Abstract
The weighted set covering problem, restricted to the class ofr-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 ink-colorabler-uniform hypergraphs. This approach, applied to hypergraphs of maximal degree bounded by Δ, yields an algorithm with approximation ratior(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 ratior(1−c/n(r−1)/r) for hypergraphs onnvertices. We discuss also the limitations of this approach.
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