Voronoi Diagram Distances

  • Michel Marie Deza
  • Elena Deza


Given a finite set A of objects A i in a space S, computing the Voronoi diagram of A means partitioning the space S into Voronoi regions V(A i ) in such a way that V(A i ) contains all points of S that are “closer” to A i than to any other object A j in A.


Voronoi Diagram Network Distance Diagram Versus Power Diagram Voronoi Edge 
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.


  1. [AACLMP98]
    Aichholzer O., Aurenhammer F., Chen D.Z., Lee D.T., Mukhopadhyay A. and Papadopoulou E. Voronoi Diagrams for Direction-Sensitive Distances, in Proc. 13th Symposium on Computational Geometry, ACM Press, New York, 1997 Google Scholar
  2. [Klei89]
    Klein R. Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science, Springer, Berlin, 1989. Google Scholar
  3. [NiSu03]
    Nishida T. and Sugihara K. FEM-Like Fast Marching Method for the Computation of the Boat–Sail Distance and the Associated Voronoi Diagram, Technical Reports, METR 2003-45, Dept. Math. Informatics, The University of Tokyo, 2003. Google Scholar
  4. [OBS92]
    Okabe A., Boots B. and Sugihara K. Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, Wiley, New York, 1992 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.École Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

Personalised recommendations