ON THE RELATION BETWEEN GRAPH DISTANCE AND EUCLIDEAN DISTANCE IN RANDOM GEOMETRIC GRAPHS - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Advances in Applied Probability Year : 2016

ON THE RELATION BETWEEN GRAPH DISTANCE AND EUCLIDEAN DISTANCE IN RANDOM GEOMETRIC GRAPHS

Abstract

Given any two vertices u, v of a random geometric graph G(n, r), denote by d_E(u, v) their Euclidean distance and by d_G(u, v) their graph distance. The problem of finding upper bounds on d_G(u, v) conditional on d_E(u, v) that hold asymptotically almost surely has received quite a bit of attention in the literature. In this paper, we improve the known upper bounds for values of r = \omega\sqrt(log n)) (i.e. for r above the connectivity threshold). Our result also improves the best known estimates on the diameter of random geometric graphs. We also provide a lower bound on d_G(u, v) conditional on d_E(u, v).
Fichier principal
Vignette du fichier
distancies-final.pdf (428.4 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01291932 , version 1 (22-03-2016)

Identifiers

  • HAL Id : hal-01291932 , version 1

Cite

Josep Diaz, Dieter Mitsche, Guillem Perarnau, Xavier Pérez-Giménez. ON THE RELATION BETWEEN GRAPH DISTANCE AND EUCLIDEAN DISTANCE IN RANDOM GEOMETRIC GRAPHS. Advances in Applied Probability, 2016. ⟨hal-01291932⟩
52 View
76 Download

Share

Gmail Facebook Twitter LinkedIn More