How to Optimally Reconfigure Average Consensus with Maximum-Degree Weights in Bipartite Regular Graphs

Abstract

The average consensus algorithm is a frequently applied iterative scheme to efficiently estimate various aggregate functions in many modern multi-agent systems. This paper addresses the average consensus with the Maximum-degree weights in bipartite regular graphs, where this algorithm does not converge as the third convergence condition is broken in these graphs. We apply a distributed mechanism (determined by five conditions) for detecting whether or not the algorithm is executed in this critical graph topology and analyze how to reconfigure it the most efficiently. The latest research suggests that its high performance is likely not to be achieved with the same values of the mixing parameter as in non-bipartite non-regular topologies. Hence, our goal is to identify the reconfiguration of the weight matrix ensuring the optimal performance of the algorithm under various conditions. Its performance is examined in randomly generated bipartite regular graphs with various connectivity and under three scenarios differing from each other in the rounding accuracy. Also, the asymptotic convergence factor of the weight matrices after reconfiguration is examined in the experimental section. Besides, the performance of a reconfigured average consensus with the Maximum-degree weights in bipartite regular graphs is compared to the Metropolis-Hastings algorithm, which also diverges in these topologies with its optimal initial configuration.