Topology for Distributed Inference on Graphs

• Published in: IEEE transactions on signal processing Vol. 56; no. 6; pp. 2609 - 2613
• Main Authors: Kar, S., Aldosari, S., Moura, J.M.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebraic connectivity; Algorithm design and analysis; Algorithms; Applied sciences; Cayley; Collaboration; Communication channels; consensus algorithm; Convergence; Distributed algorithms; distributed detection; Equivalence; Exact sciences and technology; Graph theory; Graphs; Inference; Inference algorithms; Information, signal and communications theory; Iterative algorithms; Laplace equations; Laplacian; Miscellaneous; Network topology; Ramanujan; random graphs; sensor networks; Signal processing; small-world; spectral graph theory; Telecommunications and information theory; Topology; topology optimization; Cayley; Ramanujan; consensus algorithm; Iterative method; Algebraic connectivity; Graph theory; random graphs; sensor networks; Laplacian; Optimization; Random graph; spectral graph theory; distributed detection; Spectral theory; small-world; Distributed algorithm; Convergence rate; Signal processing; topology optimization; Sensor array
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2008.923536

Let N decision-makers collaborate to reach a decision. We consider iterative distributed inference with local intersensor communication, which, under simplifying assumptions, is equivalent to distributed average consensus. We show that, under appropriate conditions, the topology given by the nonbipartite Ramanujan graphs optimizes the convergence rate of this distributed algorithm.