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

Pedro Machado Manhães de Castro 1 Olivier Devillers 2
1 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 : Routing Walking strategies Point location Random distribution
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Article dans une revue
Discrete and Computational Geometry, Springer Verlag, 2017, pp.1-20. <10.1007/s00454-017-9866-y>
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Soumis le : dimanche 26 février 2017 - 19:32:49
Dernière modification le : mardi 20 juin 2017 - 01:07:26
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Pedro Machado Manhães de Castro, Olivier Devillers. Expected Length of the Voronoi Path in a High Dimensional Poisson-Delaunay Triangulation. Discrete and Computational Geometry, Springer Verlag, 2017, pp.1-20. <10.1007/s00454-017-9866-y>. <hal-01477030>

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