Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Distributed Algorithms
Local Divergence of Markov Chains and the Analysis of Iterative Load-Balancing Schemes
FOCS '98 Proceedings of the 39th 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
A scheme for robust distributed sensor fusion based on average consensus
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Distributed average consensus with least-mean-square deviation
Journal of Parallel and Distributed Computing
Differential nested lattice encoding for consensus problems
Proceedings of the 6th international conference on Information processing in sensor networks
Automatica (Journal of IFAC)
Distributed Average Consensus using Probabilistic Quantization
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Sensor Networks With Random Links: Topology Design for Distributed Consensus
IEEE Transactions on Signal Processing - Part II
Geographic Gossip: Efficient Averaging for Sensor Networks
IEEE Transactions on Signal Processing
A theory of nonsubtractive dither
IEEE Transactions on Signal Processing
Consensus in Ad Hoc WSNs With Noisy Links—Part I: Distributed Estimation of Deterministic Signals
IEEE Transactions on Signal Processing
Distributed Average Consensus With Dithered Quantization
IEEE Transactions on Signal Processing - Part I
IEEE Transactions on Information Theory
Randomized consensus algorithms over large scale networks
IEEE Journal on Selected Areas in Communications
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We consider consensus algorithms in their most general setting and provide conditions under which such algorithms are guaranteed to converge, almost surely, to a consensus. Let {A(t), B(t)} ∈ RN×N be (possibly) stochastic, nonstationary matrices and {x(t), m(t)} ∈ RN×1 be state and perturbation vectors, respectively. For any consensus algorithm of the form x(t + 1) = A(t)x(t) + B(t)m(t), we provide conditions under which consensus is achieved almost surely, i.e., Pr{limt→∞ x(t) = c1} = 1 for some c ∈ R. Moreover, we show that this general result subsumes recently reported results for specific consensus algorithms classes, including sum-preserving, nonsum-preserving, quantized, and noisy gossip algorithms. Also provided are the ε-converging time for any such converging iterative algorithm, i.e., the earliest time at which the vector x(t) is ε close to consensus, and sufficient conditions for convergence in expectation to the average of the initial node measurements. Finally, mean square error bounds of any consensus algorithm of the form discussed above are presented.