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In this work we present a new framework for the analysis and design ofrandomized gossip algorithms for solving the average consensus problem. We showhow classical randomized iterative methods for solving linear systems can beinterpreted as gossip algorithms when applied to special systems encoding theunderlying network and explain in detail their decentralized nature. Ourgeneral framework recovers a comprehensive array of well-known gossipalgorithms as special cases, including the pairwise randomized gossip algorithmand path averaging gossip, and allows for the development of provably fastervariants. The flexibility of the new approach enables the design of a number ofnew specific gossip methods. For instance, we propose and analyze novel blockand the first provably accelerated randomized gossip protocols, and dualrandomized gossip algorithms.  From a numerical analysis viewpoint, our work is the first that explores indepth the decentralized nature of randomized iterative methods for linearsystems and proposes them as methods for solving the average consensus problem.  We evaluate the performance of the proposed gossip protocols by performingextensive experimental testing on typical wireless network topologies.

Revisiting Randomized Gossip Algorithms: General Framework, Convergence Rates and Novel Block and Accelerated Protocols