Dynamic maintenance of geometric structures made easy

A model for distributions on the possible input sequences of insertions and deletions is developed and analyzed using R, and it is shown how to apply this to maintain Voronoi diagrams, convex hulls, and planar subdivisions.

Abstract

The problem of dynamically maintaining geometric structures is considered. A technique is proposed that uses randomized incremental algorithms which are augmented to allow deletions of objects. A model for distributions on the possible input sequences of insertions and deletions is developed and analyzed using R. Seidel's backwards analysis. It is further shown how to apply this to maintain Voronoi diagrams, convex hulls, and planar subdivisions. A strikingly simple algorithm for the maintenance of convex hulls in any dimension is given. The expected running time is determined.>