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Randomized incremental construction of abstract Voronoi diagrams

Klein, Rolf and Mehlhorn, Kurt and Meiser, Stefan

MPI-I-93-105. January 1993, 29 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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:
It can handle a much wider class of abstract Voronoi
diagrams than the algorithms presented in [Kle89b, MMO91].
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.
References to related material:

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  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},