Download or read book Randomized Incremental Construction of Abstract Voronoi Diagrams written by Rolf Klein and published by . This book was released on 1993 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Abstract Voronoi diagrams were introduced by R. Klein [Kle89b, Kle88a, Kle88b] as an axiomatic basis of Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O(n log n) by a randomized algorithm, which is based on Clarkson and Shor's randomized incremental construction technique [CS89]. The new algorithm has the following advantages over previous algorithms: It can handle a much wider class of abstract Voronoi diagrams than the algorithms presented in [Kle89b, MMO91]. It can be adapted to a concrete kind of Voronoi diagram by providing a single basic operation, namely the construction of a Voronoi diagram of five sites. Moreover, all geometric decisions are confined to the basic operation, and using this operation, abstract Voronoi diagrams can be constructed in a purely combinatorial manner."