Improved approximation guarantees through higher levels of SDP hierarchies

Eden Chlamtac, Gyanit Singh

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

35 Scopus citations

Abstract

For every fixed γ ≥ 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size γn, finds an independent set of size . This improves upon a recent result of Chlamtac, which, for a fixed ε > 0, finds an independent set of size n ε in any 3-uniform hypergraph containing an independent set of size . The main feature of this algorithm is that, for fixed γ, it uses the Θ(1/γ 2)-level of a hierarchy of semidefinite programming (SDP) relaxations. On the other hand, we show that for at least one hierarchy which gives such a guarantee, 1/γ levels yield no non-trivial guarantee. Thus, this is a first SDP-based algorithm for which the approximation guarantee improves indefinitely as one uses progressively higher-level relaxations.

Original languageEnglish
Title of host publicationApproximation, Randomization and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings
Pages49-62
Number of pages14
DOIs
StatePublished - 22 Sep 2008
Externally publishedYes
Event11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008 - Boston, MA, United States
Duration: 25 Aug 200827 Aug 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5171 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008
Country/TerritoryUnited States
CityBoston, MA
Period25/08/0827/08/08

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