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The Distance-Constrained Matroid Median Problem

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Abstract

Alamdari and Shmoys introduced the following variant of the k-median problem. In this variant, we are given an instance of the k-median problem and a threshold value. Then this variant is the same as the k-median problem except that if the distance between a client i and a facility j is more than the threshold value, then i is not allowed to be connected to j. In this paper, we consider a matroid generalization of this variant of the k-median problem. First, we introduce a generalization of this variant in which the constraint on the number of opened facilities is replaced by a matroid constraint. Then we propose a polynomial-time bicriteria approximation algorithm for this problem by combining the algorithm of Alamdari and Shmoys and the algorithm of Krishnaswamy, Kumar, Nagarajan, Sabharwal, and Saha for a matroid generalization of the k-median problem.

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Acknowledgements

The author would like to thank the anonymous referees and Yoshio Okamoto for helpful comments. This research was supported by JST, PRESTO Grant Number JPMJPR1753, Japan.

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Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Naoyuki Kamiyama

  2. JST, PRESTO, Kawaguchi, Japan

    Naoyuki Kamiyama

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  1. Naoyuki Kamiyama
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Correspondence to Naoyuki Kamiyama.

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Kamiyama, N. The Distance-Constrained Matroid Median Problem. Algorithmica 82, 2087–2106 (2020). https://doi.org/10.1007/s00453-020-00688-5

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  • DOI: https://doi.org/10.1007/s00453-020-00688-5

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