On approximation of the submodular set cover problem

Authors:
Toshihiro Fujito
Affiliations:
Department of Electronics, Nagoya University, Furo, Chikusa, Nagoya 464-8603, Japan
Venue:
Operations Research Letters
Year:
1999

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Abstract

We design a primal-dural heuristic for the submodular set cover problem and analyze its performance giving an approximation bound as a generalization of the one for the set cover problem. As an application, a capacitated version of the partial vertex cover problem on hypergraphs with edge size at most d is considered. It will be shown that the problem can be approximated in polynomial time within a factor of d of the optimum, generalizing some existing results.