Hidden information and actions in multi-hop wireless ad hoc networks
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
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A randomly-deployed large-scale wireless ad hoc network is naturally represented by an r-disk graph over a random point set. For a monotonically increasing topology property, the smallest transmission radius such that the induced r-disk graph has this property is called the critical transmission radius. Instead of giving deterministic algorithms, we offer a systematic probabilistic study on the critical transmission radius. In the random geometric graphs, the critical transmission radii for monotonic-increasing properties have sharp thresholds. Therefore, by assigning transmission radius lager than the threshold, the wireless network almost surely has the corresponding property. We have conducted probabilistic studies on the critical transmission radii for k-connectivity, k-coverage, Gabriel graph, and greedy forward routing. All these critical transmission radii can be explicitly given in terms of the number of nodes.