Abstract
The capacitated K-center (CKC) problem calls for locating K service centers in the vertices of a given weighted graph, and assigning each vertex as a client to one of the centers, where each service center has a limited service capacity and thus may be assigned at most L clients, so as to minimize the maximum distance from a vertex to its assigned service center. This paper studies the fault tolerant version of this problem, where one or more service centers might fail simultaneously. We consider two variants of the problem. The first is the α-fault-tolerant capacitated K-Center ( \(\mbox{\tt $\alpha$-FT-CKC}\) ) problem. In this version, after the failure of some centers, all nodes are allowed to be reassigned to alternate centers. The more conservative version of this problem, hereafter referred to as the α-fault-tolerant conservative capacitated K-center ( \(\mbox{\tt $\alpha$-FT-CCKC}\) ) problem, is similar to the \(\mbox{\tt $\alpha$-FT-CKC}\) problem, except that after the failure of some centers, only the nodes that were assigned to those centers before the failure are allowed to be reassigned to other centers. We present polynomial time algorithms that yields 9-approximation for the \(\mbox{\tt $\alpha$-FT-CKC}\) problem and 17-approximation for the \(\mbox{\tt $\alpha$-FT-CCKC}\) problem.
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References
Bar-Ilan, J., Kortsarz, G., Peleg, D.: How to allocate network centers. J. Algorithms 15, 385–415 (1993)
Bar-Ilan, J., Kortsarz, G., Peleg, D.: Generalized Submodular Cover Problems and Applications. Theoretical Computer Science 250, 179–200 (2001)
Dyer, M., Frieze, A.M.: A simple heuristic for the p-center problem. Oper. Res. Lett. 3, 285–288 (1985)
Edmondsa, J., Fulkersona, D.R.: Bottleneck extrema. J. Combinatorial Theory 8, 299–306 (1970)
Garey, M.R., Johnson, D.S.: Computers and Intractibility: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1978)
Gonzalez, T.: Clustering to minimize the maximum intercluster distance. Theoretical Computer Science 38, 293–306 (1985)
Hochbaum, D.S., Shmoys, D.B.: Powers of graphs: A powerful approximation algorithm technique for bottleneck problems. In: Proc. 16th ACM Symp. on Theory of Computing, pp. 324–333 (1984)
Hochbaum, D.S., Shmoys, D.B.: A best possible heuristic for the k-center problem. Mathematics of Operations Research 10, 180–184 (1985)
Hochbaum, D.S., Shmoys, D.B.: A unified approach to approximation algorithms for bottleneck problems. J. ACM 33(3), 533–550 (1986)
Hsu, W.L., Nemhauser, G.L.: Easy and hard bottleneck location problems. Discrete Appl. Math. 1, 209–216 (1979)
Khuller, S., Pless, R., Sussmann, Y.: Fault tolerant k-center problems. Theoretical Computer Science 242, 237–245 (2000)
Khuller, S., Sussmann, Y.: The Capacitated K-Center Problem. SIAM J. Discrete Math. 13, 403–418 (2000)
Plesnik, J.: A heuristic for the p-center problem in graphs. Discrete Appl. Math. 17, 263–268 (1987)
Wolsey, L.A.: An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica 2, 385–393 (1982)
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Chechik, S., Peleg, D. (2012). The Fault Tolerant Capacitated k-Center Problem. In: Even, G., Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2012. Lecture Notes in Computer Science, vol 7355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31104-8_2
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DOI: https://doi.org/10.1007/978-3-642-31104-8_2
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