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Reaching approximate agreement in the presence of faults

Authors:

William E. WeihlAuthors Info & Claims

Journal of the ACM (JACM), Volume 33, Issue 3

Pages 499 - 516

https://doi.org/10.1145/5925.5931

Published: 01 May 1986 Publication History

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Abstract

This paper considers a variant of the Byzantine Generals problem, in which processes start with arbitrary real values rather than Boolean values or values from some bounded range, and in which approximate, rather than exact, agreement is the desired goal. Algorithms are presented to reach approximate agreement in asynchronous, as well as synchronous systems. The asynchronous agreement algorithm is an interesting contrast to a result of Fischer et al, who show that exact agreement with guaranteed termination is not attainable in an asynchronous system with as few as one faulty process. The algorithms work by successive approximation, with a provable convergence rate that depends on the ratio between the number of faulty processes and the total number of processes. Lower bounds on the convergence rate for algorithms of this form are proved, and the algorithms presented are shown to be optimal.

References

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Index Terms

Reaching approximate agreement in the presence of faults
1. Hardware
  1. Robustness
2. Networks
  1. Network protocols

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Reviews

Reviewer: Greg Speegle

The Byzantine generals problem is one of the most famous problems in computer science. The problem is for processes to reach agreement on some value despite the malicious effects of faulty processes. This paper presents a solution for a variant of this problem in which agreement is defined as all nonfaulty processes being within some previously defined bound. A solution is given for both the synchronous and asynchronous cases. The basic idea of the solution is to discard enough values from a set of messages that the range of responses is within the range generated by the nonfaulty processes. The most interesting aspect of this paper is the solid theoretical basis presented for the algorithms. This theoretical basis allows the authors to generate solutions for both asynchronous and synchronous communications without substantial changes to the algorithm itself. The only weakness of this paper is a lack of examples, which could clarify the theory and the algorithms. Otherwise, it is a strong paper that serves as a good example of solid techniques for solving distributed problems.

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Published In

Journal of the ACM Volume 33, Issue 3

July 1986

219 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/5925

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 1986

Published in JACM Volume 33, Issue 3

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https://doi.org/10.1016/j.conengprac.2024.106166
Yuan LIshii H(2025)Asynchronous approximate Byzantine consensus: A multi-hop relay method and tight graph conditionsAutomatica10.1016/j.automatica.2024.111908171(111908)Online publication date: Jan-2025
https://doi.org/10.1016/j.automatica.2024.111908
Delporte-Gallet CFauconnier HFraigniaud PRajsbaum STravers CKuznetsov PGelles ROlivetti D(2024)The Computational Power of Distributed Shared-Memory Models with Bounded-Size RegistersProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662789(310-320)Online publication date: 17-Jun-2024
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Abstract

References

Cited By

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Recommendations

Multidimensional approximate agreement in Byzantine asynchronous systems

Reaching Agreement in the Presence of Faults

Reaching Approximate Agreement with Mixed-Mode Faults

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