Abstract
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.
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Jain, K., Vazirani, V. An Approximation Algorithm for the Fault Tolerant Metric Facility Location Problem. Algorithmica 38, 433–439 (2004). https://doi.org/10.1007/s00453-003-1070-1
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DOI: https://doi.org/10.1007/s00453-003-1070-1