Abstract
We introduce a novel two-step approach for developing a distributed consensus algorithm, which does not require the designer to identify and exploit intricacies of the underlying system model explicitly. In a first step, which is typically done off-line only once, labels representing valid decision values (valencies) are assigned to suitable prefixes of all possible runs. The challenge here is to assign them consistently for indistinguishable runs. The second step consists in deploying a simple generic distributed consensus algorithm, which just uses the previously computed labeling. If it observes that all runs that may lead to a local state that is indistinguishable from the current local state have the same label, it decides on the value determined by this label, otherwise it has to keep on checking. We demonstate the power of our approach by developing a new and asymptotically optimal consensus algorithm for dynamic networks under eventually stabilizing message adversaries for arbitrary system sizes.
K. Winkler—Supported by the Vienna Science and Technology Fund (WWTF), grant number ICT19-045 (WHATIF), 2020–2024, and by the Austrian Science Fund (FWF) under project ADynNet (P28182).
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Notes
- 1.
It may require infinite space, however, for storing the system specification required for constructing the admissible runs.
- 2.
Full-information protocols, where everyone stores and forwards its entire view to everybody all the time, simplify the presentation and align perfectly with our goal of designing optimal algorithms.
- 3.
Note that, in contrast to [10], our process time graphs do not incorporate initial values, since we usually start from the same initial configuration.
- 4.
Obviously, just communicating and keeping track of the input values received so far would also suffice.
- 5.
Technically, the message adversary from [13] has an additional parameter, the dynamic diameter D, which we will neglect here for simplicity. Since it was shown in [4, Corollary 1] that \(D < n\), we will just conservatively assume \(D=n-1\). This has the downside of the lower bound established in Theorem 15 being formally weaker in those cases where \(D = o(n)\).
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Winkler, K., Schmid, U., Nowak, T. (2021). Valency-Based Consensus Under Message Adversaries Without Limit-Closure. In: Bampis, E., Pagourtzis, A. (eds) Fundamentals of Computation Theory. FCT 2021. Lecture Notes in Computer Science(), vol 12867. Springer, Cham. https://doi.org/10.1007/978-3-030-86593-1_32
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