[2505.03627] Revisiting Lower Bounds for Two-Step Consensus

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Computer Science > Distributed, Parallel, and Cluster Computing

arXiv:2505.03627 (cs)

[Submitted on 6 May 2025 (v1), last revised 16 Jan 2026 (this version, v2)]

Title:Revisiting Lower Bounds for Two-Step Consensus

Authors:Fedor Ryabinin, Alexey Gotsman, Pierre Sutra<br>View a PDF of the paper titled Revisiting Lower Bounds for Two-Step Consensus, by Fedor Ryabinin and 2 other authors

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Abstract:A seminal result by Lamport shows that at least $\max\{2e+f+1,2f+1\}$ processes are required to implement partially synchronous consensus that tolerates $f$ process failures and can furthermore decide in two message delays under $e$ failures. This lower bound is matched by the classical Fast Paxos protocol. However, more recent practical protocols, such as Egalitarian Paxos, provide two-step decisions with fewer processes, seemingly contradicting the lower bound. We show that this discrepancy arises because the classical bound requires two-step decisions under a wide range of scenarios, not all of which are relevant in practice. We propose a more pragmatic condition for which we establish tight bounds on the number of processes required. Interestingly, these bounds depend on whether consensus is implemented as an atomic object or a decision task. For consensus as an object, $\max\{2e+f-1,2f+1\}$ processes are necessary and sufficient for two-step decisions, while for a task the tight bound is $\max\{2e+f, 2f+1\}$.

Comments:<br>Extended version of a paper in the 2025 ACM Symposium on Principles of Distributed Computing (PODC)

Subjects:

Distributed, Parallel, and Cluster Computing (cs.DC)

Cite as:<br>arXiv:2505.03627 [cs.DC]

(or<br>arXiv:2505.03627v2 [cs.DC] for this version)

https://doi.org/10.48550/arXiv.2505.03627

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arXiv-issued DOI via DataCite

Submission history<br>From: Alexey Gotsman [view email]<br>[v1]<br>Tue, 6 May 2025 15:28:05 UTC (46 KB)

[v2]<br>Fri, 16 Jan 2026 09:36:44 UTC (44 KB)

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