Complexity of the Multi-Service Center Problem

Authors Takehiro Ito, Naonori Kakimura, Yusuke Kobayashi

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Takehiro Ito
Naonori Kakimura
Yusuke Kobayashi

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Takehiro Ito, Naonori Kakimura, and Yusuke Kobayashi. Complexity of the Multi-Service Center Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 48:1-48:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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.
  • facility location
  • graph algorithm
  • multi-service location


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