On center regions and balls containing many points

Shakhar Smorodinsky, Marek Sulovský, Uli Wagner

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

6 Scopus citations

Abstract

We study the disk containment problem introduced by Neumann-Lara and Urrutia and its generalization to higher dimensions. We relate the problem to centerpoints and lower centerpoints of point sets. Moreover, we show that for any set of n points in ℝd, there is a subset A ⊆ S of size [d+3/2] such that any ball containing A contains at least roughly 4/5ed 3n points of S. This improves previous bounds for which the constant was exponentially small in d. We also consider a generalization of the planar disk containment problem to families of pseudodisks.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
Pages363-373
Number of pages11
DOIs
StatePublished - 4 Aug 2008
Event14th Annual International Conference on Computing and Combinatorics, COCOON 2008 - Dalian, China
Duration: 27 Jun 200829 Jun 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5092 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th Annual International Conference on Computing and Combinatorics, COCOON 2008
Country/TerritoryChina
CityDalian
Period27/06/0829/06/08

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