An Improved Lower Bound to the Number of Neighbors Required for the Asymptotic Connectivity of Ad Hoc Networks

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dc.creatorSong, Sanquan
dc.creatorGoeckel, Dennis L.
dc.creatorTowsley, Don
dc.date2005-09-27
dc.date.accessioned2026-07-07T08:15:40Z
dc.date.available2026-07-07T08:15:40Z
dc.descriptionXue and Kumar have established that the number of neighbors required for connectivity of wireless networks with N uniformly distributed nodes must grow as log(N), and they also established that the actual number required lies between 0.074log(N) and 5.1774log(N). In this short paper, by recognizing that connectivity results for networks where the nodes are distributed according to a Poisson point process can often be applied to the problem for a network with N nodes, we are able to improve the lower bound. In particular, we show that a network with nodes distributed in a unit square according to a 2D Poisson point process of parameter N will be asymptotically disconnected with probability one if the number of neighbors is less than 0.129log(N). Moreover, similar number of neighbors is not enough for an asymptotically connected network with N nodes uniformly in a unit square, hence improving the lower bound.
dc.descriptionSubmitted to IEEE Transactions on Information Theory
dc.identifierhttps://arxiv.org/abs/cs/0509085
dc.identifierhttp://arxiv.org/abs/cs/0509085
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133522
dc.subjectNetworking and Internet Architecture
dc.subjectInformation Theory
dc.titleAn Improved Lower Bound to the Number of Neighbors Required for the Asymptotic Connectivity of Ad Hoc Networks
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