156Luca Becchetti and Elias Koutsoupias

Faster Regular Expression Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171Philip Bille and Mikkel Thorup

A Fast and Simple Parallel Algorithm for the Monotone DualityProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Endre Boros and Kazuhisa Makino

Unconditional Lower Bounds against Advice . . . . . . . . . . . . . . . . . . . . . . . . . 195Harry Buhrman, Lance Fortnow, and Rahul Santhanam

Approximating Decision Trees with Multiway Branches . . . . . . . . . . . . . . . 210Venkatesan T. Chakaravarthy, Vinayaka Pandit,Sambuddha Roy, and Yogish Sabharwal

Annotations in Data Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222Amit Chakrabarti, Graham Cormode, and Andrew McGregor

The Tile Complexity of Linear Assemblies . . . . . . . . . . . . . . . . . . . . . . . . . . . 235Harish Chandran, Nikhil Gopalkrishnan, and John Reif

A Graph Reduction Step Preserving Element-Connectivity andApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Chandra Chekuri and Nitish Korula

Approximating Matches Made in Heaven . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266Ning Chen, Nicole Immorlica, Anna R. Karlin,Mohammad Mahdian, and Atri Rudra

Strong and Pareto Price of Anarchy in Congestion Games . . . . . . . . . . . . . 279Steve Chien and Alistair Sinclair

A Better Algorithm for Random k-SAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292Amin Coja-Oghlan

Exact and Approximate Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304Marek Cygan and Marcin Pilipczuk

Approximation Algorithms via Structural Results for Apex-Minor-FreeGraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Erik D. Demaine, MohammadTaghi Hajiaghayi, andKen-ichi Kawarabayashi

Table of Contents – Part I XV

Node-Weighted Steiner Tree and Group Steiner Tree in PlanarGraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Philip N. Klein

On Cartesian Trees and Range Minimum Queries . . . . . . . . . . . . . . . . . . . . 341Erik D. Demaine, Gad M. Landau, and Oren Weimann

Applications of a Splitting Trick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354Martin Dietzfelbinger and Michael Rink

Quasirandom Rumor Spreading: Expanders, Push vs. Pull, andRobustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

Benjamin Doerr, Tobias Friedrich, and Thomas Sauerwald

Incompressibility through Colors and IDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 378Michael Dom, Daniel Lokshtanov, and Saket Saurabh

Partition Arguments in Multiparty Communication Complexity . . . . . . . . 390Jan Draisma, Eyal Kushilevitz, and Enav Weinreb

High Complexity Tilings with Sparse Errors . . . . . . . . . . . . . . . . . . . . . . . . . 403Bruno Durand, Andrei Romashchenko, and Alexander Shen

Tight Bounds for the Cover Time of Multiple Random Walks . . . . . . . . . . 415Robert Elsasser and Thomas Sauerwald

Online Computation with Advice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427Yuval Emek, Pierre Fraigniaud, Amos Korman, and Adi Rosen

Dynamic Succinct Ordered Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439Arash Farzan and J. Ian Munro

Universal Succinct Representations of Trees? . . . . . . . . . . . . . . . . . . . . . . . . 451Arash Farzan, Rajeev Raman, and S. Srinivasa Rao

Distortion Is Fixed Parameter Tractable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463Michael R. Fellows, Fedor V. Fomin, Daniel Lokshtanov,Elena Losievskaja, Frances A. Rosamond, and Saket Saurabh

Towards Optimal Range Medians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475Beat Gfeller and Peter Sanders

B-Treaps: A Uniquely Represented Alternative to B-Trees . . . . . . . . . . . . . 487Daniel Golovin

Testing Fourier Dimensionality and Sparsity . . . . . . . . . . . . . . . . . . . . . . . . . 500Parikshit Gopalan, Ryan O’Donnell, Rocco A. Servedio,Amir Shpilka, and Karl Wimmer

XVI Table of Contents – Part I

Revisiting the Direct Sum Theorem and Space Lower Bounds inRandom Order Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Sudipto Guha and Zhiyi Huang

Wireless Communication Is in APX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525Magnus M. Halldorsson and Roger Wattenhofer

The Ehrenfeucht-Silberger Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537Stepan Holub and Dirk Nowotka

Applications of Effective Probability Theory to Martin-LofRandomness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

Mathieu Hoyrup and Cristobal Rojas

An EPTAS for Scheduling Jobs on Uniform Processors: Using an MILPRelaxation with a Constant Number of Integral Variables . . . . . . . . . . . . . 562

Klaus Jansen

Popular Mixed Matchings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574Telikepalli Kavitha, Julian Mestre, and Meghana Nasre

Factoring Groups Efficiently . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585Neeraj Kayal and Timur Nezhmetdinov

On Finding Dense Subgraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597Samir Khuller and Barna Saha

Learning Halfspaces with Malicious Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 609Adam R. Klivans, Philip M. Long, and Rocco A. Servedio

