ExBCG-TC: Extended Borel Cayley Graph Topology Control for Ad Hoc Networks

In our previous work, we demonstrated that the Borel Cayley Graph topology control (BCG-TC) is an efficient topology control algorithm for producing an underlying network topology resembling a 4-regular Borel Cayley Graph and assuring small diameter, short average path length and superb power efficiency. But the BCG-TC networks are unlikely to be connected below a certain radio range threshold due to isolated nodes or isolated subnetworks. In this paper, we propose a topology control algorithm, EXTENDED BCG-TC (EXBCG-TC), that effectively improves network connectivity of network topology generated by BCG-TC. Our EXBCG-TC works by injecting a small number of nodes into the network and connecting them to nodes already in the network. Throughout the efficient rules for establishing connection (namely the Request Criterion and the Accept Criterion), the proportion of isolated nodes or isolated subnetworks is significantly reduced or totally eliminated. The resulting network topologies are more likely to be fully connected with radio range much smaller than the radio range threshold of the BCG-TC while preserving the outstanding network topological properties and power efficiency of BCG-TC network topologies.