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The Number of Neighbors Needed for Connectivity of Wireless Networks

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Abstract

Unlike wired networks, wireless networks do not come with links. Rather, links have to be fashioned out of the ether by nodes choosing neighbors to connect to. Moreover the location of the nodes may be random.

The question that we resolve is: How many neighbors should each node be connected to in order that the overall network is connected in a multi-hop fashion? We show that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors. If each node is connected to less than 0.074log n nearest neighbors then the network is asymptotically disconnected with probability one as n increases, while if each node is connected to more than 5.1774log n nearest neighbors then the network is asymptotically connected with probability approaching one as n increases. It appears that the critical constant may be close to one, but that remains an open problem.

These results should be contrasted with some works in the 1970s and 1980s which suggested that the “magic number” of nearest neighbors should be six or eight.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, and Coordinated Science Laboratory, University of Illinois, Urbana-Champaign, 1308 West Main Street, Urbana, IL, 61801, USA

    Feng Xue & P.R. Kumar

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  1. Feng Xue
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  2. P.R. Kumar
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Xue, F., Kumar, P. The Number of Neighbors Needed for Connectivity of Wireless Networks. Wireless Networks 10, 169–181 (2004). https://doi.org/10.1023/B:WINE.0000013081.09837.c0

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  • DOI: https://doi.org/10.1023/B:WINE.0000013081.09837.c0

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