General Scheme for Perfect Quantum Network Coding with FreeClassical Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622

Hirotada Kobayashi, Francois Le Gall, Harumichi Nishimura, andMartin Rotteler

Greedy Δ-Approximation Algorithm for Covering with ArbitraryConstraints and Submodular Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

Christos Koufogiannakis and Neal E. Young

Limits and Applications of Group Algebras for ParameterizedProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

Ioannis Koutis and Ryan Williams

Sleep with Guilt and Work Faster to Minimize Flow Plus Energy . . . . . . 665Tak-Wah Lam, Lap-Kei Lee, Hing-Fung Ting, Isaac K.K. To, andPrudence W.H. Wong

Improved Bounds for Flow Shop Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 677Monaldo Mastrolilli and Ola Svensson

Table of Contents – Part I XVII

A 3/2-Approximation Algorithm for General Stable Marriage . . . . . . . . . . 689Eric McDermid

Limiting Negations in Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701Hiroki Morizumi

Fast Polynomial-Space Algorithms Using Mobius Inversion: Improvingon Steiner Tree and Related Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

Jesper Nederlof

Superhighness and Strong Jump Traceability . . . . . . . . . . . . . . . . . . . . . . . . 726Andre Nies

Amortized Communication Complexity of Distributions . . . . . . . . . . . . . . . 738Jeremie Roland and Mario Szegedy

The Number of Symbol Comparisons in QuickSort and QuickSelect . . . . 750Brigitte Vallee, Julien Clement, James Allen Fill, andPhilippe Flajolet

Computing the Girth of a Planar Graph in O(n log n) Time . . . . . . . . . . . 764Oren Weimann and Raphael Yuster

Elimination Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774Yuli Ye and Allan Borodin

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

Table of Contents – Part II

Track B: Invited Lectures

A Survey of Stochastic Games with Limsup and Liminf Objectives . . . . 1Krishnendu Chatterjee, Laurent Doyen, and Thomas A. Henzinger

Tractable Optimization Problems through Hypergraph-BasedStructural Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Georg Gottlob, Gianluigi Greco, and Francesco Scarcello

Track B: Contributed Papers

Deciding Safety Properties in Infinite-State Pi-Calculus via BehaviouralTypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Lucia Acciai and Michele Boreale

When Are Timed Automata Determinizable? . . . . . . . . . . . . . . . . . . . . . . . . 43Christel Baier, Nathalie Bertrand, Patricia Bouyer, andThomas Brihaye

Faithful Loops for Aperiodic E-Ordered Monoids(Extended Abstract) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Martin Beaudry and Francois Lemieux

Boundedness of Monadic Second-Order Formulae over Finite Words . . . . 67Achim Blumensath, Martin Otto, and Mark Weyer

Semilinear Program Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Manuel Bodirsky, Peter Jonsson, and Timo von Oertzen

Floats and Ropes: A Case Study for Formal Numerical ProgramVerification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Sylvie Boldo

Reachability in Stochastic Timed Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Patricia Bouyer and Vojtech Forejt

Equations Defining the Polynomial Closure of a Lattice of RegularLanguages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Mario J.J. Branco and Jean-Eric Pin

Approximating Markov Processes by Averaging . . . . . . . . . . . . . . . . . . . . . . 127Philippe Chaput, Vincent Danos, Prakash Panangaden, andGordon Plotkin

XX Table of Contents – Part II

The Theory of Stabilisation Monoids and Regular Cost Functions . . . . . . 139Thomas Colcombet

A Tight Lower Bound for Determinization of Transition Labeled BuchiAutomata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Thomas Colcombet and Konrad Zdanowski

On Constructor Rewrite Systems and the Lambda-Calculus . . . . . . . . . . . 163Ugo Dal Lago and Simone Martini

On Regular Temporal Logics with Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Christian Dax, Felix Klaedtke, and Martin Lange

Forward Analysis for WSTS, Part II: Complete WSTS . . . . . . . . . . . . . . . . 188Alain Finkel and Jean Goubault-Larrecq

Qualitative Concurrent Stochastic Games with Imperfect Information . . . 200Vincent Gripon and Olivier Serre

Diagrammatic Confluence and Completion . . . . . . . . . . . . . . . . . . . . . . . . . . 212Jean-Pierre Jouannaud and Vincent van Oostrom

Complexity of Model Checking Recursion Schemes for Fragments of theModal Mu-Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Naoki Kobayashi and C.-H. Luke Ong

LTL Path Checking Is Efficiently Parallelizable . . . . . . . . . . . . . . . . . . . . . . 235Lars Kuhtz and Bernd Finkbeiner

An Explicit Formula for the Free Exponential Modality of LinearLogic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Paul-Andre Mellies, Nicolas Tabareau, and Christine Tasson

Decidability of the Guarded Fragment with the Transitive Closure . . . . . 261Jakub Michaliszyn

Weak Alternating Timed Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Pawel Parys and Igor Walukiewicz

