TY - JOUR

T1 - Approximating Coloring and Maximum Independent Sets in 3-Uniform Hypergraphs

AU - Krivelevich, Michael

AU - Nathaniel, Ram

AU - Sudakov, Benny

N1 - Funding Information:
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 O˜(n) colors is presented, improving1 5 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,findsanindependentsetofsizeΩ˜(min(n,n6γ 3)).Forcertainvaluesofγ we are able to improve this using the local ratio approach. The results are obtained through semidefinite programming relaxations of these optimization problems. 2001 Academic Press 1An extended abstract of this paper appeared in the Proceedings of the 12th Annual Symposium on Discrete Algorithms (SODA ’2001). 2Supported by a U.S.A.—Israeli BSF grant. 3Research supported in part by NSF grants DMS-0106589 and CCR-9987845 and by the State of New Jersey.

PY - 2001/10

Y1 - 2001/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0011523905&partnerID=8YFLogxK

U2 - 10.1006/jagm.2001.1173

DO - 10.1006/jagm.2001.1173

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AN - SCOPUS:0011523905

VL - 41

SP - 99

EP - 113

JO - Journal of Algorithms

JF - Journal of Algorithms

SN - 0196-6774

IS - 1

ER -