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Title:  On range matrices and wireless networks in d dimensions 
Authors:  DESAI, MP MANJUNATH, D 
Keywords:  ad hoc network graph theory matrix algebra probability 
Issue Date:  2005 
Publisher:  IEEE 
Citation:  Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, Trentino, Italy, 37 April 2005, 190196. 
Abstract:  Suppose that V = {v1, v2, ...vn} is a set of nodes randomly (uniformly) distributed in the d dimensional cube [0, x0]d, and W = {w(i, j) > 0 : 1 ≤ i, j ≤ n} is a set of numbers chosen so that w(i, j) = w(j, i) = w(j, i). Construct a graph Gn,d,W whose vertex set is V, and whose edge set consists of all pairs {ui, uj} with  ui  uj  ≤ w(i, j). In the wireless network context, the set V is a set of labeled nodes in the network and W represents the maximum distances between the node pairs for them to be connected. We essentially address the following question: "if G is a graph with vertex set V, what is the probability that G appears as a subgraph in Gn,d,W?" Our main contribution is a closed form expression for this probability under the l∞ norm for any dimension d and a suitably defined probability density function. As a corollary to the above answer, we also answer the question, "what is the probability that Qn,d,W is connected?". 
URI:  10.1109/WIOPT.2005.33 http://hdl.handle.net/10054/344 http://dspace.library.iitb.ac.in/xmlui/handle/10054/344 
ISBN:  076952267X 
Appears in Collections:  Proceedings papers

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