The Asynchronous Power Iteration: A Graph Signal Perspective

This paper considers an autonomous network in which the nodes communicate only with their neighbors at random time instances, repeatedly and independently. Polynomial graph filters studied in the context of graph signal processing are inadequate to analyze signals on this type of networks. This is due to the fact that the basic shift on a graph requires all the nodes to communicate at the same time, which cannot be assumed in an autonomous setting. In order to analyze these type of networks, this paper studies an asynchronous power iteration that updates the values of only a subset of nodes. This paper further reveals the close connection between asynchronous updates and the notion of smooth signals on the graph. The paper also shows that a cascade of random asynchronous updates smooths out any arbitrary signal on the graph.