TY - GEN

T1 - Range-clustering queries

AU - Abrahamsen, M.

AU - de Berg, M.T.

AU - Buchin, K.A.

AU - Mehr, M.

AU - Mehrabi, A.D.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Geometric data structures, clustering, k-center problem

UR - http://drops.dagstuhl.de/opus/volltexte/2017/7214/

UR - http://drops.dagstuhl.de/opus/volltexte/2017/7214/pdf/LIPIcs-SoCG-2017-5.pdf

M3 - Conference contribution

SN - 978-3-95977-038-5

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

SP - 1

EP - 16

BT - 33rd International Symposium on Computational Geometry (SoCG 2017), 14-17 July 2017, Brisbane, Australia

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

CY - Dagstuhl

ER -