Abstract
We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improved solutions for them. We obtain, for any fixed ?>0, anO(n1+?) algorithm for computing the diameter of a point set in 3-space, anO(8/5+?) algorithm for computing the width of such a set, and onO(n8/5+?) algorithm for computing the closest pair in a set ofn lines in space. All these algorithms are deterministic.
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