| Abstract (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Given a set P of points in the plane, a set of points Q is a weak ε-net with respect to a family of sets S (e.g., rectangles, disks, or convex sets) if every set of S containing ε|P | points contains a point of Q. In this paper, we determine bounds on εS i, the Preprint submitted to Elsevier Science 10 February 2008 smallest epsilon that can be guaranteed for any P when |Q | = i, for small values of i. Key words: weak epsilon-nets, rectangles, set systems, convex sets. 1 | |||||||||||||||
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