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Distributed average consensus is the main mechanism in algorithms fordecentralized computation. In distributed average consensus algorithm each nodehas an initial state, and the goal is to compute the average of these initialstates in every node. To accomplish this task, each node updates its state by aweighted average of its own and neighbors' states, by using local communicationbetween neighboring nodes. In the networks with fixed topology, convergencerate of distributed average consensus algorithm depends on the choice ofweights. This paper studies the weight optimization problem in distributedaverage consensus algorithm. The network topology considered here is a starnetwork where the branches have different lengths. Closed-form formulas ofoptimal weights and convergence rate of algorithm are determined in terms ofthe network's topological parameters. Furthermore generic K-cored star topologyhas been introduced as an alternative to star topology. The introduced topologybenefits from faster convergence rate compared to star topology. By simulationbetter performance of optimal weights compared to other common weightingmethods has been proved.

A Solution to Fastest Distributed Consensus Problem for Generic Star & K-cored Star Networks