## Product Range Spaces, Sensitive Sampling, and Derandomization (1993)

Citations: | 46 - 6 self |

### BibTeX

@MISC{Brönnimann93productrange,

author = {Hervé Brönnimann and et al.},

title = {Product Range Spaces, Sensitive Sampling, and Derandomization },

year = {1993}

}

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### OpenURL

### Abstract

We introduce the concept of a sensitive E-approx-imation, and use it to derive a more efficient algorithm for computing &-nets. We define and investigate prod-uct range spaces, for which we establish sampling the-orems analogous to the standard finite VC-dimensional case. This generalizes and simplifies results from previ-ous 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(n log3 n) deterministic algorithm for com-puting the diameter of an n-point set in 3-dimensional space.