A plant location guide for the unsure

This paper studies an extension of the k-median problem where we are given a metric space (V, d) and not just one but m client sets {Si V }m i=1, and the goal is to open k facilities F to minimize: maxi[m] jSi d(j, F) , i.e., the worst-case cost over all the client sets. This is a "min-max" or "robust" version of the k-median problem; however, note that in contrast to previous papers on robust/stochastic problems, we have only one stage of decision-making--where should we place the facilities? We present an O(log n+log m) approximation for robust k-median: The algorithm is combinatorial and very simple, and is based on reweighting/Lagrangeanrelaxation ideas. In fact, we give a general framework for (minimization) facility location problems where there is a bound on the number of open facilities. For robust and stochastic versions of such location problems, we show that if the problem satisfies a certain "projection" property, essentially the same algorit...

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Barbara M. Anthony, Vineet Goyal, Anupam Gupta, Viswanath Nagarajan
• Keywords: Algorithms, Client Sets, K-median Problem, Location Problems, SODA 2008