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.2016.66
URN: urn:nbn:de:0030-drops-62180
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6218/
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Gupta, Anupam ; Guruganesh, Guru ; Schmidt, Melanie

Approximation Algorithms for Aversion k-Clustering via Local k-Median

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LIPIcs-ICALP-2016-66.pdf (0.5 MB)

Abstract

In the aversion k-clustering problem, given a metric space, we want to cluster the points into k clusters. The cost incurred by each point is the distance to the furthest point in its cluster, and the cost of the clustering is the sum of all these per-point-costs. This problem is motivated by questions in generating automatic abstractions of extensive-form games.

We reduce this problem to a "local" k-median problem where each facility has a prescribed radius and can only connect to clients within that radius. Our main results is a constant-factor approximation algorithm for the aversion k-clustering problem via the local k-median problem.

We use a primal-dual approach; our technical contribution is a non-local rounding step which we feel is of broader interest.

BibTeX - Entry

@InProceedings{gupta_et_al:LIPIcs:2016:6218,
  author =	{Anupam Gupta and Guru Guruganesh and Melanie Schmidt},
  title =	{{Approximation Algorithms for Aversion k-Clustering via Local k-Median}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{66:1--66:13},
  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/2016/6218},
  URN =		{urn:nbn:de:0030-drops-62180},
  doi =		{10.4230/LIPIcs.ICALP.2016.66},
  annote =	{Keywords: Approximation algorithms, clustering, k-median, primal-dual}
}

Keywords: Approximation algorithms, clustering, k-median, primal-dual
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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