Abstract
We first investigate when it is possible for two nodes in a wireless network to communicate with each other. Based on the result from bond percolation in a two-dimensional lattice, as long as the probability that a sub-square is closed is less than 0.5 and each sub-square contains at least four nodes, percolation occurs. Then, we establish the conditions for full connectivity in a network graph. How two adjacent sub-squares are connected differentiates this work from others. Two adjacent sub-squares are connected if there exists a communicating path between them instead of a direct communication link. The full connectivity occurs almost surely if each sub-square contains at least one node and the probability of having an open sub-edge is no less than 0.3822. Finally, simulations are conducted to validate the proposed conditions for percolation and full connectivity.
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Chang, MK., Chien, FT., Chan, YW., Chuang, MH. (2014). Analysis on the Connectivity in Wireless Ad Hoc Networks. In: Park, J., Pan, Y., Kim, CS., Yang, Y. (eds) Future Information Technology. Lecture Notes in Electrical Engineering, vol 309. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55038-6_8
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DOI: https://doi.org/10.1007/978-3-642-55038-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55037-9
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