Ad hoc networks beyond unit disk graphs

In this paper, we study an algorithmic model for wireless ad hoc and sensor networks that aims to be sufficiently close to reality as to represent practical realworld networks while at the same time being concise enough to promote strong theoretical results. The quasi unit disk graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that—in comparison to the cost known for unit disk graphs—the complexity results of geographic routing in this model contain the additional factor 1/d 2. We prove that in quasi unit disk graphs flooding is an asymptotically message-optimal routing technique, we provide a geographic routing algorithm being most efficient in dense networks, and we show that classic geographic routing is possible with the same asymptotic performance guarantees as for unit disk graphs if d greater than or equivalent 1/square root 2.