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Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 133 (3 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
Gossip algorithms for distributed signal processing
 PROCEEDINGS OF THE IEEE
, 2010
"... Gossip algorithms are attractive for innetwork processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the co ..."
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Cited by 116 (30 self)
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Gossip algorithms are attractive for innetwork processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmittedmessages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.
Geographic Gossip: Efficient Aggregation for Sensor Networks
 in Proc. Information Processing in Sensor Networks (IPSN
, 2006
"... Gossip algorithms for aggregation have recently received significant attention for sensor network applications because of their simplicity and robustness in noisy and uncertain environments. However, gossip algorithms can waste significant energy by essentially passing around redundant information m ..."
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Cited by 111 (5 self)
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Gossip algorithms for aggregation have recently received significant attention for sensor network applications because of their simplicity and robustness in noisy and uncertain environments. However, gossip algorithms can waste significant energy by essentially passing around redundant information multiple times. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is caused by slow mixing times of random walks on those graphs. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing a simple resampling method, we can demonstrate substantial gains over previously proposed gossip protocols. In particular, for random geometric graphs, our algorithm computes the true average to accuracy 1/n a using O(n 1.5 √ log n) radio transmissions, which reduces the energy consumption by a algorithms. q n factor over standard gossip log n
WalkSums and Belief Propagation in Gaussian Graphical Models
 Journal of Machine Learning Research
, 2006
"... We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edg ..."
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Cited by 101 (16 self)
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We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlation coefficients. This representation holds for a large class of Gaussian graphical models which we call walksummable. We give a precise characterization of this class of models, and relate it to other classes including diagonally dominant, attractive, nonfrustrated, and pairwisenormalizable. We provide a walksum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. The walksum perspective leads to a better understanding of Gaussian belief propagation and to stronger results for its convergence in loopy graphs.
Broadcast gossip algorithms for consensus
 IEEE TRANS. SIGNAL PROCESS
, 2009
"... Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute the (possib ..."
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Cited by 93 (7 self)
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Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the “mixing parameter ” on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results.
Consensusbased decentralized auctions for robust task allocation
 IEEE Transactions on Robotics
, 2009
"... Abstract—This paper addresses task allocation to coordinate a fleet of autonomous vehicles by presenting two decentralized algorithms: the consensusbased auction algorithm (CBAA) and its generalization to the multiassignment problem, i.e., the consensusbased bundle algorithm (CBBA). These algorit ..."
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Cited by 79 (28 self)
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Abstract—This paper addresses task allocation to coordinate a fleet of autonomous vehicles by presenting two decentralized algorithms: the consensusbased auction algorithm (CBAA) and its generalization to the multiassignment problem, i.e., the consensusbased bundle algorithm (CBBA). These algorithms utilize a marketbased decision strategy as the mechanism for decentralized task selection and use a consensus routine based on local communication as the conflict resolution mechanism to achieve agreement on the winning bid values. Under reasonable assumptions on the scoring scheme, both of the proposed algorithms are proven to guarantee convergence to a conflictfree assignment, and it is shown that the converged solutions exhibit provable worstcase performance. It is also demonstrated that CBAA and CBBA produce conflictfree feasible solutions that are robust to both inconsistencies in the situational awareness across the fleet and variations in the communication network topology. Numerical experiments confirm superior convergence properties and performance when compared with existing auctionbased taskallocation algorithms. Index Terms—Distributed robot systems, networked robots, task allocation for multiple mobile robots. I.
Geographic gossip: Efficient averaging for sensor networks
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For re ..."
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Cited by 65 (8 self)
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Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of and, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy using 1 5 1 ( ( log) log) radio transmissions, which yields a log factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.
Belief consensus and distributed hypothesis testing in sensor networks
 Network Embedded Sensing and Control. (Proceedings of NESC’05 Worskhop), volume 331 of Lecture Notes in Control and Information Sciences
, 2006
"... Summary. In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the averageconsensus algorithm of OlfatiSaber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connec ..."
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Cited by 56 (1 self)
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Summary. In this paper, we address distributed hypothesis testing (DHT) in sensor networks and Bayesian networks using the averageconsensus algorithm of OlfatiSaber & Murray. As a byproduct, we obtain a novel belief propagation algorithm called Belief Consensus. This algorithm works for connected networks with loops and arbitrary degree sequence. Belief consensus allows distributed computation of products of n beliefs (or conditional probabilities) that belong to n different nodes of a network. This capability enables distributed hypothesis testing for a broad variety of applications. We show that this belief propagation admits a Lyapunov function that quantifies the collective disbelief in the network. Belief consensus benefits from scalability, robustness to link failures, convergence under variable topology, asynchronous features of averageconsensus algorithm. Some connections between smallword networks and speed of convergence of belief consensus are discussed. A detailed example is provided for distributed detection of multitarget formations in a sensor network. The entire network is capable of reaching a common set of beliefs associated with correctness of different hypotheses. We demonstrate that our DHT algorithm successfully identifies a test formation in a network of sensors with selfconstructed statistical models. Key words: distributed hypothesis testing, multitarget tracking, Bayesian networks, average consensus, belief propagation, sensor networks, smallworld networks 1
Distributed average consensus using probabilistic quantization
, 2007
"... In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distribut ..."
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Cited by 52 (6 self)
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In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus, which is one of the quantization values. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios. Index Terms — Distributed algorithms, average consensus, sensor networks
Distributed average consensus with dithered quantization
 the IEEE Transactions of Signal Processing
, 2008
"... In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distribut ..."
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Cited by 52 (1 self)
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In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimumlength interval containing the node values. We reveal that the length of this interval is a monotonically non–increasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.