Expected Time Analysis of Algorithms in Computational Geometry

We give a brief inexhaustive survey of recent results that can be helpful in the expected time analysis of algorithms in computational geometry. Most fast average time algorithms use one of three principles: bucketing, divide-and-conquer (merging), or quick elimination (throw-away). To illustrate the different points, the convex hull problem is taken as our prototype problem. We also discuss searching, sorting, finding the Voronoi diagram and the minimal spanning tree, identifying the set of maximal vectors, and determining the diameter of a set and the minimum covering sphere.

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