A Non-linear Lower Bound for Planar Epsilon-nets

  • Authors:

  • Noga Alon

  • Affiliations:

  • Tel Aviv University, Schools of Mathematics and Computer Science, Sackler Faculty of Exact Sciences, 69978, Tel Aviv, Israel and Institute for Advanced Study, Princeton, NJ, 08540, USA

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2012

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Abstract

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).