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 |
|---|---|
| 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 |
|---|---|
| Country | Thailand |
| City | Phuket |
| Period | 17/12/9 → 17/12/22 |
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Keywords
- Facility location
- Graph algorithm
- Multi-service location
ASJC Scopus subject areas
- Software
Cite this
Complexity of the multi-service center problem. / Ito, Takehiro; Kakimura, Naonori; Kobayashi, Yusuke.
28th International Symposium on Algorithms and Computation, ISAAC 2017. Vol. 92 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Complexity of the multi-service center problem
AU - Ito, Takehiro
AU - Kakimura, Naonori
AU - Kobayashi, Yusuke
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
VL - 92
BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ER -