A Decidable Characterization of Locally Testable Tree Languages . . . . . . 285Thomas Place and Luc Segoufin

The Complexity of Nash Equilibria in Simple Stochastic MultiplayerGames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Michael Ummels and Dominik Wojtczak

Track C: Invited Lecture

Google’s Auction for TV Ads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309Noam Nisan, Jason Bayer, Deepak Chandra, Tal Franji,Robert Gardner, Yossi Matias, Neil Rhodes, Misha Seltzer,Danny Tom, Hal Varian, and Dan Zigmond

Table of Contents – Part II XXI

Track C: Contributed Papers

Graph Sparsification in the Semi-streaming Model . . . . . . . . . . . . . . . . . . . 328Kook Jin Ahn and Sudipto Guha

Sort Me If You Can: How to Sort Dynamic Data . . . . . . . . . . . . . . . . . . . . . 339Aris Anagnostopoulos, Ravi Kumar, Mohammad Mahdian, andEli Upfal

Maximum Bipartite Flow in Networks with Adaptive Channel Width . . . 351Yossi Azar, Aleksander M ↪adry, Thomas Moscibroda,Debmalya Panigrahi, and Aravind Srinivasan

Mediated Population Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Ioannis Chatzigiannakis, Othon Michail, and Paul G. Spirakis

Rumor Spreading in Social Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375Flavio Chierichetti, Silvio Lattanzi, and Alessandro Panconesi

MANETS: High Mobility Can Make Up for Low Transmission Power . . . 387Andrea E.F. Clementi, Francesco Pasquale, and Riccardo Silvestri

Multiple Random Walks and Interacting Particle Systems . . . . . . . . . . . . . 399Colin Cooper, Alan Frieze, and Tomasz Radzik

Derandomizing Random Walks in Undirected Graphs Using LocallyFair Exploration Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

Colin Cooper, David Ilcinkas, Ralf Klasing, and Adrian Kosowski

On a Network Generalization of the Minmax Theorem . . . . . . . . . . . . . . . . 423Constantinos Daskalakis and Christos H. Papadimitriou

Rate-Based Transition Systems for Stochastic Process Calculi . . . . . . . . . . 435Rocco De Nicola, Diego Latella, Michele Loreti, and Mieke Massink

Improved Algorithms for Latency Minimization in Wireless Networks . . . 447Alexander Fanghanel, Thomas Keßelheim, and Berthold Vocking

Efficient Methods for Selfish Network Design . . . . . . . . . . . . . . . . . . . . . . . . 459Dimitris Fotakis, Alexis C. Kaporis, and Paul G. Spirakis

Smoothed Analysis of Balancing Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 472Tobias Friedrich, Thomas Sauerwald, and Dan Vilenchik

Names Trump Malice: Tiny Mobile Agents Can Tolerate ByzantineFailures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Rachid Guerraoui and Eric Ruppert

Multi-armed Bandits with Metric Switching Costs . . . . . . . . . . . . . . . . . . . . 496Sudipto Guha and Kamesh Munagala

XXII Table of Contents – Part II

Algorithms for Secretary Problems on Graphs and Hypergraphs . . . . . . . . 508Nitish Korula and Martin Pal

Leader Election in Ad Hoc Radio Networks: A Keen Ear Helps . . . . . . . . 521Dariusz R. Kowalski and Andrzej Pelc

Secure Function Collection with Sublinear Storage . . . . . . . . . . . . . . . . . . . 534Maged H. Ibrahim, Aggelos Kiayias, Moti Yung, andHong-Sheng Zhou

Worst-Case Efficiency Analysis of Queueing Disciplines . . . . . . . . . . . . . . . 546Damon Mosk-Aoyama and Tim Roughgarden

On Observing Dynamic Prioritised Actions in SOC . . . . . . . . . . . . . . . . . . 558Rosario Pugliese, Francesco Tiezzi, and Nobuko Yoshida

A Distributed and Oblivious Heap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571Christian Scheideler and Stefan Schmid

Proportional Response Dynamics in the Fisher Market . . . . . . . . . . . . . . . . 583Li Zhang

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

Assigning Papers to Referees

Kurt Mehlhorn

Max-Planck-Institut fur Informatikand

Department of Computer Science, Saarland University

Refereed conferences require every submission to be reviewed by members of aprogram committee (PC) in charge of selecting the conference program. A mainresponsibility of the PC chair is to organize the review process, in particular,to decide which papers are assigned to which member of the PC. The PC chairtypically bases her decision on input from the PC, her knowledge of submissionsand PC members, or scores that are computed automatically from keywords pro-vided by authors and PC members. From now on, we call PC members reviewersor referees.

There are many software systems available that support the PC chair inher task; for example, EasyChair [8], HotCRP [7], Softconf [2], Linklings [1],CMT [4], and Websubrev [6]. Used in more than 1300 conferences in 2008 alone[9], EasyChair is currently the most popular conference management software.The system asks the reviewers to declare conflicts of interests and to rank thepapers (for which the reviewer has no conflict of interest) into three classes: highinterest, medium interest, and low interest. This process is called bidding. Basedon this information, the system automatically computes an assignment that thePC chair can later review and modify accordingly. Creating an assignment fromscratch by hand is normally not feasible since many conferences get in excessof 500 submissions [3].

