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arXiv · 1907.04088

$r$-Gather Clustering and $r$-Gathering on Spider: FPT Algorithms and Hardness

Soh Kumabe·Takanori Maehara
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Abstract

We consider min-max $r$-gather clustering problem and min-max $r$-gathering problem. In the min-max $r$-gather clustering problem, we are given a set of users and divide them into clusters with size at least $r$; the goal is to minimize the maximum diameter of clusters. In the min-max $r$-gathering problem, we are additionally given a set of facilities and assign each cluster to a facility; the goal is to minimize the maximum distance between the users and the assigned facility. In this study, we consider the case that the users and facilities are located on a ``spider'' and propose the first fixed-parameter tractable (FPT) algorithms for both problems, which are parametrized by only the number of legs. Furthermore, we prove that these problems are NP-hard when the number of legs is arbitrarily large.

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Soh Kumabe, Takanori Maehara. 2019-07-09. $r$-Gather Clustering and $r$-Gathering on Spider: FPT Algorithms and Hardness. https://arxiv.org/abs/1907.04088

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