MPI-INF/SWS Research Reports 1991-2021

2. Number - All Departments


Randomized incremental construction of abstract Voronoi diagrams

Klein, Rolf and Mehlhorn, Kurt and Meiser, Stefan

January 1993, 29 pages.

Status: available - back from printing

Abstract Voronoi diagrams were introduced by R.~Klein 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. The new algorithm has the following advantages over previous algorithms: \begin{itemize} \item It can handle a much wider class of abstract Voronoi diagrams than the algorithms presented in [Kle89b, MMO91]. \item 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.

URL to this document:

Hide details for BibTeXBibTeX
  AUTHOR = {Klein, Rolf and Mehlhorn, Kurt and Meiser, Stefan},
  TITLE = {Randomized incremental construction of abstract Voronoi diagrams},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-93-105},
  MONTH = {January},
  YEAR = {1993},
  ISSN = {0946-011X},