Stronger bounds for weak epsilon-nets in higher dimensions

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

2 Scopus citations


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
Number of pages14
ISBN (Electronic)9781450380539
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


Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
CityVirtual, Online


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

ASJC Scopus subject areas

  • Software

Cite this