Distributed Harmonic Form Computation

Abstract

Spectral graph analysis based on Laplace operators has been ubiquitously applied in graph signal processing. Extending these tools to a generalization of graphs is helpful for several applications, such as network analysis, a sensor network coverage problem, and other fields, where the relationships between two or more vertices should be modeled. Such mathematical theories already exist, but the associated algorithms are still in their infancy. In this letter, we propose a new algorithm to compute harmonic forms, i.e., solutions of the Laplace equation, whose implementation is simple enough to be distributed among networks without central control center.