Results 1  10
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18
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 208 (5 self)
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Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of “gossip ” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the socalled Preferential Connectivity (PC) model.
A scheme for robust distributed sensor fusion based on average consensus
 Proceedings of the International Conference on Information Processing in Sensor Networks (IPSN
, 2005
"... Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximum ..."
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Cited by 140 (3 self)
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Abstract — We consider a network of distributed sensors, where each sensor takes a linear measurement of some unknown parameters, corrupted by independent Gaussian noises. We propose a simple distributed iterative scheme, based on distributed average consensus in the network, to compute the maximumlikelihood estimate of the parameters. This scheme doesn’t involve explicit pointtopoint message passing or routing; instead, it diffuses information across the network by updating each node’s data with a weighted average of its neighbors ’ data (they maintain the same data structure). At each step, every node can compute a local weighted leastsquares estimate, which converges to the global maximumlikelihood solution. This scheme is robust to unreliable communication links. We show that it works in a network with dynamically changing topology, provided that the infinitely occurring communication graphs are jointly connected. I.
On Asynchronous Iterations
, 2000
"... Asynchronous iterations arise naturally parallel computers wants minimize times. This paper reviews certain models asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains applications presented. These include nonsingular linear systems, ..."
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Cited by 57 (11 self)
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Asynchronous iterations arise naturally parallel computers wants minimize times. This paper reviews certain models asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains applications presented. These include nonsingular linear systems, nonlinear systems, initial value problems.
Infinite Products And Paracontracting Matrices
 Electronic Journal of Linear Algebra
, 1997
"... Introduction. In the investigation of chaotic iteration procedures for linear consistent systems matrices which are paracontracting with respect to some vector norm play an important role. It was shown in [EKN], that if A 1 ; : : : ; Am are finitely many kbyk complex matrices which are paracont ..."
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Cited by 13 (3 self)
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Introduction. In the investigation of chaotic iteration procedures for linear consistent systems matrices which are paracontracting with respect to some vector norm play an important role. It was shown in [EKN], that if A 1 ; : : : ; Am are finitely many kbyk complex matrices which are paracontracting with respect to the same norm, then for any sequence d i ; 1 d i m; i = 1; 2; : : : and any x 0 the sequence x i+1 = A d i x i i = 1; 2; : : : is convergent. In particular A (d) = lim i!1 A d i : : : A d1 exists for all sequences fd i g
Stability and Paracontractivity of Discrete Linear Inclusions
 Linear Algebra Appl
, 1999
"... We study stability properties of a finite set Sigma of n×nmatrices such as paracontractivity, BV and LCPstability, and their relations to each other. The conjecture on equivalence of paracontractivity and LCPstability is proved. Moreover, we prove the equivalence of the uniform BVstabilit ..."
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Cited by 11 (1 self)
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We study stability properties of a finite set Sigma of n×nmatrices such as paracontractivity, BV and LCPstability, and their relations to each other. The conjecture on equivalence of paracontractivity and LCPstability is proved. Moreover, we prove the equivalence of the uniform BVstability and the property of vanishing length of steps of any trajectory of Sigma.
Asynchronous TwoStage Iterative Methods
, 1994
"... this paper; see [12], [16], and the references given therein. We point out that, since the number of inner iterations may vary from block to block, the convergence results in Baudet [1] or Chazan and Miranker [5] cannot be applied to our situation. In Sect. 2, we derive two new convergence results f ..."
