TY - JOUR

T1 - The Distance-Constrained Matroid Median Problem

AU - Kamiyama, Naoyuki

N1 - Funding Information:
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.
Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85079712707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85079712707&partnerID=8YFLogxK

U2 - 10.1007/s00453-020-00688-5

DO - 10.1007/s00453-020-00688-5

M3 - Article

AN - SCOPUS:85079712707

VL - 82

SP - 2087

EP - 2106

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 7

ER -