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Student: Boris Oreshkin, Ph.D. student
Supervisor: Mark Coates
In this paper, we demonstrate, both theoretically and by numerical examples, that the utilization of a local prediction component can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node’s two previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighbouring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors’ values, and carry out a theoretical analysis of the improvement in convergence rate. For a chain topology on n nodes, this leads to a factor of n improvement over the optimal one-step algorithm, and for a two-dimensional grid, our approach achieves a factor of n^1/2 improvement, in terms of asymptotic convergence rate.
[Full Description] [Paper (pdf format)]
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