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DOI: 10.4230/LIPIcs.ESA.2019.1
URN: urn:nbn:de:0030-drops-111225
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11122/
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Adamczyk, Marek ; Byrka, Jaroslaw ; Marcinkowski, Jan ; Meesum, Syed M. ; Wlodarczyk, Michal

Constant-Factor FPT Approximation for Capacitated k-Median

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LIPIcs-ESA-2019-1.pdf (0.5 MB)


Abstract

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 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon.

BibTeX - Entry

@InProceedings{adamczyk_et_al:LIPIcs:2019:11122,
  author =	{Marek Adamczyk and Jaroslaw Byrka and Jan Marcinkowski and Syed M. Meesum and Michal Wlodarczyk},
  title =	{{Constant-Factor FPT Approximation for Capacitated k-Median}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Michael A. Bender and Ola Svensson and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11122},
  URN =		{urn:nbn:de:0030-drops-111225},
  doi =		{10.4230/LIPIcs.ESA.2019.1},
  annote =	{Keywords: K-median, Clustering, Approximation Algorithms, Fixed Parameter Tractability}
}

Keywords: K-median, Clustering, Approximation Algorithms, Fixed Parameter Tractability
Seminar: 27th Annual European Symposium on Algorithms (ESA 2019)
Issue Date: 2019
Date of publication: 06.09.2019


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