Approximating Coloring and Maximum Independent Sets in 3-Uniform Hypergraphs

Michael Krivelevich, Ram Nathaniel, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

Abstract

We discuss approximation algorithms for the coloring problem and the maximum independent set problem in 3-uniform hypergraphs. An algorithm for coloring 3-uniform 2-colorable hypergraphs in Õ(n1/5) colors is presented, improving previously known results. Also, for every fixed γ > 1/2, we describe an algorithm that, given a 3-uniform hypergraph H on n vertices with an independent set of size γn, finds an independent set of size Ω̃(min(n, n6γ-3)). For certain values of γ we are able to improve this using the local ratio approach. The results are obtained through semidefinite programming relaxations of these optimization problems.

Original languageEnglish
Pages (from-to)99-113
Number of pages15
JournalJournal of Algorithms
Volume41
Issue number1
DOIs
StatePublished - Oct 2001

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