Small clique detection and approximate Nash equilibria

Lorenz Minder, Dan Vilenchik

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

Recently, Hazan and Krauthgamer showed [12] that if, for a fixed small ε, an ε-best ε-approximate Nash equilibrium can be found in polynomial time in two-player games, then it is also possible to find a planted clique in Gn, 1/2 of size C logn, where C is a large fixed constant independent of ε. In this paper, we extend their result to show that if an ε-best ε-approximate equilibrium can be efficiently found for arbitrarily small ε > 0, then one can detect the presence of a planted clique of size (2 + δ) logn in Gn, 1/2 in polynomial time for arbitrarily small δ > 0. Our result is optimal in the sense that graphs in Gn, 1/2 have cliques of size (2 - o(1)) log n with high probability.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings
Pages673-685
Number of pages13
DOIs
StatePublished - 6 Nov 2009
Externally publishedYes
Event12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009 - Berkeley, CA, United States
Duration: 21 Aug 200923 Aug 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5687 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009
Country/TerritoryUnited States
CityBerkeley, CA
Period21/08/0923/08/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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