Approximate Set Covering in Uniform Hypergraphs

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Abstract

The weighted set covering problem, restricted to the class of r-uniform hypergraphs, is considered. We propose a new approach, based on a recent result of Aharoni, Holzman, and Krivelevich about the ratio of integer and fractional covering numbers in k-colorable r-uniform hypergraphs. This approach, applied to hypergraphs of maximal degree bounded by Δ, yields an algorithm with approximation ratio r(1 - c/Δ1/(r-1)). Next, we combine this approach with an adaptation of the local ratio theorem of Bar-Yehuda and Even for hypergraphs and present a general framework of approximation algorithms, based on subhypergraph exclusion. An application of this scheme is described, providing an algorithm with approximation ratio r(1 - c/n(r-1)/r) for hypergraphs on n vertices. We discuss also the limitations of this approach.

Original languageEnglish
Pages (from-to)118-143
Number of pages26
JournalJournal of Algorithms
Volume25
Issue number1
DOIs
StatePublished - Oct 1997

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