Brief Announcement: Deterministic Consensus and Checkpointing with Crashes: Time and Communication Efficiency

Chlebus, Bogdan S.; Kowalski, Dariusz R.; Olkowski, Jan

doi:10.1145/3519270.3538471

Cited by 4 publications

(1 citation statement)

References 15 publications

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“…There are a number of solutions optimizing consensus in incomplete topologies [2,6,17,23,24]. Chlebus et al [6] optimize the speed of achieving Byzantine consensus in arbitrary topologies. The connectivity is subject to 2f +1 bound.…”

Section: Introductionmentioning

confidence: 99%

Consensus on Unknown Torus with Dense Byzantine Faults

Oglio¹,

Hood²,

Sharma³

et al. 2023

Preprint

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We present a solution to consensus on a torus with Byzantine faults. Any solution to classic consensus that is tolerant to f Byzantine faults requires 2f + 1 node-disjoint paths. Due to limited torus connectivity, this bound necessitates spatial separation between faults. Our solution does not require this many disjoint paths and tolerates dense faults.Specifically, we consider the case where all faults are in the one column. We address the version of consensus where only processes in fault-free columns must agree. We prove that even this weaker version is not solvable if the column may be completely faulty. We then present a solution for the case where at least one row is fault-free. The correct processes share orientation but do not know the identities of other processes or the torus dimensions. The communication is synchronous.To achieve our solution, we build and prove correct an all-to-all broadcast algorithm BAT that guarantees delivery to all processes in fault-free columns. We use this algorithm to solve our weak consensus problem. Our solution, CBAT , runs in O(H + W ) rounds, where H and W are torus height and width respectively. We extend our consensus solution to the fixed message size model where it runs in O(H 3 W 2 ) rounds. Our results are immediately applicable if the faults are located in a single row, rather than a column.

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