An Approximation Algorithm for Uniform Capacitated k-Median Problem with \(1+\epsilon \) Capacity Violation

  • Jarosław Byrka
  • Bartosz Rybicki
  • Sumedha Uniyal
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)


We study the Capacitated k-Median problem, for which all the known constant factor approximation algorithms violate either the number of facilities or the capacities. While the standard LP-relaxation can only be used for algorithms violating one of the two by a factor of at least two, Li [10, 11] gave algorithms violating the number of facilities by a factor of \(1+\epsilon \) exploring properties of extended relaxations.

In this paper we develop a constant factor approximation algorithm for hard Uniform Capacitated k-Median violating only the capacities by a factor of \(1\,+\,\epsilon \). The algorithm is based on a configuration LP. Unlike in the algorithms violating the number of facilities, we cannot simply open extra few facilities at selected locations. Instead, our algorithm decides about the facility openings in a carefully designed dependent rounding process.


Integral Solution Child Group Fractional Solution Open Facility Root Group 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jarosław Byrka
    • 1
  • Bartosz Rybicki
    • 1
  • Sumedha Uniyal
    • 2
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.IDSIAUniversity of LuganoLuganoSwitzerland

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