New Lower Bound on the Critical Density in Continuum Percolation

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 λc for Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λc ≈ 1.44, while the best theoretical bounds obtained thus far are 0.696 < λc < 3.372. By using a probabilistic analysis which incorporates the clustering effect in random geometric graphs, we develop a new class of lower bounds for λc. In particular, the lower bound is substantially improved to λc > 0.833. This graph theoretical viewpoint provides a new approach and a deep insight for the problem.