# An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

Conference paper

First Online:

## Abstract

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·H_{k}, where *k* is the maximum requirement and H_{k} 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.

## Preview

Unable to display preview. Download preview PDF.

## References

- 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.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.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.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.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