A Scalable Distributed Dynamical Systems Approach to Learn the Strongly Connected Components and Diameter of Networks
Emily A. Reed (University of Southern California)
Guilherme Ramos (Universidade do Porto)
Paul Bogdan (University of Southern California)
Sergio Pequito (TU Delft - Team Sergio Pequito)
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Abstract
Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of machine learning and control theory problems. In this article, we provide for the first time a scalable distributed solution for these two problems by leveraging dynamical consensus-like protocols to find the SCCs. The proposed solution has a time complexity of O(NDd in-degreemax), where N is the number of vertices in the network,D is the (finite) diameter of the network, and din-degreemax is the maximum in-degree of the network. Additionally, we prove that our algorithm terminates in D+2 iterations, which allows us to retrieve the finite diameter of the network. We perform exhaustive simulations that support the outperformance of our algorithm against the state of the art on several random networks, including Erdős-Rényi, Barabási-Albert, and Watts-Strogatz networks.