Distributed topology control in wireless ad hoc networks using β-skeletons

We propose a novel approach for sparse topology generation in wireless ad hoc networks based on a graph structure known as β-skeletons. Two efficient algorithms are presented in this paper for creating a connected topology from an underlying β-skeleton. One algorithm is a distributed algorithm that runs on each component of the β-skeleton. It creates a connected structure from the disconnected β-skeleton graph using a distributed leader election algorithm. The running time of this algorithm is O(nlogn), The other is a localized algorithm that uses two-hop neighborhood information to generate a connected topology, with a running time of O(n). Simulations show consistent decrease in node degree in the resulting topology. The observed decrease is greater than 33% in comparison to the relative neighborhood graph (RNG) and greater than 50% in comparison to other topology structures such as, the Gabriel graph (GG) and the Yao construction on GG.