Range-clustering queries

M. Abrahamsen, M.T. de Berg, K.A. Buchin, M. Mehr, A.D. Mehrabi

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry (SoCG 2017), 14-17 July 2017, Brisbane, Australia
Place of PublicationDagstuhl
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages1-16
Number of pages16
ISBN (Print)978-3-95977-038-5
Publication statusPublished - 2017

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)

Keywords

  • Geometric data structures, clustering, k-center problem

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  • Cite this

    Abrahamsen, M., de Berg, M. T., Buchin, K. A., Mehr, M., & Mehrabi, A. D. (2017). Range-clustering queries. In 33rd International Symposium on Computational Geometry (SoCG 2017), 14-17 July 2017, Brisbane, Australia (pp. 1-16). [5] (Leibniz International Proceedings in Informatics (LIPIcs)). Schloss Dagstuhl - Leibniz-Zentrum für Informatik.