Range-clustering queries

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In a geometric k-clustering problem the goal is to partition a set of points in Rd 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 S P ∩ Q. We obtain the following results. • We present a general method to compute a (1 + ϵ)-approximation to a range-clustering query, where ϵ > 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 ℝ1 in ℝ2 for k = 2 or 3, we present data structures that answer range-clustering queries exactly.

Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry (SoCG 2017)
EditorsBoris Aronov, Matthew J. Katz
Number of pages16
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication date2017
Article number5
ISBN (Electronic)978-3-95977-038-5
DOIs
Publication statusPublished - 2017
Event33rd International Symposium on Computational Geometry - Brisbane, Australia
Duration: 4 Jul 20177 Jul 2017
Conference number: 33

Conference

Conference33rd International Symposium on Computational Geometry
Nummer33
LandAustralia
ByBrisbane
Periode04/07/201707/07/2017
SeriesLeibniz International Proceedings in Informatics
Volume77
ISSN1868-8969

    Research areas

  • Clustering, Geometric data structures, K-center problem

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