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149
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.
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.
Distributed stochastic subgradient projection algorithms for convex optimization
 Journal of Optimization Theory and Applications
, 2010
"... Abstract. We consider a distributed multiagent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the iterates to its neighbors. Then, each agent combines ..."
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Cited by 87 (1 self)
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Abstract. We consider a distributed multiagent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the iterates to its neighbors. Then, each agent combines weighted averages of the received iterates with its own iterate, and adjusts the iterate by using subgradient information (known with stochastic errors) of its own function and by projecting onto the constraint set. The goal of this paper is to explore the effects of stochastic subgradient errors on the convergence of the algorithm. We first consider the behavior of the algorithm in mean, and then the convergence with probability 1 and in mean square. We consider general stochastic errors that have uniformly bounded second moments and obtain bounds on the limiting performance of the algorithm in mean for diminishing and nondiminishing stepsizes. When the means of the errors diminish, we prove that there is mean consensus between the agents and mean convergence to the optimum function value for diminishing stepsizes. When the mean errors diminish sufficiently fast, we strengthen the results to consensus and convergence of the iterates to an optimal solution with probability 1 and in mean square.
Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication
 IEEE Transactions on Information Theory
, 2012
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Incremental stochastic subgradient algorithms for convex optimization
 SIAM J. OPTIM
, 2008
"... In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a ..."
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Cited by 49 (7 self)
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In this paper we study the effect of stochastic errors on two constrained incremental subgradient algorithms. We view the incremental subgradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental subgradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the subgradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing stepsize is used. We also obtain almost sure bounds on the algorithm’s performance when a constant stepsize is used. We then consider the Markov randomized incremental subgradient method, which is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant stepsizes, respectively.
Average consensus on networks with quantized communication
 Intern. Journ. on Nonlinear and Robust Control
, 2008
"... communication ..."
Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes
"... algorithm to locate sensors (with unknown locations) in 1, with respect to a minimal number of +1anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fu ..."
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Cited by 39 (6 self)
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algorithm to locate sensors (with unknown locations) in 1, with respect to a minimal number of +1anchors with known locations. The sensors and anchors, nodes in the network, exchange data with their neighbors only; no centralized data processing or communication occurs, nor is there a centralized fusion center to compute the sensors ’ locations. DILOC uses the barycentric coordinates of a node with respect to its neighbors; these coordinates are computed using the Cayley–Menger determinants, i.e., the determinants of matrices of internode distances. We show convergence of DILOC by associating with it an absorbing Markov chain whose absorbing states are the states of the anchors. We introduce a stochastic approximation version extending DILOC to random environments, i.e., when the communications among nodes is noisy, the communication links among neighbors may fail at random times, and the internodes distances are subject to errors. We show a.s. convergence of the modified DILOC and characterize the error between the true values of the sensors ’ locations and their final estimates given by DILOC. Numerical studies illustrate DILOC under a variety of deterministic and random operating conditions. Index Terms—Absorbing Markov chain, anchor, barycentric coordinates, Cayley–Menger determinant, distributed iterative
Sensor networks with random links: Topology design for distributed consensus
 IEEE Trans. on Signal Processing, http://arxiv.org/PS cache/arxiv/pdf/0704/0704.0954v1.pdf
, 2007
"... In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signaltonoise ratio (SNR) is usually a ..."
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Cited by 38 (15 self)
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In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signaltonoise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a nonrandom network at a fraction of the communication cost.
Gossip consensus algorithms via quantized communication
, 2009
"... This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise “gossip” communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literatur ..."
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Cited by 33 (5 self)
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This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise “gossip” communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.