Stochastic Analysis of Empty-Region Graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2021

Stochastic Analysis of Empty-Region Graphs


Given a set of points $X$, an empty-region graph is a graph in which $p$, $q \in X$ are neighbors if some region defined by $(p, q)$ does not contain any point of $X$. We provide expected analyses of the degree of a point and the possibility of having far neighbors in such a graph when $X$ is a planar Poisson point process. Namely the expected degree of a point in the empty axis-alignedellipse graph for a Poisson point process of intensity $\lambda$ in the unit square is $\Theta(\ln\lambda)$. It is $\Theta(\ln\beta)$ if the ellipses are constrained to have an aspect ratio between 1 and $\beta>1$, and $\Theta(\beta)$ when the aspect ratio is constrained but ellipses are not axis-aligned.
Fichier principal
Vignette du fichier
paper12.pdf (1.54 Mo) Télécharger le fichier
Vignette du fichier
vignette.png (32.42 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Format Figure, Image

Dates and versions

hal-03296186 , version 1 (22-07-2021)


  • HAL Id : hal-03296186 , version 1


Olivier Devillers, Charles Duménil. Stochastic Analysis of Empty-Region Graphs. CCCG 2021 - 33rd Canadian Conference on Computational Geometry, Aug 2021, Halifax / Virtual, Canada. ⟨hal-03296186⟩
76 View
56 Download


Gmail Mastodon Facebook X LinkedIn More