Ad hoc networks beyond unit disk graphs

Authors:
Fabian Kuhn;Roger Wattenhofer;Aaron Zollinger
Affiliations:
Microsoft Research, Mountain View, CA;ETH Zurich, Zurich, Switzerland;Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA
Venue:
Wireless Networks
Year:
2008

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Abstract

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 real-world 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/d2. 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 ≥ 1/√2.