Decentralized estimation and control of algebraic connectivity of random ad-hoc networks

In this paper, we propose a decentralized algorithm for the estimation and control of connectivity of random ad hoc networks. First, we introduce a novel stochastic power iteration method that allows each node to estimate and track the expected algebraic connectivity of a random graph. The proposed method is then used to adapt the power transmitted by each node in order to drive the network connectivity toward a desired value. Numerical results illustrate the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures.