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Decemmber 2011 Asymptotics of geometrical navigation on a random set of points in the plane
Nicolas Bonichon, Jean-François Marckert
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Adv. in Appl. Probab. 43(4): 899-942 (Decemmber 2011). DOI: 10.1239/aap/1324045692

Abstract

A navigation on a set of points S is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where S is a nonuniform Poisson point process (in a finite domain) with intensity going to +∞. We show the convergence of the traveller's path lengths, and give the number of stages and the geometry of the traveller's trajectories, uniformly for all starting points and targets, for several navigations of geometric nature. Other costs are also considered. This leads to asymptotic results on the stretch factors of random Yao graphs and random θ-graphs.

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Nicolas Bonichon. Jean-François Marckert. "Asymptotics of geometrical navigation on a random set of points in the plane." Adv. in Appl. Probab. 43 (4) 899 - 942, Decemmber 2011. https://doi.org/10.1239/aap/1324045692

Information

Published: Decemmber 2011
First available in Project Euclid: 16 December 2011

zbMATH: 1238.60014
MathSciNet: MR2867939
Digital Object Identifier: 10.1239/aap/1324045692

Subjects:
Primary: 60B10, 60D05, 60G55, 68W40

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 4 • Decemmber 2011
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