New Approximability Results for the Robust k-Median Problem

  • Sayan Bhattacharya
  • Parinya Chalermsook
  • Kurt Mehlhorn
  • Adrian Neumann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)


We consider a variant of the classical k-median problem, introduced by Anthony et al.[1]. In the Robust k-Median problem, we are given an n-vertex metric space (V,d) and m client sets \(\left\{ S_i \subseteq V \right\}_{i=1}^m\). We want to open a set F ⊆ V of k facilities such that the worst case connection cost over all client sets is minimized; that is, minimize \(\max_{i}\sum_{v \in S_i} d(F,v)\). Anthony et al. showed an O(logm) approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing Ω(logm/ loglogm) approximation hardness, unless \({\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})\). This result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.


Approximation Algorithm Hardness Result Line Metrics Approximability Result Polynomial Time Approximation Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sayan Bhattacharya
    • 1
  • Parinya Chalermsook
    • 1
  • Kurt Mehlhorn
    • 1
  • Adrian Neumann
    • 1
  1. 1.Max-Planck Institut für InformatikGermany

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