The talk will be based on the paper Assigning Papers to Referees [5] by NaveenGarg, Telikepalli Kavitha, Amit Kumar, Kurt Mehlhorn, and Julian Mestre. Thepaper is available at

http://www.mpi-inf.mpg.de/~mehlhorn/ftp/RefereeAssignment.pdf

In this paper, we propose to optimize a number of criteria that aim at achiev-ing fairness among referees/papers. Some of these variants can be solved op-timally in polynomial time, while others are NP-hard, in which case we designapproximation algorithms. Experimental results strongly suggest that the assign-ments computed by our algorithms are considerably better than those computedby popular conference management software.

References

1. Linklings, http://www.linklings.com/2. Sofconf, http://www.softconf.com/3. Apers, P.: Acceptance rates major database conferences,

http://wwwhome.cs.utwente.nl/~apers/rates.html

S. Albers et al. (Eds.): ICALP 2009, Part I, LNCS 5555, pp. 1–2, 2009.c© Springer-Verlag Berlin Heidelberg 2009

2 K. Mehlhorn

4. Chaudhuri, S.: Microsoft’s academic conference management service,http://cmt.research.microsoft.com/cmt/

5. Garg, N., Kavitha, T., Kumar, A., Mehlhorn, K., Mestre, J.: Assigning Papers toReferees (2008),http://www.mpi-inf.mpg.de/~mehlhorn/ftp/RefereeAssignment.pdf

6. Halevi, S.: Websubrev, http://people.csail.mit.edu/shaih/websubrev/7. Kohler, E.: HotCRP, http://www.cs.ucla.edu/~kohler/hotcrp/8. Voronkov, A.: EasyChair, http://www.easychair.org9. Voronkov, A.: EasyChair - users, http://www.easychair.org/users.cgi

Algorithmic Game Theory: A Snapshot

Christos H. Papadimitriou�

Division of Computer Science, U.C. Berkeleychristos@cs.berkeley.edu

Abstract. Algorithmic game theory is the research area in the interfacebetween the theories of algorithms, networks, and games, which emergedmore than a decade ago motivated by the advent of the Internet. “Snap-shot” means several things: very personal point of view, of topical andpossibly ephemeral interest, and put together in a hurry.

1 Introduction

Algorithmic game theory is arguably at a watershed point of its development.The field has grown tremendously in community size and stature. The basicproblem areas have been defined and progress has been made — enough to jus-tify a field-crystallizing edited book [36]. The emergence, and persistence, ofimportant questions still outpace the exciting answers (see below for an idiosyn-cratic collection of both), but now it is a race. Economists are starting to payattention, so we better have something meaningful — to them — to say.

2 Computing an Equilibrium

Games are thought experiments for understanding and predicting the behaviorof rational strategic agents. The predictions of the theory are called equilibria,of which the Nash equilibrium is perhaps the most famous. One of the earliestgoals of algorithmic game theory was to understand the complexity of comput-ing equilibria. This was quite predictable, given our field’s obsessions, but it alsoentails an important contribution to the other side, as algorithmic issues haveinfluenced and shaped the debate on equilibrium concepts. We now know thatcomputing a Nash equilibrium is PPAD-complete ([13], see [14] for a high-levelexposition), even for 2-player games [8]; as a result, the most important questionin this realm now is: Is there a polynomial-time approximation scheme (PTAS)for computing a Nash equilibrium? The standard approximation concept usedin the literature is additive with normalized positive payoffs; for relative (multi-plicative) approximation when negative payoffs are allowed, a negative answer isnow known [11]. A quasipolynomial-time approximation scheme for this problemhad been known for some time [31]; in fact the algorithm in [31] is of a special

� Supported by NSF grants CCF-0635319, CCF-0515259, a gift from Yahoo! Research,and a MICRO grant.

S. Albers et al. (Eds.): ICALP 2009, Part I, LNCS 5555, pp. 3–11, 2009.c© Springer-Verlag Berlin Heidelberg 2009

4 C.H. Papadimitriou

interesting kind called oblivious, in that it examines possible solutions withoutlooking at the game except to check the quality of the approximation. It can beshown [15] that the algorithm in [31] is nearly optimal among oblivious ones.

