, Volume 7, Issue 1, pp 381-413

First online:

Randomized incremental construction of Delaunay and Voronoi diagrams

  • Leonidas J. GuibasAffiliated withComputer Science Department, Stanford UniversityDEC Systems Research Center
  • , Donald E. KnuthAffiliated withComputer Science Department, Stanford University
  • , Micha SharirAffiliated withCourant Institute of Mathematical Sciences, New York UniversitySchool of Mathematical Sciences, Tel Aviv University

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In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “on-line” than earlier similar methods, takes expected timeO(nℝgn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.

Key words

Delaunay triangulation Voronoi diagram randomized algorithms