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


Author(s): Edelsbrunner, Herbert; Glazyrin, Alexey; Musin, Oleg R; Nikitenko, Anton
Article Title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
Affiliation IST Austria
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.
Journal Title: Combinatorica
ISSN: 1439-6912
Publisher: Springer  
Date Published: 2016-12-22
Start Page: Epub ahead of print
URL:
DOI: 10.1007/s00493-016-3308-y
Notes: This research is partially supported by the Russian Government under the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by NSF grants DMS-1101688, DMS-1400876.
Open access: yes (repository)
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