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Algorithmica

, Volume 34, Issue 1, pp 39–46 | Cite as

Splitting a Delaunay Triangulation in Linear Time

  • Chazelle
  • Devillers
  • Hurtado
  • Mora
  • Sacristan
  • Teillaud
Article

Abstract

Computing the Delaunay triangulation of n points requires usually a minimum of Ω(n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time.

Key words. Computational geometry, Delaunay triangulation, Voronoi diagrams, Randomized algorithms. 

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Copyright information

© Springer-Verlag New York 2002

Authors and Affiliations

  • Chazelle
    • 1
  • Devillers
    • 2
  • Hurtado
    • 3
  • Mora
    • 3
  • Sacristan
    • 3
  • Teillaud
    • 2
  1. 1.Computer Science Department, Princeton University, 35 Olden Street, Princeton, NJ 08544, USA. chazelle@cs.princeton.edu. http://ftp.cs.princeton.edu/~chazelle/.US
  2. 2.INRIA, BP93, 06902 Sophia-Antipolis, France. Olivier.Devillers@sophia.inria.fr, Monique.Teillaud@sophia.inria.fr. www-sop.inria.fr/prisme/.FR
  3. 3.Departamento de Matemàtica Aplicada II, Universidad Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain. hurtado@ma2.upc.es, mora@ma2.upc.es, vera@ma2.upc.es. www-ma2.upc.es/~geomc/.ES

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