Complexity of the multi-service center problem

Takehiro Ito, Naonori Kakimura, Yusuke Kobayashi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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
Title of host publication28th International Symposium on Algorithms and Computation, ISAAC 2017
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume92
ISBN (Electronic)9783959770545
DOIs
Publication statusPublished - 2017 Dec 1
Event28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand
Duration: 2017 Dec 92017 Dec 22

Other

Other28th International Symposium on Algorithms and Computation, ISAAC 2017
CountryThailand
CityPhuket
Period17/12/917/12/22

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Keywords

  • Facility location
  • Graph algorithm
  • Multi-service location

ASJC Scopus subject areas

  • Software

Cite this

Ito, T., Kakimura, N., & Kobayashi, Y. (2017). Complexity of the multi-service center problem. In 28th International Symposium on Algorithms and Computation, ISAAC 2017 (Vol. 92). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2017.48