Critical Density Thresholds in Distributed Wireless Networks

Abstract

We present experimental and analytical results showing "zero-one" phase transitions for network connec-tivity, multi-path reliability, neighbor count, Hamiltonian cycle formation, multiple-clique formation, and probabilistic flooding. These transitions are characterized by critical density thresholds such that a global property exists with negligible probability on one side of the threshold, and exists with high probability on the other. We discuss the connections between these phase transitions and some known results on random graphs, and indicate their significance for the design of resource-efficient wireless networks.