Complexity of the multi-service center problem

Takehiro Ito, Naonori Kakimura, Yusuke Kobayashi

Research output: Contribution to journalArticlepeer-review

Abstract

The multi-service center problem is a variant of facility location problems. In the problem, we consider locating p facilities on a graph, each of which provides distinct service required by all vertices. Each vertex incurs the cost determined by the sum of the weighted distances to the p facilities. The aim of the problem is to minimize the maximum cost among all vertices. This problem is known to be NP-hard for general graphs, while it is solvable in polynomial time when p is a fixed constant. In this paper, we give sharp analyses for the complexity of the problem from the viewpoint of graph classes and weights on vertices. We first propose a polynomial-time algorithm for trees when p is a part of input. In contrast, we prove that the problem becomes strongly NP-hard even for cycles. We also show that when vertices are allowed to have negative weights, the problem becomes NP-hard for paths of only three vertices and strongly NP-hard for stars.

Original languageEnglish
Pages (from-to)18-27
Number of pages10
JournalTheoretical Computer Science
Volume842
DOIs
Publication statusPublished - 2020 Nov 24

Keywords

  • Facility location
  • Graph algorithm
  • Multi-service location

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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