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Asynchronous Distributed Matrix Balancing and Application to Suppressing Epidemic

This paper presents an efficient asynchronous distributed algorithm for the problem of balancing a nonnegative matrix using a network of processors, each of which has access to a portion of the global matrix. The goal of the algorithm is for the processors to collaborate through local information exchange so that each processor can determine its local weighting coefficients that balance the matrix. Our algorithm is of Gauss-Seidel type with strict relaxation and converges geometrically under mild assumptions on the communication model between neighboring processors. The analysis of our algorithm is based on a novel reformulation of matrix balancing as a network consensus problem, from which an upper bound on the convergence rate can be derived. Finally, we demonstrate the applicability of the algorithm to a problem of optimally allocating curing resources for suppressing epidemic spread in a directed weighted network, where the spreading dynamic is captured by a susceptible-infected-susceptible model.