Small weak epsilon-nets

Boris Aronov, Franz Aurenhammer, Ferran Hurtado, Stefan Langerman, David Rappaport, Carlos Seara, Shakhar Smorodinsky

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Given a set P of points in the plane, a set of points Q is a weak -net with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing |P| points contains a point of Q. In this paper, we determine bounds on iS, the smallest epsilon that can be guaranteed for any P when |Q|=i, for small values of i.

Original languageEnglish
Pages (from-to)455-462
Number of pages8
JournalComputational Geometry: Theory and Applications
Volume42
Issue number5
DOIs
StatePublished - 1 Jul 2009

Keywords

  • Convex sets
  • Rectangles
  • Set systems
  • Weak epsilon-nets

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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