Fault-tolerant Agreement in Synchronous Message-passing Systems

Raynal, Michel

doi:10.2200/s00294ed1v01y201009dct003

Cited by 49 publications

(60 citation statements)

References 67 publications

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“…Charron-Bost and Schiper [2] proved that this bound does not hold for crash-tolerant consensus algorithms, where it is possible to decide by the end of round f +1. Michel Raynal [24] presents a thorough study of earlydeciding algorithms in a crash-fault model.…”

Section: Related Workmentioning

confidence: 99%

“…Definition 4.1). This is of particular interest as with crash faults it is possible to achieve that all nodes decide within f + 1 rounds [24]. Theorem 3.6.…”

Section: Recall That F Ementioning

confidence: 99%

“…The following variant of the simple (not early-stopping) crash-tolerant algorithm given in [24] that sends O(nt) messages is (f + 1)-deciding and resilient to t orderly crashes.…”

Section: Definition 44 (Orderly Crashes)mentioning

confidence: 99%

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Early-deciding consensus is expensive

Dolev

Lenzen

2013

Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

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In consensus, the n nodes of a distributed system seek to take a consistent decision on some output, despite up to t of them crashing or even failing maliciously, i.e., behaving "Byzantine". It is known that it is impossible to guarantee that synchronous, deterministic algorithms consistently decide on an output in fewer than f + 1 rounds in executions in which the actual number of faults is f ≤ t. This even holds if faults are crash-only, and in this case the bound can be matched precisely. However, the question of whether this can be done efficiently, i.e., with little communication, so far has not been addressed.In this work, we show that algorithms tolerating Byzantine faults and deciding within f + 2 rounds must send Ω(nt + t 2 f ) messages; as a byproduct, our analysis shows that decision within f +1 rounds is impossible in this setting (unless f = t). Moreover, we prove that any crash-resilient algorithm deciding in f + 1 rounds has worst-case message complexity Ω(n 2 f ). Interestingly, this changes drastically if we restrict the fault model further. If crashes are orderly, i.e., in each round, each node picks an order in which its messages are sent, and crashing nodes successfully transmit a prefix of their sequence, deciding in f + 1 rounds can be guaranteed with O(nt) messages. Categories and Subject Descriptors General TermsAlgorithms, Reliability, Theory Keywords lower bounds; cubic message complexity; Byzantine faults; crash faults; early-stopping Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit

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Section: Related Workmentioning

confidence: 99%

“…Definition 4.1). This is of particular interest as with crash faults it is possible to achieve that all nodes decide within f + 1 rounds [24]. Theorem 3.6.…”

Section: Recall That F Ementioning

confidence: 99%

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Early-deciding consensus is expensive

Dolev

Lenzen

2013

Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

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“…Most of the literature on consensus concerns the presence of processor faults, that can be either crash or Byzantine, starting from the seminal paper [22]; see the recent book [23] for a comprehensive survey. In [18] the authors showed a randomized consensus for crash faults with optimal communication complexity.…”

Section: Related Workmentioning

confidence: 99%

Communication Complexity of Consensus in Anonymous Message Passing Systems

Fusco

2011

Lecture Notes in Computer Science

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Abstract. We consider the message complexity of achieving consensus in synchronous anonymous message passing systems. Unlabeled processors (nodes) communicate through links of a network. In each round every processor can exchange messages with all neighbors and the duration of each transmission is one round. An adversary wakes up some subset of processors at possibly different times and assigns them arbitrary numerical input values. All other processors are dormant and do not have input values. Any message wakes up a dormant processor. The goal of consensus is to wake up all processors and have them agree on one of the input values. We seek deterministic consensus algorithms using as few messages as possible. As opposed to most of the literature on consensus, the difficulty of our scenario are not faults (we assume that the network is fault-free) but the arbitrary network topology combined with the anonymity of nodes. For unknown n-node networks we show a consensus algorithm using O(n 2 ) messages; this complexity is optimal for this class. We show that if the network is known, then the complexity of consensus decreases significantly. Our main contribution is an algorithm that uses O(n 3/2 log 2 n) messages on any n-node network and we show that some networks require Ω(n log n) messages to achieve consensus. We also observe that availability of distinct labels of nodes helps to improve complexity of consensus for known networks but has no effect for the class of unknown networks. Indeed, even with labeled nodes, Ω(n 2 ) messages are sometimes necessary if the network is unknown but for known labeled networks consensus can be always achieved with O(n) messages.

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“…a) Synchronous broadcast/receive systems: In a synchronous system, the processes execute a sequence of rounds, where a round is a bounded time slot such that any message send at the beginning of a slot is received by the end of the same slot by its receiver [15]. In such a system, a collision occurs when a process receives several messages during the same round (time slot), or when two neighbor processes send message to each other during the same round.…”

Section: Introductionmentioning

confidence: 99%

Providing Collision-Free and Conflict-Free Communication in General Synchronous Broadcast/Receive Networks

Bouabdallah

Lakhlef

Raynal

et al. 2017

2017 IEEE 31st International Conference on Advanced Information Networking and Applications (AINA)

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Abstract-This work considers the problem of communication in dense and large scale wireless networks composed of resourcelimited nodes. In this kind of networks, a massive amount of data is becoming increasingly available, and consequently implementing protocols achieving error-free communication channels constitutes an important challenge. Indeed, in this kind of networks, the prevention of message conflicts and message collisions is a crucial issue. In terms of graph theory, solving this issue amounts to solve the distance-2 coloring problem in an arbitrary graph. The paper presents a distributed algorithm providing the processes with such a coloring. This algorithm is itself collision-free and conflict-free. It is particularly suited to wireless networks composed of nodes with communication or local memory constraints.

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Fault-tolerant Agreement in Synchronous Message-passing Systems

Cited by 49 publications

References 67 publications

Early-deciding consensus is expensive

Early-deciding consensus is expensive

Communication Complexity of Consensus in Anonymous Message Passing Systems

Providing Collision-Free and Conflict-Free Communication in General Synchronous Broadcast/Receive Networks

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