Range-clustering queries
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Range-clustering queries. / Abrahamsen, Mikkel; de Berg, Mark; Buchin, Kevin; Mehr, Mehran; Mehrabi, Ali D.
33rd International Symposium on Computational Geometry (SoCG 2017). ed. / Boris Aronov; Matthew J. Katz. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. 5 (Leibniz International Proceedings in Informatics, Vol. 77).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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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
Y2 - 4 July 2017 through 7 July 2017
ER -
ID: 188452797