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The authors design the weights in consensus algorithms with spatially correlated random topologies. These arise with: Networks with spatially correlated random link failures and networks with randomized averaging protocols. They show that the weight optimization problem is convex for both symmetric and asymmetric random graphs. With symmetric random networks, they choose the consensus Mean Squared Error (MSE) convergence rate as optimization criterion and explicitly express this rate as a function of the link formation probabilities, the link formation spatial correlations, and the consensus weights. They prove that the MSE convergence rate is a convex, non-smooth function of the weights, enabling global optimization of the weights for arbitrary link formation probabilities and link correlation structures.
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