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Published May 2019 | public
Book Section - Chapter

Node-asynchronous Implementation of Rational Filters on Graphs

Abstract

This paper considers a node-asynchronous implementation of rational ("IIR") filters on graphs, in which the nodes are assumed to wake up randomly and independently from each other, and communicate only with their immediate neighbors. The underlying graph is allowed to be directed, possibly with a non-diagonalizable adjacency matrix. Since the nodes are allowed to act independently, the proposed implementation is practical for very large or autonomous networks where synchronization is difficult to achieve. Furthermore, the proposed algorithm is 1-hop localized on the graph irrespective of the order of the filter. The method is shown to converge in the mean-squared sense under a boundedness assumption on the filter as well as the graph operator. The result follows from the convergence of a more general randomized asynchronous state recursion, which is also presented in this paper. The algorithm is simulated on a random geometric graph, which numerically verifies the convergence.

Additional Information

© 2019 IEEE. This work was supported in parts by the ONR grants N00014-17-1-2732 and N00014-18-1-2390, the NSF grant CCF-1712633, and the Electrical Engineering Carver Mead Research Seed Fund of the California Institute of Technology.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023