Bounds on hop distance in greedy routing approach in wireless ad hoc networks

Wireless ad hoc networks are generally characterised by random node locations and multi-hop routes. A quantitative knowledge of the relation between hop count and Euclidean distance could provide a better understanding of important network parameters such as end-to-end delay, power consumption along the route, and node localisation. In this paper, we present an analytic approach to capture the statistics on hop count for a given source-to-destination Euclidean distance in a greedy routing approach. We also show that, for a given hop count, the bounds on Euclidean distance can be computed from the distribution characteristics of per-hop progress.