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arXiv · 1411.6337

The Voronoi Functional is Maximized by the Delaunay Triangulation in the Plane

Herbert Edelsbrunner·Alexey Glazyrin·Oleg R. Musin·Anton Nikitenko
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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.

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Herbert Edelsbrunner, Alexey Glazyrin, Oleg R. Musin, Anton Nikitenko. 2014-11-24. The Voronoi Functional is Maximized by the Delaunay Triangulation in the Plane. https://doi.org/10.1007/s00493-016-3308-y

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