ENGLISH

Concrete and Abstract Voronoi Diagrams

By Rolf Klein (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1989
ISBN
3540520554, 9783540520559
DOI
10.1007/3-540-52055-4
Language
english
Format
DJVU
Filesize
2 MB (1735138 bytes)
Series
Lecture Notes in Computer Science 400
Edition
1
Pages
169\165
Library
Kolxo3
DPI
300
Scanned
yes
Time added
2010-02-04 11:10:02
Data Structures; Algorithm Analysis and Problem Co

Description

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.

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