Distributed Network Design for Laplacian Eigenvalue Placement

Victor M. Preciado, Michael M. Zavlanos

Abstract: We propose a distributed iterative algorithm in which a group of n autonomous agents self-organize the structure of their communication network in order to control the network's Laplacian eigenvalue spectrum. We assume that every agent has only access to a local (“myopic”) view of the network around it and that there is no centralized coordinator. With every iteration of our algorithm, the agents share local information about their myopic views of the network in order to distributedly find the most beneficial global edge addition/deletion, defined as the one that minimizes a pseudometric defined in the space of Laplacian spectra. The proposed pseudometric is defined in terms of the Laplacian spectral moments and allows for an efficient distributed implementation. The proposed approach is greedy in nature and stable by construction, that is, it locally minimizes the distance of the network's eigenvalue spectrum to a desired spectrum. We illustrate the performance of our approach with several numerical simulations.