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 -