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＜電子ブック＞
Concrete and Abstract Voronoi Diagrams / by Rolf Klein
(Lecture Notes in Computer Science. ISSN:16113349 ; 400)

版	1st ed. 1989.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1989
本文言語	英語
大きさ	IV, 169 p : online resource
著者標目	*Klein, Rolf author SpringerLink (Online service)
件　名	LCSH:Computer science LCSH:Application software LCSH:Information storage and retrieval systems LCSH:Artificial intelligence -- Data processing  全ての件名で検索 LCSH:Algorithms LCSH:Computer graphics FREE:Theory of Computation FREE:Computer and Information Systems Applications FREE:Information Storage and Retrieval FREE:Data Science FREE:Algorithms FREE:Computer Graphics
一般注記	Voronoi diagrams in nice metrics -- Abstract Voronoi diagrams -- Computing abstract Voronoi diagrams -- Acyclic partitions -- Concluding remarks 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 HTTP:URL=https://doi.org/10.1007/3-540-52055-4

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