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·Hk, where k is the maximum requirement and Hk is the k-th harmonic number. Our algorithm is along the lines of  for the generalized Steiner network problem. It runs in phases, and each phase, using a generalization of the primal-dual algorithm of  for the metric facility location problem, reduces the maximum residual requirement by 1.
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