Stronger bounds for weak epsilon-nets in higher dimensions

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1 Scopus citations

Abstract

Given a finite point set P in Rd, and >0 we say that N? Rd is a weak -net if it pierces every convex set K with |K P|? ? |P|. Let d? 3. We show that for any finite point set in Rd, and any ?>0, there exist a weak -net of cardinality O(1/?d-1/2+?), where ?>0 is an arbitrary small constant. This is the first improvement of the bound of O?(1/?d) that was obtained in 1993 by Chazelle, Edelsbrunner, Grigni, Guibas, Sharir, and Welzl for general point sets in dimension d? 3.

Original languageEnglish
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages989-1002
Number of pages14
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Keywords

  • computational geometry
  • convex sets
  • epsilon-nets
  • selection theorems

ASJC Scopus subject areas

  • Software

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