Topology control for MANETs

We deal with the problem of topology control for mobile ad hoc networks. Based on an asymptotic result on k-connectivity, a simple scheme for topology control is proposed. The scheme is used to generate several topologies under highly mobile conditions. Through simulation and analysis we show that this scheme results in high connectivity even under mobile conditions as the number of nodes increase. We also show that even though the scheme uses varying transmit power, the overall power consumption in the network remains relatively the same, and is less than using constant transmit power as the number of nodes increases. In order to use the scheme, the nodes need to be uniformly distributed. We prove that under periodic boundary conditions the stationary distribution of nodes, moving according to (a variant of) the random waypoint model, is uniform.