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On the Phase Transition Width of K-Connectivity in Wireless Multihop Networks

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3 Author(s)
Xiaoyuan Ta ; Sch. of Electr. & Inf. Eng., Univ. of Sydney, Sydney, NSW ; Guoqiang Mao ; Anderson, B.D.O.

In this paper, we study the phase transition behavior of k-connectivity (k=1,2,...) in wireless multihop networks where a total of n nodes are randomly and independently distributed following a uniform distribution in the unit cube [0,1]d (d = 1,2,3), and each node has a uniform transmission range r(n). It has been shown that the phase transition of k-connectivity becomes sharper as the total number of nodes n increases. In this paper, we investigate how fast such phase transition happens and derive a generic analytical formula for the phase transition width of k-connectivity for large enough n and for any fixed positive integer k in d-dimensional space by resorting to a Poisson approximation for the node placement. This result also applies to mobile networks where nodes always move randomly and independently. Our simulations show that to achieve a good accuracy, n should be larger than 200 when k = 1 and d = 1; and n should be larger than 600 when k les 3 and d = 2, 3. The results in this paper are important for understanding the phase transition phenomenon; and it also provides valuable insight into the design of wireless multihop networks and the understanding of its characteristics.

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Mobile Computing, IEEE Transactions on  (Volume:8 ,  Issue: 7 )