Matrix analysis
Lifting Markov chains to speed up mixing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
TAG: a Tiny AGgregation service for ad-hoc sensor networks
ACM SIGOPS Operating Systems Review - OSDI '02: Proceedings of the 5th symposium on Operating systems design and implementation
Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Gossip-Based Computation of Aggregate Information
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A decentralized algorithm for spectral analysis
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Fastest Mixing Markov Chain on a Graph
SIAM Review
Geographic gossip: efficient aggregation for sensor networks
Proceedings of the 5th international conference on Information processing in sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast Distributed Algorithms for Computing Separable Functions
IEEE Transactions on Information Theory
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Motivated by applications of distributed linear estimation, distributed control, and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a nonreversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation pseudo-lifting. We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control.