Small Weak Epsilon-Nets in Three Dimensions
نویسندگان
چکیده
We study the problem of finding small weak ε-nets in three dimensions and provide new upper and lower bounds on the value of ε for which a weak ε-net of a given small constant size exists. The range spaces under consideration are the set of all convex sets and the set of all halfspaces in R3.
منابع مشابه
Small weak epsilon nets
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 εi , the Preprint submitted to Elsevier Science 10 February 2008 smallest epsilon that can be guaranteed for any P when |Q| = i, for small values...
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