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Ad Hoc网络渐近连通所需邻居数的一个改进下界

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

Sanquan Song, Dennis L. Goeckel, Don Towsley

摘要:

Xue和Kumar已经确定了具有N个均匀分布节点的无线网络的连通性所需的邻居数量必须以log(N)的形式增长,并且他们还确定了所需的实际数量介于0.074log(N)和5.1774log(N)之间。在这篇简短的论文中,通过认识到节点根据泊松点过程分布的网络的连通性结果通常可以应用于具有N个节点的网络的问题,我们能够提高下界。特别地,我们证明了一个网络的节点分布在一个单位正方形根据一个二维泊松点过程的参数N将渐近断开概率为1,如果邻居的数量小于0.129log(N)。此外,对于单位正方形内均匀分布N个节点的渐近连通网络,相似的邻居数是不够的,因此改进了下界。

英文摘要:

Xue 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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