A Non-linear Lower Bound for Planar Epsilon-Nets

We show that the minimum possible size of an -net for point objects and line (or rectangle)ranges in the plane is (slightly) bigger than linear in 1/ . This settles a problem raised by Matousek, Seidel and Welzl in 1990.

• Type: Journal
• Year: 2010
• Where: FOCS
• Authors: Noga Alon
• Keywords: FOCS 2010, Linear, Minimum Possible Size, Point Objects, Theoretical Computer Science