TY - GEN

T1 - Complexity of the multi-service center problem

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kobayashi, Yusuke

N1 - Funding Information:
∗ This work is partially supported by JST ERATO Grant Number JPMJER1201, JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16H03118, JP16K00004, JP16K16010 and JP17K00028, Japan.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - Facility location

KW - Graph algorithm

KW - Multi-service location

UR - http://www.scopus.com/inward/record.url?scp=85038565684&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038565684&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2017.48

DO - 10.4230/LIPIcs.ISAAC.2017.48

M3 - Conference contribution

AN - SCOPUS:85038565684

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017

A2 - Tokuyama, Takeshi

A2 - Okamoto, Yoshio

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 28th International Symposium on Algorithms and Computation, ISAAC 2017

Y2 - 9 December 2017 through 22 December 2017

ER -