We study a general framework for broadcast gossip algorithms which use companion variables to solve the average consensus problem. Each node maintains an initial state and a companion variable. Iterative updates are performed asynchronously whereby one random node broadcasts its current state and companion variable and all other nodes receiving the broadcast update their state and companion variable. We provide conditions under which this scheme is guaranteed to converge to a consensus solution, where all nodes have the same limiting values, on any strongly connected directed graph. Under stronger conditions, which are reasonable when the underlying communication graph is undirected, we guarantee that the consensus value is equal to the average, both in expectation and in the mean-squared sense. Our analysis uses tools from non-negative matrix theory and perturbation theory. The perturbation results rely on a parameter being sufficiently small. We characterize the allowable upper bound as well as the optimal setting for the perturbation parameter as a function of the network topology, and this allows us to characterize the worst-case rate of convergence. Simulations illustrate that, in comparison to existing broadcast gossip algorithms, the approaches proposed in this paper have the advantage that they simultaneously can be guaranteed to converge to the average consensus and they converge in a small number of broadcasts.
In this paper, we propose a new decentralized algorithm to solve the consensus on the average problem on sensor networks through a gossip algorithm based on broadcasts. We directly extend previous results by not requiring that the digraph representing the network topology be balanced. Our algorithm is an improvement with respect to known gossip algorithms based on broadcasts in that the average of the initial state is preserved after each broadcast. The nodes are assumed to know their out-degree anytime they transmit information. Abstract —In this paper we propose a new decentralized algorithm to solve the consensus on the average problem on arbitrary strongly connected digraphs through a gossip algorithm based on broadcasts. We directly extend previous results by not requiring that the digraph is balanced. Our algorithm is an improvement respect to known gossip algorithms based on broadcasts in that the average of the initial state is preserved after each broadcast. The nodes are assumed to know their out-degree anytime they transmit information. The algorithm convergence analysis is preliminary and performance is shown by simulations.