Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Cygan, Marek; Kociumaka, Tomasz http://www.dagstuhl.de/lipics License
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URN: urn:nbn:de:0030-drops-44625
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Constant Factor Approximation for Capacitated k-Center with Outliers

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Abstract

The k-center problem is a classic facility location problem, where given an edge-weighted graph G=(V,E) one is to find a subset of k vertices S, such that each vertex in V is "close" to some vertex in S. The approximation status of this basic problem is well understood, as a simple 2-approximation algorithm is known to be tight. Consequently different extensions were studied. In the capacitated version of the problem each vertex is assigned a capacity, which is a strict upper bound on the number of clients a facility can serve, when located at this vertex. A constant factor approximation for the capacitated k-center was obtained last year in [Cygan, Hajiaghayi and Khuller, FOCS'12], which was recently improved to a 9-approximation in [An, Bhaskara and Svensson, arXiv'13]. In a different generalization of the problem some clients (denoted as outliers) may be disregarded. Here we are additionally given an integer p and the goal is to serve exactly p clients, which the algorithm is free to choose. In [Charikar et al., SODA'01] the authors presented a 3-approximation for the k-center problem with outliers. In this paper we consider a common generalization of the two extensions previously studied separately, i.e. we work with the capacitated k-center with outliers. We present the first constant factor approximation algorithm with approximation ratio of 25 even for the case of non-uniform hard capacities.

BibTeX - Entry

@InProceedings{cygan_et_al:LIPIcs:2014:4462,
  author =	{Marek Cygan and Tomasz Kociumaka},
  title =	{{Constant Factor Approximation for Capacitated k-Center with Outliers}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{251--262},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Ernst W. Mayr and Natacha Portier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4462},
  URN =		{urn:nbn:de:0030-drops-44625},
  doi =		{10.4230/LIPIcs.STACS.2014.251},
  annote =	{Keywords: approximation algorithms, k-center, capacities, outliers, LP rounding}
}

Keywords: approximation algorithms, k-center, capacities, outliers, LP rounding
Seminar: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)
Issue date: 2014
Date of publication: 2014


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