Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation

Pedro Machado Manhães de Castro; Olivier Devillers

Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation

Pedro Machado Manhães de Castro ¹ Olivier Devillers ²

1 UFPE - Universidade Federal de Pernambuco [Recife]

2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm

Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry

Abstract : Let X be a d dimensional Poisson point process. We prove that the expected length of the Voronoi path between two points at distance 1 in the Delaunay triangulation associated with X is sqrt(2d/π) + O(d^(−1/2) when d → ∞. In any dimension, we also provide a precise interval containing the actual value; in 3D the expected length is between 1.4977 and 1.50007.

Keywords : Random distribution Point location Routing Walking strategies

Document type :

Journal articles

Domain :

Computer Science [cs] / Computational Geometry [cs.CG]

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https://hal.inria.fr/hal-01477030
Contributor : Olivier Devillers <>
Submitted on : Sunday, February 26, 2017 - 7:32:49 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM
Long-term archiving on : Saturday, May 27, 2017 - 12:33:05 PM

Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation

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Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation

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168

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