Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Lifting Markov chains to speed up mixing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
FOCS '00 Proceedings of the 41st Annual 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
Reversal of Markov Chains and the Forget Time
Combinatorics, Probability and Computing
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
Location-Aided Fast Distributed Averaging
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Neighborhood gossip: Concurrent averaging through local interference
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Broadcast gossip algorithms for consensus
IEEE Transactions on Signal Processing
Order-optimal consensus through randomized path averaging
IEEE Transactions on Information Theory
Geographic Gossip: Efficient Averaging for Sensor Networks
IEEE Transactions on Signal Processing
The capacity of wireless networks
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial filtering for fast convergence in distributed consensus
IEEE Transactions on Signal Processing
Fast distributed average consensus algorithms based on advection-diffusion processes
IEEE Transactions on Signal Processing
Distributed averaging in dense wireless networks
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Order-optimal consensus through randomized path averaging
IEEE Transactions on Information Theory
Fast decentralized averaging via multi-scale gossip
DCOSS'10 Proceedings of the 6th IEEE international conference on Distributed Computing in Sensor Systems
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Existing works on distributed consensus explore linear iterations based on reversible Markov chains, which contribute to the slow convergence of the algorithms. It has been observed that by overcoming the diffusive behavior of reversible chains, certain nonreversible chains lifted from reversible ones mix substantially faster than the original chains. In this paper, the idea of Markov chain lifting is studied to accelerate the convergence of distributed consensus, and two general pseudoalgorithms are presented. These pseudoalgorithms are then instantiated through a class of location-aided distributed averaging (LADA) algorithms for wireless networks, where nodes' coarse location information is used to construct nonreversible chains that facilitate distributed computing and cooperative processing. Our first LADA algorithm is designed for grid networks; for a k × k grid network, it achieves an ε-averaging time of O(klog(ε-1). Based on this algorithm, in a wireless network with transmission range r, an ε-averaging time of O(r-1 log(ε-1)) can be attained through a centralized algorithm. Subsequently, a distributed LADA algorithm is presented, achieving the same scaling law in averaging time as the centralized scheme in wireless networks for all r satisfying the connectivity requirement; the constructed chain also attains the optimal scaling law in terms of an important mixing metric, the fill time, in its class. Finally, a cluster-based LADA algorithm is proposed, which, requiring no central coordination, provides the additional benefit of reduced message complexity compared with the distributed LADA algorithm.