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

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## 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.

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### References

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