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International Symposium on Stabilization, Safety, and Security of Distributed Systems

SSS 2017: Stabilization, Safety, and Security of Distributed Systems pp 109–125Cite as

An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10616))

Abstract

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay ’94 – in the model, an omniscient adversary can corrupt up to f nodes in each round, and at the beginning of each round, faults may “move” in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. ’16 proposed a simple iterative approximate consensus algorithm which requires at least \(4f+1\) nodes. This paper proposes a novel technique of using “confession” (a mechanism to allow other nodes to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only \(\lceil 7f/2\rceil + 1\) nodes, an \(\lfloor f/2 \rfloor \) improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms.

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Notes

  1. 1.

    Using the technique from [1], nodes can also estimate the number of required rounds and decide when to “output” the state variable v.

  2. 2.

    There are other scenarios not discussed in the proof for brevity; however, m is the only value that works for each of the scenarios.

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Authors and Affiliations

  1. Computer Science, Boston College, Boston, MA, USA

    Lewis Tseng

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  1. Lewis Tseng
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Correspondence to Lewis Tseng .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Paul Spirakis

  2. Chalmers University of Technology, Gothenburg, Sweden

    Philippas Tsigas

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Tseng, L. (2017). An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-69084-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69083-4

  • Online ISBN: 978-3-319-69084-1

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