But how about special cases for which exact polynomial algorithms exist? Itis quite remarkable that zero-sum games are essentially the only special caseof the problem that we know how to solve — for 80 years now [48]. This canbe generalized slightly to bimatrix games whose matrices, or their sum, areof low rank [25,31]. In another page of this volume [16] we show an interestinggeneralization to networks whose edges are zero-sum games (see below for furtherdiscussion). Strictly competitive games, apparently defined by Aumann, is anintriguing class of games generalizing the zero-sum ones; these are the gameswhich have, along with zero-sum games, the following property: if both playersswitch from a pair of mixed strategies to another, then one is winning and theother is losing. Unfortunately, and rather astonishingly, it was recently shown[1] that this well studied and often mentioned “generalization” is void: zero-sumgames (and their trivial affine variants) are the only examples! Finally on thesubject of polynomially solvable special cases, recall that correlated equilibria areefficiently computable in general games via linear programming (essentially bydesign); for a nontrivial extension to succinctly representable games see [37,38].

Symmetry. Nash points out in his 1951 paper [34] that a modification of hisproof establishes that a symmetric game (i.e., a game in which all players areidentical) has a symmetric equilibrium (all identical players do the same thing).But are symmetric games easier? A beautiful reduction due to Gale, Kuhn andTucker [20], which actually predated Nash’s result, establishes that finding anequilibrium in a symmetric 2-player game cannot be easier than finding a Nashequilibrium in a general game (which we now know, is not easy at all). Thereduction creates a game whose strategy space is the union of the two strategyspaces. Interestingly, in that same volume with [20], there is an independentproof of the same fact by Brown and von Neumann [5] based on the product ofthe strategy spaces. Somewhat surprisingly, neither reduction, or straightforwardmodification, works for three players, so it is currently open whether finding anequilibrium in a symmetric three-player game is easier than finding an equilib-rium in a general game. We conjecture that symmetric games are no easier thangeneral ones, for any number of players. Note also that it is not known how hardit is to find a non-symmetric Nash equilibrium in a symmetric game — it is atleast PPAD-hard.

But symmetry does have definite dividends in multiplayer games. There is apolynomial-time algorithm (albeit, one relying on decision algorithms for realclosed fields and therefore not very efficient with current technology) for findingsymmetric Nash equilibria in symmetric games with n players and few (aboutlogn) strategies [38]. A very important class of games results from a particu-lar relaxed kind of symmetry called anonymity: the players have different utilityfunctions, but these depend on the strategy the player chooses, and on how manyof the other players choose each strategy — not on the identities of the playerswho choose them (think of the game “shall I drive or take the bus?”). That is,

Algorithmic Game Theory: A Snapshot 5

the utilities are symmetric functions of the other players’ choices. There is nowa host of positive algorithmic results for such games culminating in an nO(log2 1

ε )

PTAS [15]. These algorithms rely on results approximating, with more and moresophisticated techniques, the distribution of sums of binomial/multinomial vari-ables, via other such sums whose probabilities are multiples of ε. There is noknown limit to possible improvements: for all we know, this class of games can besolved exactly in polynomial time — I do believe that they are PPAD-complete.

Price Equilibria. Nash’s theorem not only launched Game Theory, but also in-spired the price equilibrium theorems of Arrow and Debreu [2], a very importantrealm of positive results in Microeconomics. Algorithms for finding such priceequilibria had been an open question for some time. We now have polynomialalgorithms for certain special cases (all falling within the subclass of “marketswith gross substitutability,” that is, markets in which increasing the price of agood never decreases the demand of other goods, a case long known to havepositive algorithmic properties akin to convexity, see Chapters 5 and 6 of [36]).One particular algorithm [10], again for such a special case, is of an interestingand realistic sort that can be called “a price adjustment mechanism:” we look atthe prices and the excess demands, and possibly also the history of both, and,based on this information, we adjust the prices. In contrast, all other knownalgorithms for price equilibria zero in to the equilibrium via much less naturalprimitives such as pivoting or hyperplane separation. We also have, at long last,some intractability results for classes of markets (consumer utilities) that do notfall in the gross substitutability category [9,7], as well as an exponential lowerbound (without complexity assumptions) for any price adjustment mechanismthat works in general markets [42].

3 Choosing an Equilibrium

The multiplicity of Nash equilibria has always been a tension between the algo-rithmic and game-theoretic perspective. Somewhat forgotten is an answer pro-vided decades ago by two great game theorists [22], page 144: Players can beassumed to have prior ideas about how their opponents will play, and to start bybest-responding to those. If now the players’ beliefs evolve from that prior to therealities of the actual response, this creates a linear tracing procedure which, inthe absence of degeneracies, points to one equilibrium. It would be interesting torevisit this idea from the complexity-theoretic point of view. Is the linear trac-ing procedure, for example, PSPACE-complete? Incidentally, another importantidea in [22], risk dominance of equilibria, was recently taken on in [32].

But the ultimate conceptual contribution to game theory is the introduction ofa meaningful, compelling, and influential equilibrium concept. I believe that thenovel point of view of algorithmic game theory (with its computational angle andInternet zeitgeist) is capable of producing very interesting ideas here — besides,the recent negative complexity results for Nash equilibria provide new motivationtoward this goal. The territory explored so far extends almost exclusively in the

6 C.H. Papadimitriou

direction of learning and repeated games, see [18] for an early discussion and[21,17] for some later attempts.

