Self-Stabilizing Algorithm for Geometric Spanner Construction in a Wireless Sensor Network

We present a distributed algorithm for creation of geometric spanners in a wireless sensor network. Given any connected network, we show that the algorithm terminates inO(1) time, irrespective of network size. Our algorithm uses an underlying clustering algorithm as a foundation for creating spanners and only relies on the periodic heartbeat messages associated with cluster maintenance for the creation of the spanners.The algorithm is also shown to stabilize locally in the presence of node additions and deletions.The performance of our algorithm is verified using large scale simulations. The average path length ratio for routing along the spanner for large networks is shown to be less than 2.