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

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : Let $X_n$ be a $d$ dimensional Poisson point process of intensity $n$. We prove that the expected length of the Voronoi path between two points at distance 1 in the Delaunay triangulation associated with $X_n$ is $\sqrt{\frac{2d}{\pi}}+O(d^{-\frac{1}{2}})$ for all $n\in\mathbb{N}$ and $d\rightarrow\infty$. In any dimension, we provide a precise interval containing the exact value, in 3D the expected length is between 1.4977 and 1.50007.
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Reports

Cited literature [9 references]

https://hal.inria.fr/hal-01353735
Contributor : Olivier Devillers <>
Submitted on : Wednesday, August 17, 2016 - 3:38:33 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:26 PM
Long-term archiving on: : Friday, November 18, 2016 - 12:00:04 PM

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• HAL Id : hal-01353735, version 1

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Pedro Machado Manhães de Castro, Olivier Devillers. Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation. [Research Report] RR-8947, Inria. 2016. ⟨hal-01353735⟩

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