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Valuated matroid-based algorithm for submodular welfare problem

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Abstract

An algorithm for the submodular welfare problem is proposed based on the theory of discrete convex analysis. The proposed algorithm is a heuristic method built upon the valuated matroid partition algorithms, and gives the exact optimal solution for a reasonable subclass of submodular welfare problems. The algorithm has a guaranteed approximation ratio for a special case. Computational results show fairly good performance of the proposed algorithm.

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Notes

  1. “Set \(k\)-cover problem” is originally considered by Slijepcevic and Potkonjak (2001), which is slightly different from this problem.

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Acknowledgments

This work is supported by KAKENHI (21360045, 26280004) and the Aihara Project, the FIRST program from JSPS. The first author is supported by JST, ERATO, Kawarabayashi Project.

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Authors and Affiliations

  1. Department of Mathematics and Systems Engineering, Shizuoka University, Shizuoka, Japan

    Takanori Maehara

  2. Department of Mathematical Informatics, University of Tokyo, Tokyo, Japan

    Kazuo Murota

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  1. Takanori Maehara
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  2. Kazuo Murota
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Correspondence to Takanori Maehara.

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Maehara, T., Murota, K. Valuated matroid-based algorithm for submodular welfare problem. Ann Oper Res 229, 565–590 (2015). https://doi.org/10.1007/s10479-015-1835-3

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  • DOI: https://doi.org/10.1007/s10479-015-1835-3

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