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Small Weak Epsilon-Nets Boris Aronov

Summary: Small Weak Epsilon-Nets
Boris Aronov
Franz Aurenhammer
Ferran Hurtado
Stefan Langerman§
David Rappaport¶
Carlos Seara Shakhar Smorodinsky
February 28, 2006
Given a set P of points in the plane, a set Q points is a weak -net with respect to a family of
sets S (e.g. rectangles, disks, or convex sets) if every set of S containing |P| points contains a
point of Q. In this paper, we determine bounds on S
i , the largest epsilon that can be guaranteed
for any P when |Q| = i, for small values of i.
1 Introduction
Let P be a set of n points in R2. A point q (not necessarily in P) is called a centerpoint of P if each
closed half-plane containing q contains at least n
3 points of P, or, equivalently, any convex set that
contains more than 2
3 n points of P must also contain q. It is a well known fact that a centerpoint


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz


Collections: Computer Technologies and Information Sciences