Recent Results on the Average Time Behavior of Some Algorithms in Computational Geometry

Abstract

We give a brief inexhaustive survey of recent results that can be helpful in the average 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 vextors, and determining the diameter of a set and the minimum covering sphere.