A Non-linear Lower Bound for Planar Epsilon-nets

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28 Scopus citations


We show that the minimum possible size of an ε-net for point objects and line (or rectangle)-ranges in the plane is (slightly) bigger than linear in 1/ε. This settles a problem raised by Matoušek, Seidel and Welzl (Proc. 6th Annu. ACM Sympos. Comput. Geom., pp. 16-22, 1990).

Original languageEnglish (US)
Pages (from-to)235-244
Number of pages10
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Mar 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


  • Epsilon nets
  • VC-dimension
  • Weak epsilon nets


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