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.SoCG.2017.5
URN: urn:nbn:de:0030-drops-72147
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7214/
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Abrahamsen, Mikkel ; de Berg, Mark ; Buchin, Kevin ; Mehr, Mehran ; Mehrabi, Ali D.

Range-Clustering Queries

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LIPIcs-SoCG-2017-5.pdf (0.6 MB)

Abstract

In a geometric k-clustering problem the goal is to partition a set of points in R^d into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S: given a query box Q and an integer k > 2, compute an optimal k-clustering for the subset of S inside Q. We obtain the following results.

* We present a general method to compute a (1+epsilon)-approximation to a range-clustering query, where epsilon>0 is a parameter that can be specified as part of the query. Our method applies to a large class of clustering problems, including k-center clustering in any Lp-metric and a variant of k-center clustering where the goal is to minimize the sum (instead of maximum) of the cluster sizes.

* We extend our method to deal with capacitated k-clustering problems, where each of the clusters should not contain more than a given number of points.

* For the special cases of rectilinear k-center clustering in R^1, and in R^2 for k = 2 or 3, we present data structures that answer range-clustering queries exactly.

BibTeX - Entry

@InProceedings{abrahamsen_et_al:LIPIcs:2017:7214,
  author =	{Mikkel Abrahamsen and Mark de Berg and Kevin Buchin and Mehran Mehr and Ali D. Mehrabi},
  title =	{{Range-Clustering Queries}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7214},
  URN =		{urn:nbn:de:0030-drops-72147},
  doi =		{10.4230/LIPIcs.SoCG.2017.5},
  annote =	{Keywords: Geometric data structures, clustering, k-center problem}
}

Keywords: Geometric data structures, clustering, k-center problem
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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