Range-clustering queries

TY - GEN

T1 - Range-clustering queries

AU - Abrahamsen, Mikkel

AU - de Berg, Mark

AU - Buchin, Kevin

AU - Mehr, Mehran

AU - Mehrabi, Ali D.

N1 - Conference code: 33

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Clustering

KW - Geometric data structures

KW - K-center problem

UR - http://www.scopus.com/inward/record.url?scp=85029942906&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.SoCG.2017.5

DO - 10.4230/LIPIcs.SoCG.2017.5

M3 - Article in proceedings

AN - SCOPUS:85029942906

T3 - Leibniz International Proceedings in Informatics

BT - 33rd International Symposium on Computational Geometry (SoCG 2017)

A2 - Aronov, Boris

A2 - Katz, Matthew J.

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

T2 - 33rd International Symposium on Computational Geometry

Y2 - 4 July 2017 through 7 July 2017

ER -