The Voronoi Functional is Maximized by the Delaunay Triangulation in the Plane
Metric Geometry
2017-05-25 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1411.6337,
title = {The Voronoi Functional is Maximized by the Delaunay Triangulation in the Plane},
author = {Herbert Edelsbrunner and Alexey Glazyrin and Oleg R. Musin and Anton Nikitenko},
journal= {arXiv preprint arXiv:1411.6337},
year = {2017}
}
Comments
11 pages, 9 figures