, Volume 7, Issue 1, pp 381–413

Randomized incremental construction of Delaunay and Voronoi diagrams

  • Leonidas J. Guibas
  • Donald E. Knuth
  • Micha Sharir

DOI: 10.1007/BF01758770

Cite this article as:
Guibas, L.J., Knuth, D.E. & Sharir, M. Algorithmica (1992) 7: 381. doi:10.1007/BF01758770


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 triangulationVoronoi diagramrandomized algorithms

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Leonidas J. Guibas
    • 1
    • 2
  • Donald E. Knuth
    • 1
  • Micha Sharir
    • 3
    • 4
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA
  2. 2.DEC Systems Research CenterPalo AltoUSA
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  4. 4.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael