License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.73
URN: urn:nbn:de:0030-drops-62112
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6211/
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Demirci, Gökalp ; Li, Shi

Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation

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LIPIcs-ICALP-2016-73.pdf (0.6 MB)

Abstract

We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural LP relaxation for the problem, one can only hope to get the violation factor down to 2. Li [SODA'16] introduced a novel LP to go beyond the limit of 2 and gave a constant-factor approximation algorithm that opens (1 + epsilon)*k facilities.

We use the configuration LP of Li [SODA'16] to give a constant-factor approximation for the Capacitated k-Median problem in a seemingly harder configuration: we violate only the capacities by 1 + epsilon. This result settles the problem as far as pseudo-approximation algorithms are concerned.

BibTeX - Entry

@InProceedings{demirci_et_al:LIPIcs:2016:6211,
  author =	{G{\"o}kalp Demirci and Shi Li},
  title =	{{Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{73:1--73:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6211},
  URN =		{urn:nbn:de:0030-drops-62112},
  doi =		{10.4230/LIPIcs.ICALP.2016.73},
  annote =	{Keywords: Approximation Algorithms, Capacitated k-Median, Pseudo Approximation, Capacity Violation}
}

Keywords: Approximation Algorithms, Capacitated k-Median, Pseudo Approximation, Capacity Violation
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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