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Fully dynamic delaunay triangulation in logarithmic expected time per operation

  • Olivier Devillers
  • Stefan Meiser
  • Monique Teillaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)

Abstract

The Delaunay Tree is a hierarchical data structure that has been introduced in [4] and analysed in [5,2]. For a given set of sites S in the plane and an order of insertion for these sites, the Delaunay Tree stores all the successive Delaunay triangulations. As proved before, the Delaunay Tree allows the insertion of a site in logarithmic expected time and linear expected space, when the insertion sequence is randomized.

In this paper, we describe an algorithm removing a site from the Delaunay Tree. This can be done in logarithmic expected time, where by expected we mean averaging over all already inserted sites for the choice of the deleted sites. The algorithm has been effectively coded and experimental results are given.

Keywords

Computational Geometry Delaunay Triangulation Neighbor Pointer Neighborhood Relation Conflict Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Olivier Devillers
    • 1
  • Stefan Meiser
    • 2
  • Monique Teillaud
    • 3
  1. 1.INRIAValbonne cedex
  2. 2.Max Planck Institut für InformatikSaarbrücken
  3. 3.INRIAValbonne cedex

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