Research Article
Analytical Lower Bounds on the Critical Density in Continuum Percolation
@INPROCEEDINGS{10.1109/WIOPT.2007.4480080, author={Zhenning Kong and Edmund M. Yeh}, title={Analytical Lower Bounds on the Critical Density in Continuum Percolation}, proceedings={1st International ICST Workshop on Spatial Stochastic Models for Wireless Networks}, publisher={IEEE}, proceedings_a={SPASWIN}, year={2008}, month={3}, keywords={Analytical models Bonding Decoding Large-scale systems Lattices Mathematical model Probability density function Random variables Solid modeling Wireless networks}, doi={10.1109/WIOPT.2007.4480080} }- Zhenning Kong
Edmund M. Yeh
Year: 2008
Analytical Lower Bounds on the Critical Density in Continuum Percolation
SPASWIN
IEEE
DOI: 10.1109/WIOPT.2007.4480080
Abstract
Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density lambdac (d) for d-dimensional Poisson random geometric graphs in continuum percolation theory. By using a probabilistic analysis which incorporates the clustering effect in random geometric graphs, we develop a new class of analytical lower bounds for the critical density lambdac (d) in d-dimensional Poisson random geometric graphs. The lower bounds are the tightest known to date. In particular, for the two-dimensional case, the analytical lower bound is improved to lambdac (2) ges 0.7698. For the three-dimensional case, we obtain lambdac (3) ges 0.4494.
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