$r$-Gather Clustering and $r$-Gathering on Spider: FPT Algorithms and Hardness
Abstract
We consider min-max -gather clustering problem and min-max -gathering problem. In the min-max -gather clustering problem, we are given a set of users and divide them into clusters with size at least ; the goal is to minimize the maximum diameter of clusters. In the min-max -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.
Keywords
Cite
@article{arxiv.1907.04088,
title = {$r$-Gather Clustering and $r$-Gathering on Spider: FPT Algorithms and Hardness},
author = {Soh Kumabe and Takanori Maehara},
journal= {arXiv preprint arXiv:1907.04088},
year = {2019}
}