Small Worlds and Rapid Mixing with a Little More Randomness on Random Geometric Graphs

We theoretically and experimentally analyze the process of adding sparse random links to a random wireless networks modeled as a random geometric graph. While this process has been previously proposed, we are the first to (i) theoretically consider sparse new-wiring (with asymptotically less than constant fraction of nodes allowed very small constant new wired edges), (ii) prove bounds for any new-wiring process upon random geometric graphs, and (iii) consider the effect of such sparse new-wiring upon the spectral gap of the resultant normalized Laplacian. In particular, we consider the following models of adding new wired edges: Divide the normalized space into bins of length k r 2 √