Asymptotically optimal trade-off between local and global connectivity in wireless networks

We analyze large, random network topologies that arise in ad hoc or sensor networks. A fundamental requirement of communication in these systems is reachability, that is, to have a connected network topology. It is known, however, that the price for full connectivity is very high, as it requires unbounded local complexity, i.e., it forces the nodes to have infinitely growing degrees to achieve asymptotic connectivity. This means a lack of scalability, which is known to hold for a quite general class of random network topology models. Therefore, an important step in analyzing the performance of such networks is to explore the trade-off between the fraction of nodes that still belong to a connected component vs. a bound imposed on local connectivity, i.e., on the node degrees. We investigate this issue in a model that is more general than previously investigated random wireless network topology models. In our general model we derive an asymptotically optimal trade-off between node degrees and the fraction of nodes that form a connected component.