We consider a fault tolerant version of the metric facility location problem in which every city, j, is required to be connected to rj facilities. We give the first non-trivial approximation algorithm for this problem, having an approximation guarantee of 3 ċ Hk, where k is the maximum requirement and Hk 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.
['Kamal Jain', 'Vijay V. Vazirani']
An approximation algorithm for the fault tolerant metric facility location problem