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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.

OriginalsprogEngelsk
Titel33rd International Symposium on Computational Geometry (SoCG 2017)
RedaktørerBoris Aronov, Matthew J. Katz
Antal sider16
ForlagSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publikationsdato2017
Artikelnummer5
ISBN (Elektronisk)978-3-95977-038-5
DOI
StatusUdgivet - 2017
Begivenhed33rd International Symposium on Computational Geometry - Brisbane, Australien
Varighed: 4 jul. 20177 jul. 2017
Konferencens nummer: 33

Konference

Konference33rd International Symposium on Computational Geometry
Nummer33
LandAustralien
ByBrisbane
Periode04/07/201707/07/2017
NavnLeibniz International Proceedings in Informatics
Vol/bind77
ISSN1868-8969

ID: 188452797