Reprint of: Weak ε-nets have basis of size

Nabil H. Mustafa, Saurabh Ray

Research output: Contribution to journalArticle

Abstract

Given a set P of n points in Rd and ε> 0, we consider the problem of constructing weak ε-nets for P. We show the following: pick a random sample Q of size O(1/ε log(1/ε)) from P. Then, with constant probability, a weak ε-net of P can be constructed from only the points of Q . This shows that weak ε-nets in Rd can be computed from a subset of P of size O(1/ε log(1/ε)) with only the constant of proportionality depending on the dimension, unlike all previous work where the size of the subset had the dimension in the exponent of 1/ε. However, our final weak ε-nets still have a large size (with the dimension appearing in the exponent of 1/ε).

Original languageEnglish (US)
Pages (from-to)565-571
Number of pages7
JournalComputational Geometry: Theory and Applications
Volume43
Issue number6-7
DOIs
StatePublished - Aug 2010

Keywords

  • Combinatorial geometry
  • Hitting convex sets
  • Weak ε-nets

ASJC Scopus subject areas

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

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