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Title:  On the clustering properties of exponential random networks 
Authors:  KARAMCHANDANI, NIKHIL MANJUNATH, D IYER, SRIKANTH K 
Keywords:  exponential distribution wireless sensor networks 
Issue Date:  2005 
Publisher:  IEEE 
Citation:  Proceedings of the Sixth IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks, Taormina, Italy, 1316 June 2005, 177182. 
Abstract:  We consider the clustering properties of onedimensional sensor networks where the nodes are randomly deployed. Unlike most other work on randomly deployed networks, ours assumes that the node locations are drawn from a non uniform distribution. Specifically, we consider an 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 ksized component and components of size ≥k. Asymptotics in the number of nodes in the network are computed for these probabilities. An interesting result is that, as the number of nodes, n, 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 nonzero 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. 
URI:  10.1109/WOWMOM.2005.70 http://hdl.handle.net/10054/345 http://dspace.library.iitb.ac.in/xmlui/handle/10054/345 
ISBN:  0769523420 
Appears in Collections:  Proceedings papers

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