Gracefully degrading consensus and k -set agreement in directed dynamic networks

Biely, Martin; Robinson, Peter; Schmid, Ulrich; Schwarz, Manfred; Winkler, Kyrill

doi:10.1016/j.tcs.2018.02.019

Cited by 30 publications

(56 citation statements)

References 29 publications

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“…Our topological results shed some new light on the now standard technique of bivalence-based impossibility proofs introduced in the celebrated FLP paper [10], which have been generalized in [17] and used in many different contexts: Our results reveal that the forever bivalent executions constructed inductively in bivalence proofs such as [22,23] and [6,24] are just the common limit of two infinite sequence of executions α 0 , α 1 , . .…”

Section: Bivalence-based Impossibilitiesmentioning

confidence: 72%

“…[15]. For example, eventually stabilizing message adversaries like the vertex-stable source component (VSSC) message adversaries described in [6,24] guarantee that some rounds with "good" communication graphs (a VSSC, which allows a consensus algorithm to terminate) occur eventually. However, limits of these sequences, in which the VSSC would never appear, are of course not in the message adversary.…”

Section: Introductionmentioning

confidence: 99%

“…We prove that consensus can be solved, using our universal algorithm, if and only if the ε-approximations are broadcastable for some ε. For non-compact message adversaries (like [6,9,24]), the ε-approximation does not work, so one needs to apply our universal algorithm based on the connected components directly.…”

Section: Introductionmentioning

confidence: 99%

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Topological Characterization of Consensus under General Message Adversaries

Nowak

Schmid

Winkler

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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In this paper, we provide a rigorous characterization of consensus solvability in synchronous directed dynamic networks controlled by an arbitrary message adversary using point-set topology: We extend the approach introduced by Alpern and Schneider in 1985 by introducing two novel topologies on the space of infinite executions: the process-view topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. We establish some simple but powerful topological results, which not only lead to a topological explanation of bivalence arguments, but also provide necessary and sufficient topological conditions on the admissible graph sequences of a message adversary for solving consensus. In particular, we characterize consensus solvability in terms of connectivity of the set of admissible graph sequences. For non-compact message adversaries, which are not limit-closed in the sense that there is a convergent sequence of graph sequences whose limit is not permitted, this requires the exclusion of all "fair" and "unfair" limit sequences that coincide with the forever bivalent runs constructed in bivalence proofs. For both compact and non-compact message adversaries, we also provide tailored characterizations of consensus solvability, i.e., tight conditions for impossibility and existence of algorithms, based on the broadcastability of the connected components of the set of admissible graph sequences.

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Section: Bivalence-based Impossibilitiesmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Topological Characterization of Consensus under General Message Adversaries

Nowak

Schmid

Winkler

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

Self Cite

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“…To the best of our knowledge, only three papers have studied the problem of k-set agreement in dynamic systems. Biely et al in [2] presented an algorithm for gracefully degrading consensus in synchronous dynamic networks. The algorithm solves consensus if the network conditions allow for it, and falls back on solving k-set agreement, otherwise.…”

Section: Agreement In Dynamic Systemsmentioning

confidence: 99%

“…sume synchronous communications (as in [1], [2], [3], [4]) or make strong assumptions on the number of process failures [5].…”

Section: Introductionmentioning

confidence: 99%

Solving k-Set Agreement Using Failure Detectors in Unknown Dynamic Networks

Jeanneau

Rieutord

Arantes

et al. 2017

IEEE Trans. Parallel Distrib. Syst.

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The failure detector abstraction has been used to solve agreement problems in asynchronous systems prone to crash failures, but so far it has mostly been used in static and complete networks. This paper aims to adapt existing failure detectors in order to solve agreement problems in unknown, dynamic systems. We are specifically interested in the k-set agreement problem. The problem of k-set agreement is a generalization of consensus where processes can decide up to k different values. Although some solutions to this problem have been proposed in dynamic networks, they rely on communication synchrony or make strong assumptions on the number of process failures. In this paper we consider unknown dynamic systems modeled using the formalism of Time-Varying Graphs, and extend the definition of the existing ΠΣx,y failure detector to obtain the ΠΣ ⊥,x,y failure detector, which is sufficient to solve k-set agreement in our model. We then provide an implementation of this new failure detector using connectivity and message pattern assumptions. Finally, we present an algorithm using ΠΣ ⊥,x,y to solve k-set agreement.

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