The Fault Tolerant Capacitated k-Center Problem

  • Shiri Chechik
  • David Peleg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)


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.


Feasible Solution Service Center Weighted Graph Free Node Nondecreasing Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bar-Ilan, J., Kortsarz, G., Peleg, D.: How to allocate network centers. J. Algorithms 15, 385–415 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bar-Ilan, J., Kortsarz, G., Peleg, D.: Generalized Submodular Cover Problems and Applications. Theoretical Computer Science 250, 179–200 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Dyer, M., Frieze, A.M.: A simple heuristic for the p-center problem. Oper. Res. Lett. 3, 285–288 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Edmondsa, J., Fulkersona, D.R.: Bottleneck extrema. J. Combinatorial Theory 8, 299–306 (1970)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractibility: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1978)Google Scholar
  6. 6.
    Gonzalez, T.: Clustering to minimize the maximum intercluster distance. Theoretical Computer Science 38, 293–306 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    Hochbaum, D.S., Shmoys, D.B.: A best possible heuristic for the k-center problem. Mathematics of Operations Research 10, 180–184 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Hochbaum, D.S., Shmoys, D.B.: A unified approach to approximation algorithms for bottleneck problems. J. ACM 33(3), 533–550 (1986)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hsu, W.L., Nemhauser, G.L.: Easy and hard bottleneck location problems. Discrete Appl. Math. 1, 209–216 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Khuller, S., Pless, R., Sussmann, Y.: Fault tolerant k-center problems. Theoretical Computer Science 242, 237–245 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Khuller, S., Sussmann, Y.: The Capacitated K-Center Problem. SIAM J. Discrete Math. 13, 403–418 (2000)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Plesnik, J.: A heuristic for the p-center problem in graphs. Discrete Appl. Math. 17, 263–268 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Wolsey, L.A.: An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica 2, 385–393 (1982)MathSciNetzbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shiri Chechik
    • 1
  • David Peleg
    • 1
  1. 1.Department of Computer ScienceThe Weizmann InstituteRehovotIsrael

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