Distributed stopping for average consensus using double linear iterative strategies

We consider how double linear iterative strategies for asymptotic average consensus can be adapted so that the nodes can determine, in a distributed fashion, a stopping criterion that allows them to terminate (in finite time) the execution of the iterations when approximate average consensus has been reached. The nodes are said to have reached approximate average consensus when each of them has a value that is close to the desirable average (in a way that we precisely define). We consider both undirected and directed graphs, and compare the number of iterations and transmissions required by the proposed protocols against previously proposed stopping protocols for approximate average consensus.