Optimization and Analysis of Distributed Averaging With Short Node Memory
Abstract
In this paper, we demonstrate, both theoretically and by numerical examples, that adding a local prediction component to the update rule 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 that can be obtained using this acceleration methodology. For a chain topology on n nodes, this leads to a factor of n improvement over the onestep algorithm, and for a twodimensional grid, our approach achieves a factor of n^1/2 improvement, in terms of the number of iterations required to reach a prescribed level of accuracy.
 Publication:

IEEE Transactions on Signal Processing
 Pub Date:
 May 2010
 DOI:
 10.1109/TSP.2010.2043127
 arXiv:
 arXiv:0903.3537
 Bibcode:
 2010ITSP...58.2850O
 Keywords:

 Computer Science  Distributed;
 Parallel;
 and Cluster Computing;
 Computer Science  Information Theory;
 Computer Science  Multiagent Systems
 EPrint:
 doi:10.1109/TSP.2010.2043127