Repeated Games. The study of repeated games is, of course, a time honoredbranch of classical game theory, the source of powerful models, as well as thejustification for concepts such as the mixed Nash equilibrium (and the arena ofearly interactions between game theory and Computer Science, recall for example[41]). Part of the conventional wisdom in repeated games is that the equilibriumspace is much richer and better behaved than that of one-shot games by dintof an important cluster of insights and results known as the Folk Theorem: anyreasonable combination of payoffs can be realized by a Nash equilibrium of therepeated game (for example, in the repeated prisoner’s dilemma nearly-always-collaboration is possible). It was recently pointed out in [4] that this fundamentalresult comes with serious, if somewhat covert, computational difficulties: Nashequilibria in repeated games are no more easily accessible (for three or moreplayers) than those of one-shot games.

Learning. The point of repetition in games is to help players adjust to the gameand to each other — that is to say, to learn. Learning in games has a long history,see Chapter 4 of [36]; it had been known for some time that a particular flavorof learning known as no-regret learning — which in a very real sense is a novelequilibrium concept — converges to the Nash equilibrium in zero-sum games[19], and, in a different variant, to correlated equilibria in general games [24].More recently, important connections between no-regret learning and the priceof anarchy (see the next section) has been brought to the fore, see for example[3,47,28].

But of course nobody believes seriously that learning can fathom the in-tractable, converge fast to a Nash equilibrium in general games; surprisingly,we have very little concrete information on this. It can be shown through com-munication complexity arguments [23] that in n-player games exponential time,in n, is needed to converge to a Nash equilibrium (pure or mixed) by learningalgorithms — but then in such games the input would be exponential in n, andthe proof entails pointing out that all this information must be exchanged forcoordinated convergence to equilibrium. It was recently pointed out that a classof learning-type algorithms [12] fail to converge in polynomial time (in the accu-racy) to a Nash equilibrium even for two-person games with three strategies perplayer — they do in the case of zero-sum games, and in the case of two strategies.Can we come up with exponential lower bounds (independent of any complexityassumptions) on restricted classes of algorithms for finding Nash equilibria inbimatrix games? Since our ambition here falls short of proving that P �= NP,we better restrict ourselves to algorithms that are incapable of identifying — orapproximating — the payoff matrices.

Incidentally, a very early instance of the learning approach to games is JuliaRobinson’s 1950 proof [43] that a particular algorithm called fictitious play (bothplayers know all payoffs, assume that the other player’s mixed strategy is cap-tured by the histogram of her past plays, and best-respond to that) converges in

Algorithmic Game Theory: A Snapshot 7

the case of zero-sum games — but the best known upper bound on the numberof iterations needed to converge is exponential in the number of strategies (it isimplicit in Robinson’s inductive proof [43]). Karlin1 conjectured fifty years agothat the true convergence rate is in fact quadratic.

4 Networks and Games

Scott Shenker’s famous quote “The Internet is an equilibrium — we just have toidentify the game” captures perfectly the complex of reasons that made game-theoretic thought relevant to Computer Science ca. the late 1990s. The Internetis a computational artifact that was not designed (except in the loosest andbroadest sense) by an entity but emerged from the unstructured interaction ofmany. The area of the “price of anarchy” (see [30] and Chapter 17 of [36]) seeksto gauge the loss of performance inherent in such process — the paradigmaticwork in this area is Roughgarden’s thesis [46,45] on the price of anarchy inrouting.

The model of [46], in which routing decisions are made by flows, is an adapta-tion of classical models from transportation theory, and has little relevance to theInternet. It was recently shown [40] that, if routing decisions are made by eachedge of the network so as to minimize downstream congestion experienced by theflows through the edge, then the price of anarchy becomes unbounded. However,if, instead, the edges charge per-unit-of-flow prices to their upstream neighborsand maximize revenue minus cost, it is shown (under assumptions) that the priceof anarchy becomes one. In other words, this is another instance in which prices,magically, usher in efficiency. One important cluster of questions is, how do theconventions and protocols of today’s Internet, such as the BGP protocol gov-erning the interactions between autonomous systems, limit this ideal efficiency?Examples of features of BGP that may be sources of inefficiency are: Long-termagreements that are oblivious to fluctuations in downstream congestion condi-tions; and selection of a single downstream routing path per destination.

But networks are changing. Social networks such as Facebook are only thelatest and most explicit examples of the important networks of interactions be-tween entities that had always been Internet’s raison d’ etre — enabled by itand embedded in it in a variety of ways. I believe that it is productive to un-derstand such networks as graphs whose edges are games played by the nodes— the so called graphical polymatrix games, in which each node chooses a com-mon strategy to play in all incident games, and receives the sum of the resultingpayoffs. In fact, such modeling is not new: past work on the spreading of tech-nologies and ideas in a social network [29], for example, falls squarely into thisframework, with coordination games at the edges (see [32] for recent work onthe convergence of such games). In a paper in this volume [16], a simple butrather surprising result is shown: If the edges of the graph are zero-sum games,then the whole game has the minmax property and is easily solvable. In fact,1 Sam Karlin (1924–2007), a giant of early game theory among other fields, whose

work is not as broadly known to our community as one would have expected.

