Revisiting simultaneous consensus with crash failures

Moses, Yoram; Raynal, Michel

doi:10.1016/j.jpdc.2009.01.001

Cited by 13 publications

(11 citation statements)

References 15 publications

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“…Roughly speaking, our algorithm is obtained by running a condition-based algorithm that is based on [14], that runs for t + 1 − δ rounds in parallel with a simultaneous consensus algorithm based on [3,12], that in turn decides in t + 1 − D rounds, where D depends on the failure pattern. If D ≥ δ then the latter algorithm halts first, and the decision value that it produces is adopted.…”

Section: Content Of the Papermentioning

confidence: 99%

“…The proof relies on notions introduced in [3,10,12]. We are unable to present the definitions and the proof in the main text due to page limitation.…”

Section: On the Optimality Of The Algorithm: T + 1 − Min(d δ) Is A Lmentioning

confidence: 99%

“…It is shown in [2,12] that the earliest round number at the end of which a common decision can be simultaneously taken is RS t,F = (t + 1) − D where D is a non-negative integer whose value depends on the actual failure pattern F . 1 More precisely, let C[r] be the set of the processes that are seen as crashed by (at least) one of the processes that survive (i.e., do not crash before the end of) round r. For any r, let d r = max(0, |C[r]| − r).…”

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confidence: 99%

“…So, when considering the bound (t + 1) − D, D represents the number of rounds that could be saved with respect to the worst case t + 1 bound, while guaranteeing simultaneous agreement. Algorithms that solve simultaneous consensus optimally are described in [3,12]. It is interesting to notice that the greatest values of D are obtained when many processes crash early.…”

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confidence: 99%

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No Double Discount: Condition-Based Simultaneity Yields Limited Gain

Moses

Raynal

2008

Lecture Notes in Computer Science

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Abstract:Assuming each process proposes a value, the consensus problem requires the non-faulty processes to agree on the same value that has to be a proposed value. Solutions to the consensus problem in synchronous systems are based on the round-based model, namely, the progress of the processes is according to synchronous rounds. Simultaneous consensus requires that the non-faulty processes decide not only on the same value, but decide during the very same round. It has been shown by Dwork and Moses that, in a synchronous system prone to t process crashes, the earliest round at which a common decision can be simultaneously obtained is (t + 1) − D where D is a non-negative integer determined by the actual failure pattern F .The condition-based approach to solve consensus assumes that the input vector belongs to a set C (a set of input vectors satisfying a property called legality). Interestingly, the conditions for synchronous consensus define a hierarchy of sets of conditions S This paper considers the synchronous condition-based consensus problem with simultaneous decision. It first presents a simple algorithm that directs the processes to decide simultaneously at the end of the round RS t,d,F = min((t + 1) − D, d + 1) (i.e., RS t,d,F = (t + 1) − max(D, δ) with δ = t − d). The paper then shows that RS t,d,F is a lower bound for the condition-based simultaneous consensus problem. It thus follows that the algorithm designed is optimal in each and every run, and not just in the worst case: For every choice of failure pattern by the adversary (and every input configuration), the algorithm reaches simultaneous as fast as any correct algorithm could do under the same conditions. This shows that, contrary to what could be hoped, when considering condition-based consensus with simultaneous decision, we can benefit from the best of both actual worlds (either the failure world when RS t,d,F = (t + 1) − D, or the condition world when RS t,d,F = d + 1), but we cannot benefit from the sum of savings offered by both. Only one discount applies. Key-words:Agreement problem, Condition-based agreement, Consensus, Distributed algorithm, Early decision, Lower bound, Modularity, Process crash failure, Round-based computation model, Simultaneity, Synchronous message-passing system. Utiliser les conditions pour une décision simultanée donne peu de gain Résumé : Ce rapport montre qu'utiliser les conditions pour une décision simultanée ne donne qu'un gain limité.

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Section: Content Of the Papermentioning

confidence: 99%

“…The proof relies on notions introduced in [3,10,12]. We are unable to present the definitions and the proof in the main text due to page limitation.…”

Section: On the Optimality Of The Algorithm: T + 1 − Min(d δ) Is A Lmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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No Double Discount: Condition-Based Simultaneity Yields Limited Gain

Moses

Raynal

2008

Lecture Notes in Computer Science

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“…In the language of [MR09], we say that round k is premature in a run r = A[ ı, F ] if k < t+1−W (F ), since we shall see that no nontrivial fact can be be common knowledge at the end of a premature round. Specifically, the analysis of connectivity in the similarity graph performed in [DM90] showed the following.…”

Section: Wastementioning

confidence: 99%

Transforming worst-case optimal solutions for simultaneous tasks into all-case optimal solutions

Herlihy

Moses

Tuttle

2011

Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

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Decision tasks require that nonfaulty processes make decisions based on their input values. Simultaneous decision tasks require that nonfaulty processes decide in the same round. Most decision tasks have known worst-case lower bounds. Most also have known worst-case optimal protocols that halt in the number of rounds given by the worst-case lower bound, and some have early-stopping protocols that can halt earlier than the worst-case lower bound (sometimes in as early as two rounds). We consider what might be called earliest-possible protocols for simultaneous decision tasks. We present a new technique that converts worst-case optimal decision protocols into all-case optimal simultaneous decision protocols: For every behavior of the adversary, the all-case optimal protocol decides as soon as any protocol can decide in a run with the same adversarial behavior. Examples to which this can be applied include set consensus, condition-based consensus, renaming and order-preserving renaming. Some of these tasks can be solved significantly faster than the classical simultaneous consensus task. A byproduct of the analysis is a proof that improving on the worst-case bound for any simultaneous task by even a single round is as hard as reaching simultaneous consensus.

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Global Synchronization and Consensus Using Beeps in a Fault-Prone MAC

Hounkanli

Miller

Pełc

2017

Algorithms for Sensor Systems

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Consensus is one of the fundamental tasks studied in distributed computing. Processors have input values from some set V and they have to decide the same value from this set. If all processors have the same input value, then they must all decide this value. We study the task of consensus in a Multiple Access Channel (MAC) prone to faults, under a very weak communication model called the beeping model. Communication proceeds in synchronous rounds. Some processors wake up spontaneously, in possibly different rounds decided by an adversary. In each round, an awake processor can either listen, i.e., stay silent, or beep, i.e., emit a signal. In each round, a fault can occur in the channel independently with constant probability 0 < p < 1. In a fault-free round, an awake processor hears a beep if it listens in this round and if one or more other processors beep in this round. A processor still dormant in a fault-free round in which some other processor beeps is woken up by this beep and hears it. In a faulty round nothing is heard, regardless of the behaviour of the processors.An algorithm working with error probability at most ǫ, for a given ǫ > 0, is called ǫ-safe. Our main result is the design and analysis, for any constant ǫ > 0, of a deterministic ǫ-safe consensus algorithm that works in time O(log w) in a fault-prone MAC, where w is the smallest input value of all participating processors. We show that this time cannot be improved, even when the MAC is fault-free. The main algorithmic tool that we develop to achieve our goal, and that might be of independent interest, is a deterministic algorithm that, with arbitrarily small constant error probability, establishes a global clock in a fault-prone MAC in constant time.

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Revisiting simultaneous consensus with crash failures

Cited by 13 publications

References 15 publications

No Double Discount: Condition-Based Simultaneity Yields Limited Gain

No Double Discount: Condition-Based Simultaneity Yields Limited Gain

Transforming worst-case optimal solutions for simultaneous tasks into all-case optimal solutions

Global Synchronization and Consensus Using Beeps in a Fault-Prone MAC

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