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Cited by 11 (3 self)
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this paper; see [12], [16], and the references given therein. We point out that, since the number of inner iterations may vary from block to block, the convergence results in Baudet [1] or Chazan and Miranker [5] cannot be applied to our situation. In Sect. 2, we derive two new convergence results for block twostage iterative methods. We then investigate asynchronous variations of our twostage methods. These asynchronous methods arise naturally in parallel computations if one tries to reduce idle times of the processors. In Sects. 3 and 4, we introduce two different asynchronous models for block twostage methods and investigate their convergence. As our major result, we establish convergence for both asynchronous models under the same conditions as those for the synchronous method. In the rest of this section we present some notation, definitions and preliminary results which we refer to later. We say that a vector x is nonnegative (positive), denoted x 0 (x ? 0), if all its entries are nonnegative (positive). Similarly, a matrix B is said to be nonnegative, denoted B O, if all its entries are nonnegative or, equivalently, if it leaves invariant the set of all nonnegative vectors. We compare two matrices
Convergence of infinite products of matrices and innerouter iteration schemes,” Electron
 Trans. Numer. Anal
, 1994
"... Dedicated to Wilhelm Niethammer on the occasion of his sixtieth birthday. Abstract. We develop conditions under which a product ∏∞ i=0 Ti of matrices chosen from a possibly infinite set of matrices S = {Tjj ∈ J} converges. We obtain the following conditions which are sufficient for the convergence ..."
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Cited by 10 (0 self)
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Dedicated to Wilhelm Niethammer on the occasion of his sixtieth birthday. Abstract. We develop conditions under which a product ∏∞ i=0 Ti of matrices chosen from a possibly infinite set of matrices S = {Tjj ∈ J} converges. We obtain the following conditions which are sufficient for the convergence of the product: There exists a vector norm such that all matrices in S are nonexpansive with respect to this norm and there exists a subsequence {ik} ∞ k=0 of the sequence of the nonnegative integers such that the corresponding sequence of operators { } ∞ Tik k=0 converges to an operator which is paracontracting with respect to this norm. We deduce the continuity of the limit of the product of matrices as a function of the sequences {ik} ∞ k=0. But more importantly, we apply our results to the question of the convergence of inner–outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.
On Communication Requirements for Multiagent Consensus Seeking
 Proceedings of the Workshop on Networked Embedded Sensing and Control
, 2005
"... Several consensus protocols have been proposed in the literature and their convergence properties studied via a variety of methods. In all these methods, the communication topologies play a key role in the convergence of consensus processes. The goal of this paper is two fold. First, we explore comm ..."
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Cited by 9 (1 self)
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Several consensus protocols have been proposed in the literature and their convergence properties studied via a variety of methods. In all these methods, the communication topologies play a key role in the convergence of consensus processes. The goal of this paper is two fold. First, we explore communication topologies, as implied by the communication assumptions, that lead to consensus among agents. For this, several important results in the literature are examined and the focus is on different classes of communication assumptions being made, such as synchronism, connectivity, and direction of communication. In the latter part of this paper, we show that the confluent iteration graph unifies various communication assumptions and proves to be fundamental in understanding the convergence of consensus processes. In particular, based on asynchronous iteration methods for nonlinear paracontractions, we establish a new result which shows that consensus is reachable under directional, timevarying and asynchronous topologies with nonlinear protocols. This result extends the existing ones in the literature and have many potential applications. 1
On the Convergence of Asynchronous Iteration Methods for Nonlinear Paracontractions and Consistent Linear Systems
, 1998
"... In [6] the authors introduced the concept of paracontracting operators for fixed point problems and their solution with asynchronous iteration methods. We will extend their results essentially with respect to the criterion of contraction for the pool of operators, from which a common fixed point is ..."
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Cited by 7 (0 self)
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In [6] the authors introduced the concept of paracontracting operators for fixed point problems and their solution with asynchronous iteration methods. We will extend their results essentially with respect to the criterion of contraction for the pool of operators, from which a common fixed point is searched and a more general kind of asynchronous iterations, which we will call confluent. As an application of this theory, we will consider asynchronous iteration methods for consistent linear systems Ax = b ; where A is a singular Mmatrix. In [7] Lubachevski and Mitra investigated asynchronous iteration methods for the Perronvector problem, e.g. determining a positive solution of Tx = ae(T ) x ; where T is an irreducible nonnegative matrix and its spectral radius is known. We will show that we can extend their results by using the developed theory of paracontractions and confluence to the reducibleaffine case which arises, if we have those kind of linear systems. Key words: Asynchron...
Distributed Average Consensus with TimeVarying Metropolis Weights
, 2006
"... Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the value ..."
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Cited by 7 (0 self)
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Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weights used in each step. We show that with these weights, the values at every node converge to the average, provided the infinitely occurring communication graphs are jointly connected.