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 an earlier result for the generalized Steiner network problem. It runs in phases, and each phase, using a generalization of the primal–dual algorithm for the metric facility location problem, reduces the maximum residual requirement by one.