Chaotic relaxation

Chazan, D.; Miranker, Willard L.

doi:10.1016/0024-3795(69)90028-7

Cited by 481 publications

(268 citation statements)

References 3 publications

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“…On the practical side our results are primarily relevant to asynchronous distributed computation and chaotic relaxation algorithms [1,2,3,8,11,12] and other types of asynchronous distributed systems [4,22]. In particular, they suggest a unified methodology for analyzing and designing distributed algorithms.…”

Section: Introductionmentioning

confidence: 87%

“…Several authors have obtained sufficient conditions for convergence of asynchronous distributed or chaotic relaxation algorithms [1,2,3,8,11,12,18,19], for linear and nonlinear problems. Chaotic relaxation differs from the relaxation algorithms mentioned in the preceding paragraph, in that a possibility of using outdated values of the variables is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…Chaotic relaxation differs from the relaxation algorithms mentioned in the preceding paragraph, in that a possibility of using outdated values of the variables is introduced. In fact, Chazan and Miranker obtained ncessary and sufficient conditions for convergence, for the case of chaotic relaxation algorithms for the solution of linear equations [8]. There are no necessary conditions for convergence, however, for the case of nonlinear iterative processes.…”

Section: Introductionmentioning

confidence: 99%

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On the stability of asynchronous iterative processes

Tsitsiklis

1987

Math. Systems Theory

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We consider an iterative process in which one out of a finite set of possible operators is applied at each iteration. We obtain necessary and sufficient conditions for convergence to a common fixed point of these operators, when the order at which different operators are applied is left completely free, except for the requirement that each operator is applied infinitely many times. The theory developed is similar in spirit to Lyapunov stability theory. We also derive some very different, qualitatively, results for partially asynchronous iterative processes, that is for the case where certain requirements are imposed on the order at which the different operators are applied.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the stability of asynchronous iterative processes

Tsitsiklis

1987

Math. Systems Theory

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“…The formulation involves a far more flexible type of asynchronism that can be obtained with the use of synchronizers [4]. Algorithmic convergence is often difficult to establish for chaotic models, but powerful results are now available to aid in this process [14,18,21]. The algorithm given here is more complex than a related algorithm for strictly convex arc costs [14], and requires a novel method of convergence proof.…”

Section: Asynchronous Implementation Of E-relaxationmentioning

confidence: 99%

Dual coordinate step methods for linear network flow problems

Bertsekas

Eckstein

1988

Mathematical Programming

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We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of e-complementary slackness, and most do not explicitly manipulate any "global" objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the e-relaxation algorithm for the minimum-cost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement e-relaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.

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“…This computation is readily formulated in asynchronous iteration [32]. We have implemented a distributed, dynamic computation [27] of pageranks in CoorSet.…”

Section: Distributed Computation Of Google Pageranksmentioning

confidence: 99%

CoorSet: A Development Environment for Associatively Coordinated Components

Kane

Browne

2004

Lecture Notes in Computer Science

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Abstract.A development environment for applications specified in an extended version of a previously developed coordination model based on associatively broadcast interactions is presented. The previous associative broadcast coordination model is extended to incorporate more complex specifications for interactions including multiple message interactions and fault-tolerance by replication. The runtime system is extended to facilitate construction and application of distributed implementation of coordination systems. An interface definition language based on the extended coordination model and a compiler for the language are defined and described. Three example applications, a generalized readers/writers problem including replication, a "greedy reuse" algorithm and a distributed computation Google pageranks are presented.

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Chaotic relaxation

Cited by 481 publications

References 3 publications

On the stability of asynchronous iterative processes

On the stability of asynchronous iterative processes

Dual coordinate step methods for linear network flow problems

CoorSet: A Development Environment for Associatively Coordinated Components

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