Constant-factor FPT approximation for capacitated k-median

Marek Adamczyk, Jarosław Byrka, Jan Marcinkowski, Syed M. Meesum, Michał Włodarczyk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2O(k log k)nO(1) and achieves an approximation ratio of 7 + ε.

Original languageEnglish
Title of host publication27th Annual European Symposium on Algorithms, ESA 2019
EditorsMichael A. Bender, Ola Svensson, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771245
StatePublished - 1 Sep 2019
Externally publishedYes
Event27th Annual European Symposium on Algorithms, ESA 2019 - Munich/Garching, Germany
Duration: 9 Sep 201911 Sep 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference27th Annual European Symposium on Algorithms, ESA 2019


  • Approximation algorithms
  • Clustering
  • Fixed parameter tractability
  • K-median

ASJC Scopus subject areas

  • Software


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