Let T be a d-dimensional toroidal grid of n^d points. For a given range parameter ω, and a positive integer k ≤q d, we say that two points in T are mutually visible if they differ in at most k coordinates and are a distance at most ω apart, where distance is measured using the \ellₚ norm. We obtain a random d-dimensional line-of-sight graph G by placing a node at each point in T independently with some fixed probability p^* and connecting all pairs of mutually visible nodes. We prove an asymptotically tight connectivity result for this random graph.

Source : oai:HAL:hal-00980756v1

Volume: Vol. 15 no. 2

Section: Analysis of Algorithms

Published on: May 15, 2013

Submitted on: December 13, 2010

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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