Distributed Finite-Time Computation of Digraph Parameters: Left-Eigenvector, Out-Degree and Spectrum

Abstract

Many of the algorithms that have been proposed in the field of distributed computation rely on assumptions that require nodes to be aware of some global parameters. In this paper, we propose algorithms to compute some network parameters in a distributed fashion and in a finite number of steps. More specifically, given an arbitrary strongly connected network of interconnected nodes, by adapting a distributed finite-time approach, we develop distributed strategies that enable nodes to compute the following network parameters: the left-eigenvector, the out-degree, and the spectrum of weighted adjacency matrices.