8 C.H. Papadimitriou

the nodes/players can converge to the equilibrium via distributed learning, andeach of them has a value capturing the sum total of the advantages in both herposition in the network and in the structure of the incident games. Incidentally,economists are getting increasingly interested in the effects of network structureon markets and other economic interactions, and the point of view in this para-graph may be an important opportunity for our field to contribute to moderneconomic thought.

5 Mechanism Design

Mechanism design [44] seeks to create games in which the desired (socially op-timum or, more generally, beneficial to the designer) behavior emerges as anequilibrium of selfish participants, independently of the participants’s unknowntrue preferences; this is done, of course, by providing appropriate incentives thatwill make “gaming the system” unpalatable. It is a mature and much lauded(see the above reference) area of economic theory, which, however, had beenperceived as a little too rich in sweeping positive results. The area of algorith-mic mechanism design (see [35] and Chapter 9 of [36]) addresses this concernby fathoming the intriguing tradeoffs between the effectiveness of the designedmechanism and the computational complexity of its implementation.

Perhaps the most classical sweeping positive result in mechanism design isthe so-called VCG mechanism (named after the economists Vickrey, Clarke andGroves who devised it): If monetary incentives are possible (and inconsequential,which is another important aspect where computer scientists beg to differ, see forexample [26]), then essentially anything goes: there are appropriate incentivesthat will elicit essentially any desired behavior of the agents. But algorithmicgame theory researchers have pointed out that the VCG approach to mechanismdesign is paved with computational obstacles, as the computation of such pay-ments is often an intractable problem. Now in computer science we know howto deal with such intractability: We approximate. Unfortunately, incentives arefragile, and work only if computed exactly. This three-way tension between com-plexity, approximability, and incentive compatibility, has created an exciting anddeep research area. A recent result has connected, for the first time, this tradeoffwith classical complexity theory: It was shown that there is an NP-completeoptimization problem that can be approximated well (within a small constantfactor) in polynomial time but which, unless NP = BPP, cannot be approxi-mated well (better than the square root of the problem’s natural parameter)in an incentive-compatible way [39]. And in more recent work [33,6] steps havebeen made towards extending this result to the central problem of combinatorialauctions (see Chapter 11 of [36]).

Mechanism design is about important realities which lie at the roots of theremarkable convergence of computational and economic thought over the pastdecade or so: computational systems are no longer entities whose only job is toproduce correct outputs for the data on their input tape. They must encapsu-late incentives so they are invoked with the right inputs — let alone invoked

Algorithmic Game Theory: A Snapshot 9

at all. . . Turing’s question “what can be computed?” is being revisited oncemore (as it has been revisited several times in the past century to accommodateconsiderations of complexity, distributed computation and on-line computation,for example): Which functions can be computed, and with what accuracy, whenthe inputs are owned by entities that are keenly interested in the outcome of thecomputation?

Acknowledgment. Many thanks to Costis Daskalakis and Tim Roughgarden forfeedback on an earlier version.

References

1. Adler, I., Daskalakis, C., Papadimitriou, C.H.: Manuscript (2009)2. Arrow, K.J., Debreu, G.: Existence of equilibria for a competitive economy. Econo-

metrica 22(3), 265–290 (1954)3. Blum, A., Hajiaghayi, M., Ligett, K., Roth, A.: Regret minimization and the price

of total anarchy. In: STOC (2008)4. Borgs, C., Chayes, J.T., Immorlica, N., Kalai, A.T., Mirrokni, V.S., Papadimitriou,

C.H.: The myth of the folk theorem. In: STOC 2008, pp. 365–372 (2008)5. Brown, G.W., von Neumann, J.: Solutions of games by differential equations. In:

Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, PrincetonUniversity Press, Princeton (1950)

6. Buchfuhrer, D., Umans, C.: Limits on the social welfare of maximal-in-range auc-tion mechanisms (manuscript, 2009)

7. Chen, X., Dai, D., Du, Y., Teng, S.: Settling the complexity of Arrow-Debreuequilibria in markets with linearly separable utilities (manuscript, 2009)

8. Chen, X., Deng, X.: Settling the complexity of two-player Nash equilibrium. In:FOCS (2006)

9. Codenotti, B., Saberi, A., Varadarajan, K., Ye, Y.: Leontief economies encodenonzero sum two-player games. In: Proceedings of the seventeenth annual ACM-SIAM Symposium on Discrete Algorithms, SODA (2006)

10. Cole, R., Fleischer, L.: Fast-converging tatonnement algorithms for one-time andongoing market problems. In: Proceedings of the 40th annual ACM Symposium onTheory of Computing, STOC (2008)

