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Product range spaces, sensitive sampling, and derandomization

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3 Author(s)
Bronnimann, H. ; Dept. of Comput. Sci., Princeton Univ., NJ, USA ; Chazelle, B. ; Matousek, J.

We introduce the concept of a sensitive ε-approximation, and use it to derive a more efficient algorithm for computing ε-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(nlog3 n) deterministic algorithm for computing the diameter of an n-point set in 3-dimensional space

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993

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