The Voronoi functional is maximized by the Delaunay triangulation in the plane

Authors

Herbert Edelsbrunner
Alexey Glazyrin, The University of Texas Rio Grande Valley
Oleg R. Musin, The University of Texas Rio Grande Valley
Anton Nikitenko

Document Type

Article

Publication Date

12-22-2016

Abstract

We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.

Comments

Copyright © 2016, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg

Recommended Citation

Edelsbrunner, H., Glazyrin, A., Musin, O.R. et al. The Voronoi functional is maximized by the Delaunay triangulation in the plane. Combinatorica 37, 887–910 (2017). https://doi.org/10.1007/s00493-016-3308-y

Publication Title

Combinatorica

DOI

10.1007/s00493-016-3308-y