Expansion properties of (secure) wireless networks
ACM Transactions on Algorithms (TALG)
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We study the connectivity properties of a family of random graphs that closely model the Bluetooth's device discovery process, where each device tries to connect to other devices within its visibility range in order to establish reliable communication channels yielding a connected topology. Specifically, we provide both analytical and experimental evidence that when the visibility range of each node (i.e. device) is limited to a vanishing function of n, the total number of nodes in the system, full connectivity can still be achieved with high probability by letting each node connect only to a ‘small’ number of visible neighbors. Our results extend previous studies, where connectivity properties were analyzed only for the case of a constant visibility range, and provide evidence that Bluetooth can indeed be used for establishing large ad hoc networks. Copyright © 2008 John Wiley & Sons, Ltd.