An improved bound for weak epsilon-nets in the plane

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15 Scopus citations

Abstract

We show that for any finite point set P in the plane and ϵ > 0 there exist O(1/ϵ3/2+γ) points, for arbitrary small γ > 0, that pierce every convex set K with |K ∩ P| ≥ ϵ|P|. This is the first improvement of the bound of O (1/ϵ 2 ) that was obtained in 1992 by Alon, Bárány, Füredi and Kleitman for general point sets in the plane.

Original languageEnglish
Title of host publicationProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
EditorsMikkel Thorup
PublisherIEEE Computer Society
Pages224-235
Number of pages12
ISBN (Electronic)9781538642306
DOIs
StatePublished - 30 Nov 2018
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: 7 Oct 20189 Oct 2018

Conference

Conference59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Country/TerritoryFrance
CityParis
Period7/10/189/10/18

Keywords

  • Arrangements of lines
  • Convex sets
  • Epsilon-nets
  • Piercing numbers
  • Transversals
  • VC-dimension

ASJC Scopus subject areas

  • Computer Science (all)

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