Local search algorithms for the red-blue median problem

M. Hajiaghayi, R. Khandekar, G. Kortsarz

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the following red-blue median problem which is a generalization of the well-studied k-median problem. The input consists of a set of red facilities, a set of blue facilities, and a set of clients in a metric space and two integers kr,kb ≥0. The problem is to open at most kr red facilities and at most kb blue facilities and minimize the sum of distances of clients to their respective closest open facilities. We show, somewhat surprisingly, that the following simple local search algorithm yields a constant factor approximation for this problem. Start by opening any kr red and kb blue facilities. While possible, decrease the cost of the solution by closing a pair of red and blue facilities and opening a pair of red and blue facilities. We also improve the approximation factor for the prize-collecting k-median problem from 4 (Charikar et al. in Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pp. 642-641, 2001) to 3+ϵ, which matches the current best approximation factor for the k-median problem.

Original languageEnglish
Pages (from-to)795-814
Number of pages20
Issue number4
StatePublished - 1 Aug 2012
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media, LLC 2011.


  • Facility location
  • Local search algorithms
  • Prize-collecting
  • k-median


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