On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
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We introduce the concept of a sensitive /spl epsi/-approximation, and use it to derive a more efficient algorithm for computing /spl epsi/-nets. We define and investigate product range spaces, for which we establish sampling theorems analogous to the standard finite VC-dimensional case. This generalizes and simplifies results from previous works. We derive a simpler optimal deterministic convex hull algorithm, and by extending the method to the intersection of a set of balls with the same radius, we obtain an O(nlog/sup 3/ n) deterministic algorithm for computing the diameter of an n-point set in 3-dimensional space.