Near-optimal self-stabilising counting and firing squads

C. Lenzen, J. Rybicki, Distributed Computing (2018).

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Journal Article | Published | English
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Abstract
Consider a fully-connected synchronous distributed system consisting of n nodes, where up to f nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous C-counting problem, all nodes need to eventually agree on a counter that is increased by one modulo C in each round for given C>1. In the self-stabilising firing squad problem, the task is to eventually guarantee that all non-faulty nodes have simultaneous responses to external inputs: if a subset of the correct nodes receive an external “go” signal as input, then all correct nodes should agree on a round (in the not-too-distant future) in which to jointly output a “fire” signal. Moreover, no node should generate a “fire” signal without some correct node having previously received a “go” signal as input. We present a framework reducing both tasks to binary consensus at very small cost. For example, we obtain a deterministic algorithm for self-stabilising Byzantine firing squads with optimal resilience f<n/3, asymptotically optimal stabilisation and response time O(f), and message size O(log f). As our framework does not restrict the type of consensus routines used, we also obtain efficient randomised solutions.
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Date Published
2018-09-12
Journal Title
Distributed Computing
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Lenzen C, Rybicki J. Near-optimal self-stabilising counting and firing squads. Distributed Computing. 2018. doi:10.1007/s00446-018-0342-6
Lenzen, C., & Rybicki, J. (2018). Near-optimal self-stabilising counting and firing squads. Distributed Computing. https://doi.org/10.1007/s00446-018-0342-6
Lenzen, Christoph, and Joel Rybicki. “Near-Optimal Self-Stabilising Counting and Firing Squads.” Distributed Computing, 2018. https://doi.org/10.1007/s00446-018-0342-6.
C. Lenzen and J. Rybicki, “Near-optimal self-stabilising counting and firing squads,” Distributed Computing, 2018.
Lenzen C, Rybicki J. 2018. Near-optimal self-stabilising counting and firing squads. Distributed Computing.
Lenzen, Christoph, and Joel Rybicki. “Near-Optimal Self-Stabilising Counting and Firing Squads.” Distributed Computing, Springer, 2018, doi:10.1007/s00446-018-0342-6.
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