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  4. Weighted Gossip: Distributed Averaging Using Non-Doubly Stochastic Matrices
 
conference paper

Weighted Gossip: Distributed Averaging Using Non-Doubly Stochastic Matrices

Bénézit, Florence  
•
Blondel, Vincent
•
Thiran, Patrick  
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2010
Proceedings of ISIT'10
IEEE International Symposium on Information Theory

This paper presents a general class of gossip-based averaging algorithms, which are inspired from Uniform Gossip [1]. While Uniform Gossip works synchronously on complete graphs, weighted gossip algorithms allow asynchronous rounds and converge on any connected, directed or undirected graph. Unlike most previous gossip algorithms [2]–[6], Weighted Gossip admits stochastic update matrices which need not be doubly stochastic. Double-stochasticity being very restrictive in a distributed setting [7], this novel degree of freedom is essential and it opens the perspective of designing a large number of new gossip-based algorithms. To give an example, we present one of these algorithms, which we call One-Way Averaging. It is based on random geographic routing, just like Path Averaging [5], except that routes are one way instead of round trip. Hence in this example, getting rid of double stochasticity allows us to add robustness to Path Averaging.

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