Approximation algorithms using hierarchies of semidefinite programming relaxations

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

51 Scopus citations

Abstract

We introduce a framework for studying semidefinite programming (SDP) relaxations based on the Lasserre hierarchy in the context of approximation algorithms for combinatorial problems. As an application of our approach we give improved approximation algorithms for two problems. We show that for some fixed constant ε > 0, given a 3-uniform hypergraph containing an independent set of size (1/2 - ε)n, we can find an independent set of size Ω(nε). This improves upon the result of Krivelevich, Nathaniel and Sudakov, who gave an algorithm finding an independent set of size Ω̃(n6γ-3) for hypergraphs with an independent set of size γn (but no guarantee for γ ≤ 1/2). We also give an algorithm which finds an O(n0.2072)-coloring given a 3-colorable graph, improving upon the work of Arora, Chlamtac and Charikar. Our approach stands in contrast to a long series of inapproximability results in the Lovász Schrijver linear programming (LP) and SDP hierarchies for other problems.

Original languageEnglish
Title of host publicationProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007
Pages691-701
Number of pages11
DOIs
StatePublished - 1 Dec 2007
Externally publishedYes
Event48th Annual Symposium on Foundations of Computer Science, FOCS 2007 - Providence, RI, United States
Duration: 20 Oct 200723 Oct 2007

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference48th Annual Symposium on Foundations of Computer Science, FOCS 2007
Country/TerritoryUnited States
CityProvidence, RI
Period20/10/0723/10/07

ASJC Scopus subject areas

  • Engineering (all)

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