11. Daskalakis, C.: The complexity of approximating a Nash equilibrium (submitted,2009)

12. Daskalakis, C., Frongillo, R., Pierrakos, G., Papadimitriou, C.H., Valiant, G.: Inpreparation (2009)

13. Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computinga Nash equilibrium. In: STOC 2006 (2006); SIAM Journal on Computing, specialissue for 2006 STOC (to appear)

14. Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computinga Nash equilibrium. CACM 58(2), 89–97 (2009)

15. Daskalakis, C., Papadimitriou, C.H.: On oblivious PTAS’s for Nash equilibrium.In: STOC (2009)

16. Daskalakis, C., Papadimitriou, C.H.: On a network generalization of the minmaxtheorem. In: Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W.(eds.) ICALP 2009. LNCS, vol. 5555, Springer, Heidelberg (2009)

10 C.H. Papadimitriou

17. Fabrikant, A., Papadimitriou, C.H.: The complexity of game dynamics: BGP os-cillations, sink equilibria, and beyond. In: SODA 2008, pp. 844–853 (2008)

18. Friedmand, E.J., Shenker, S.J.: Learning and implementation on the Internet,Working paper (1997)

19. Freund, Y., Schapire, R.E.: Adaptive game playing using multiplicative weights.Games and Economic Behavior 29, 79–103 (1999)

20. Gale, D., Kuhn, H.W., Tucker, A.W.: On symmetric games. In: Kuhn, H.W.,Tucker, A.W. (eds.) Contributions to the Theory of Games, Princeton UniversityPress, Princeton (1950)

21. Goemans, M.X., Mirrokni, V.S., Vetta, A.: Sink Equilibria and Convergence. In:FOCS 2005, pp. 142–154 (2005)

22. Harsanyi, J.C., Selten, R.: A General Theory of Equilibrium Selection in Games.MIT Press Classis, Cambridge (1982)

23. Hart, S., Mansour, Y.: The communication complexity of uncoupled Nash equilib-rium procedures. In: STOC 2007 (2007)

24. Hart, S., Mas-Colell, A.: A simple adaptive procedure leading to correlated equi-librium. Econometrica 68(5), 1127–1150 (2000)

25. Kannan, R., Theobald, T.: Games of fixed rank: A hierarchy of bimatrix games.In: SODA (2007)

26. Karlin, A.R., Kempe, D., Tamir, T.: Frugality of truthful mechanisms. In: FOCS(2005)

27. Kearns, M.J., Littman, M.L., Singh, S.P.: Graphical Models for Game Theory. In:UAI (2001)

28. Kleinberg, R., Piliouras, G., Tardos, E.: Multiplicative updates outperform genericno-regret learning in congestion games. In: STOC (2009)

29. Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence througha social network. In: SIGKDD (2003)

30. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison,S. (eds.) STACS 1999, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

31. Lipton, R., Markakis, E., Mehta, A.: Playing large games using simple strategies.In: ACM EC (2003)

32. Montanari, A., Saberi, A.: Convergence to Equilibrium in Local Interaction Games(2008)

33. Mossel, E., Papadimitriou, C.H., Schapira, M., Singer, Y.: Combinatorial Auctions:VC v. VCG (submitted, 2009)

34. Nash, J.: Noncooperative Games. Annals of Mathematics 54, 289–295 (1951)35. Nisan, N., Ronen, A.: Algorithmic Mechanism Design. In: STOC (1999)36. Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory.

Cambridge University Press, New York (2007)37. Papadimitriou, C.H.: Computing correlated equilibria in multiplayer games. In:

STOC (2005)38. Papadimitriou, C.H., Roughgarden, T.: Computing equilibria in multi-player

games. In: SODA 2005 (2005); J.ACM (full version, 2008)39. Papadimitriou, C.H., Schapira, M., Singer, Y.: On the hardness of being truthful.

In: FOCS (2008)40. Papadimitriou, C.H., Valiant, G.: Selfish routers and the price of anarchy (submit-

ted, 2009)41. Papadimitriou, C.H., Yannakakis, M.: On complexity as bounded rationality (ex-

tended abstract). In: STOC 1994, pp. 726–733 (1994)42. Papadimitriou, C.H., Yannakakis, M.: An impossibility theorem for price adjust-

ment mechanisms (manuscript, 2009)

Algorithmic Game Theory: A Snapshot 11

43. Robinson, J.: An iterative method of solving a game. Annals of Mathematics (1951)44. Royal Swedish Academy of Sciences Mechanism Design Theory (2007),

http://nobelprize.org/nobelprizes/economics/laureates/

2007/ecoadv07.pdf

45. Roughgarden, T.: Selfish Routing. MIT Press, Cambridge (2002)46. Roughgarden, T., Tardos, E.: How bad is selfish routing? JACM (2002)47. Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: STOC (2009)48. von Neumann, J.: Zur Theorie der Gesellschaftsspiele. Math. Annalen 100, 295–320

(1928)