An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

  • Kamal Jain 
  • Vijay V. Vazirani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1913)


We consider a fault tolerant version of the metric facility location problem in which every city, j, is required to be connected to r j facilities. We give the first non-trivial approximation algorithm for this problem, having an approximation guarantee of 3·Hk, where k is the maximum requirement and Hk is the k-th harmonic number. Our algorithm is along the lines of [2] for the generalized Steiner network problem. It runs in phases, and each phase, using a generalization of the primal-dual algorithm of [4] for the metric facility location problem, reduces the maximum residual requirement by 1.


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  1. 1.
    A. Agrawal, P. Klein, and R. Ravi.When trees collide: An approximation algorithm for the generalized Steiner problem on networks. SIAM J. on Computing, 24:440–456, 1995.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    M. Goemans, A. Goldberg, S. Plotkin, D. Shmoys, E. Tardos, and D. Williamson. Improved approximation algorithms for network design problems. Proc. 5th ACMSIAM Symp. on Discrete Algorithms, 223–232, 1994.Google Scholar
  3. 3.
    M. X. Goemans, D. P. Williamson. A general approximation technique for constrained forest problems. SIAM Journal of Computing, 24:296–317, 1995.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    K. Jain and V. V. Vazirani. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. To appear in JACM.Google Scholar
  5. 5.
    D. P. Williamson, M. X. Goemans, M. Mihail, and V. V. Vazirani. A primal-dual approximation algorithm for generalized Steiner network problems. Combinatorica, 15:435–454, December1995.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kamal Jain 
    • 1
  • Vijay V. Vazirani
    • 1
  1. 1.College of ComputingGeorgia Institute of TechnologyAtlanta

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