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Published Articles >> Table of Contents >> Abstract
Sixth IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM'05)
pp. 177-182
On the Clustering Properties of Exponential Random Networks
Nikhil Karamchandani, Indian Institute of Technology - Bombay
D. Manjunath, Indian Institute of Technology - Bombay
Srikanth K. Iyer, Indian Institute of Technology - Kanpur
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DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/WOWMOM.2005.70
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| Abstract |
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We consider the clustering properties of one-dimensional sensor
networks where the nodes are randomly deployed. Unlike most
other work on randomly deployed networks, we assume that the
node locations are drawn from a non uniform distribution. Specifically,
we consider the exponential distribution.
We first obtain the probability that there exists a path between
two labeled nodes in a randomly deployed network and obtain the
limiting behavior of this probability. The probability mass function
(pmf) for the number of components in the network is then
obtained. We show that the number of components in the network
converges in distribution. We also derive the probabilities for different
locations of the components. We then obtain the probability
for the existence of a k-sized component and components of size
≥ k. Asymptotics in the number of nodes in the network are computed
for these probabilities. An interesting result that we obtain
is that as the number of nodes in the network tends to infinity, a
giant component in which a specific fraction α of the nodes form
a component almost surely does not exist for any 0 < α < 1.
However, the probability converges to a non-zero value for α = 1.
Another result is that for 0 < α < 1, we can find an n₀ such
that for n > n₀, the network almost surely does not have a giant
component.
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 Additional Information
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Citation:
Nikhil Karamchandani, D. Manjunath, Srikanth K. Iyer,
"On the Clustering Properties of Exponential Random Networks,"
wowmom,
pp. 177-182,
Sixth IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM'05),
2005
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