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Power efficient topologies in an ad-hoc network can reduce battery usage and increase the lifetime of a network. Topology control algorithms including a local minimum spanning tree (LMST), distributed relative neighbourhood graph (DRNG) and K-Neigh graphs are computed by using the location or the distance information of the network nodes. Inaccurate distance or location information can lead to disconnected topology graphs. Furthermore, a distance based topology graph may not necessarily be connected due to wireless signal attenuation and propagation characteristics. In a realistic scenario, a small link distance may correspond to a large transmission power as the signal may need to transverse through obstacles. Hence it is imperative to include the environment characteristics when generating power efficient connected topology graphs. In this paper we identify the topology construction procedures that may lead to disconnected network topologies. We propose a new procedure that can work in conjunction with the neighbour discovery protocol to provide a better connected and power efficient network topology. Simulations indicate that the proposed algorithm provides a significant improvement in the connectivity of power base DRNG graphs.