A plant location guide for the unsure

Barbara M. Anthony, Vineet Goyal, Anupam Gupta, Viswanath Nagarajan

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 {S i ⊆ V} m i=1, and the goal is to open k facilities F to minimize: max i∈[m]j∈S i 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 algorithm gives a logarithmic approximation ratio in both versions. We use our framework to give the first approximation algorithms for robust/stochastic versions of k-tree, capacitated k-median, and fault-tolerant k-median.

Original languageEnglish (US)
Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
Number of pages10
StatePublished - 2008
Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
Duration: Jan 20 2008Jan 22 2008

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Other19th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CitySan Francisco, CA

ASJC Scopus subject areas

  • Software
  • General Mathematics


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