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We propose a weight design method to increase the convergence rate ofdistributed consensus. Prior work has focused on symmetric weight design due tocomputational tractability. We show that with proper choice of asymmetricweights, the convergence rate can be improved significantly over even thesymmetric optimal design. In particular, we prove that the convergence rate ina lattice graph can be made independent of the size of the graph withasymmetric weights. We then use a Sturm-Liouville operator to approximate thegraph Laplacian of more general graphs. A general weight design method isproposed based on this continuum approximation. Numerical computations showthat the resulting convergence rate with asymmetric weight design is improvedconsiderably over that with symmetric optimal weights and Metropolis-Hastingsweights.

Improving Convergence Rate of Distributed Consensus Through Asymmetric Weights