Discrete & Computational Geometry

, Volume 47, Issue 2, pp 235–244 | Cite as

A Non-linear Lower Bound for Planar Epsilon-nets

  • Noga AlonEmail author


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 \(\frac{1}{\epsilon}\). This settles a problem raised by Matoušek, Seidel and Welzl (Proc. 6th Annu. ACM Sympos. Comput. Geom., pp. 16–22, 1990).


Epsilon nets Weak epsilon nets VC-dimension 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Schools of Mathematics and Computer Science, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Institute for Advanced StudyPrincetonUSA

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