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