Distributed Spanners with Bounded Degree for Wireless Ad Hoc Networks

In this paper, we review some new distributed algorithms that construct sparse subgraphs with bounded degree of the unit disk graph efficiently for wireless ad hoc networks. They maintain a linear number of links while still preserving power-efficient routes for any pair of nodes. It was open whether the Yao plus reverse Yao graph and the symmetric Yao graph are spanners. We show that the Yao plus reverse Yao graph has a bounded power stretch factor 2 in civilized unit disk graph. In addition, we review a recent example by M. Grunewald et al. [6] to show that the symmetric Yao graph does not have a constant bounded stretch factor. Finally, we conduct simulations to study the practical performances of these structures. All structures have small power stretch factors for randomly generated unit disk graphs in our experiments.

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