Abstract
We design the weights in consensus algorithms for spatially correlated random topologies. These arise with 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the weight optimization problem is convex for both symmetric and asymmetric random graphs. With symmetric random networks, we choose the consensus mean-square error (MSE) convergence rate as the optimization criterion and explicitly express this rate as a function of the link formation probabilities, the link formation spatial correlations, and the consensus weights. We prove that the MSE convergence rate is a convex, nonsmooth function of the weights, enabling global optimization of the weights for arbitrary link formation probabilities and link correlation structures. We extend our results to the case of asymmetric random links. We adopt as optimization criterion the mean-square deviation (MSdev) of the nodes' states from the current average state. We prove that MSdev is a convex function of the weights. Simulations show that significant performance gain is achieved with our weight design method when compared with other methods available in the literature.
Highlights
This paper finds the optimal weights for the consensus algorithm in correlated random networks
We extend our results to the case of asymmetric random links, adopting as an optimization criterion the mean squared deviation rate ψ(W ), and show that ψ(W ) is a convex function of the weights
We study the performance of probability based weights (PBW), comparing it with the standard weight choices available in the literature: in subsection VI-A, we compare it with the Metropolis weights (MW), discussed in [29], and the supergraph based weights (SGBW)
Summary
This paper finds the optimal weights for the consensus algorithm in correlated random networks. We provide insights into weight design with a simple example of complete random network that admits closed form solution for the optimal weights and convergence rate and show how the optimal weights depend on the number of nodes, the link formation probabilities, and their correlations. We extend our results to the case of asymmetric random links, adopting as an optimization criterion the mean squared deviation (from the current average state) rate ψ(W ), and show that ψ(W ) is a convex function of the weights. We provide two different models of random networks with correlated link failures; in addition, we study the broadcast gossip algorithm [12], as an example of randomized protocol with asymmetric links.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
