An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

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 kth 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 5] for the metric facility location problem, reduces the maximum residual requirement by one.