An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem

We consider a fault tolerant version of the metric facility locationproblem in which every city, j, is required to be connected to r _j facilities. We give the first non-trivial approximation algorithm forthis problem, having an approximation guarantee of 3 · H _k , wherek is the maximum requirement and H _k is the kth harmonicnumber. Our algorithm is along the lines of [2] for thegeneralized Steiner network problem. It runs in phases, and eachphase, using a generalization of the primal–dual algorithm of[5] for the metric facility location problem, reduces themaximum residual requirement by one.