### 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 language | English |
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Title of host publication | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Volume | 92 |

ISBN (Electronic) | 9783959770545 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

Event | 28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand Duration: 2017 Dec 9 → 2017 Dec 22 |

### Other

Other | 28th International Symposium on Algorithms and Computation, ISAAC 2017 |
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Country | Thailand |

City | Phuket |

Period | 17/12/9 → 17/12/22 |

### Keywords

- Facility location
- Graph algorithm
- Multi-service location

### ASJC Scopus subject areas

- Software

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## Cite this

*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