Concrete and Abstract Voronoi Diagrams - Lecture Notes in Computer Science - Rolf-dieter Klein - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783540520559 - December 20, 1989
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Rolf-dieter Klein
Concrete and Abstract Voronoi Diagrams - Lecture Notes in Computer Science 1989 edition

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The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.

173 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released December 20, 1989
ISBN13 9783540520559
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 173
Dimensions 156 × 234 × 9 mm   ·   254 g
Language English   French  

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