Please use this identifier to cite or link to this item: doi:10.22028/D291-26122
Title: On the construction of abstract Voronoi diagrams, II
Author(s): Klein, Rolf
Mehlhorn, Kurt
Meiser, Stefan
Language: English
Year of Publication: 1989
OPUS Source: Saarbrücken, 1989
Free key words: Voronoi diagrams
randomized algorithms
DDC notations: 004 Computer science, internet
Publikation type: Report
Abstract: Abstract Voronoi Diagrams are defined by a system of bisecting curves in the plane, rather than by the concept of distance [K88a,b]. Mehlhorn, Meiser, Ó'Dúnlaing [MMO] showed how to construct such diagrams in time O(n log n) by a randomized algorithm if the bisecting curves are in general position. In this paper we drop the general position assumption. Moreover, we show that the only geometric operation in the algorithm is the construction of a Voronoi diagram for five sites. Using this operation, abstract Voronoi diagrams can be constructed in a purley combinatorial manner. This has the following advantages. On the one hand, the construction of a five-site-diagram is the only operation depending on the particular type of bisecting curves and we can therefore apply the algorithm to all concrete diagrams by simply replacing this operation. On the other hand, this is the only operation computing intersection points; thus, problems arising from instable numerical computations can occur only there.
Link to this record: urn:nbn:de:bsz:291-scidok-41768
Series name: Technischer Bericht / A / Fachbereich Informatik, Universität des Saarlandes
Series volume: 1989/03
Date of registration: 5-Sep-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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