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Connectivity for line-of-sight networks in higher dimensions

Abstract : 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.
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Luc Devroye, Linda Farczadi. Connectivity for line-of-sight networks in higher dimensions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 2 (2), pp.71--86. ⟨hal-00980756⟩

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