Distributed Multivalued Consensus

Babaee, Arta; Draief, Moez

doi:10.1007/978-1-4471-4594-3_28

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…In [1,3,4,6,18,31,22], the same dynamics has been analyzed under different distributed models and/or under very different initial assumptions (among others, under the assumption that k is an absolute constant). In these settings, important aspects of the complex dependence of the dynamics' evolution on the overall shape of the initial color configuration are missed.…”

Section: Md(c)mentioning

confidence: 99%

“…They prove that this dynamics has "parallel" convergence time O(log n) whenever the bias Ω √ n log n . In [4,6,18,31,25,22], the same dynamics for the binary case or when k is an absolute constant [22] has been analyzed in different distributed models. Last but not least, interest for this dynamics was stim-ulated by recent findings in biology: notably, as shown in [8], the structure and dynamics of the "approximate majority" protocol (as it is called there and in [3]) is to a great extent similar to a mechanism that is collectively implemented in the network that regulates the mitotic entry of the cell cycle in eukaryotes.…”

Section: Md(c)mentioning

confidence: 99%

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Plurality Consensus in the Gossip Model

Becchetti¹,

Clementi²,

Natale³

et al. 2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study Plurality Consensus in the GOSSIP Model over a network of n anonymous agents. Each agent supports an initial opinion or color. We assume that at the onset, the number of agents supporting the plurality color exceeds that of the agents supporting any other color by a sufficiently-large bias, though the initial plurality itself might be very far from absolute majority. The goal is to provide a protocol that, with high probability, brings the system into the configuration in which all agents support the (initial) plurality color.We consider the Undecided-State Dynamics, a wellknown protocol which uses just one more state (the undecided one) than those necessary to store colors.We show that the speed of convergence of this protocol depends on the initial color configuration as a whole, not just on the gap between the plurality and the second largest color community. This dependence is best captured by a novel notion we introduce, namely, the monochromatic distance md(c) which measures the distance of the initial color configurationc from the closest monochromatic one. In the complete graph, we prove that, for a wide range of the input parameters, this dynamics converges within O(md(c) log n) rounds. We prove that this upper bound is almost tight in the strong sense: Starting from any color configurationc, the convergence time is Ω(md(c)).Finally, we adapt the Undecided-State Dynamics to obtain a fast, random walk-based protocol for plurality consensus on regular expanders. This protocol converges in O(md(c) polylog(n)) rounds using only polylog(n) local memory. A key-ingredient to achieve the above bounds is a new analysis of the maximum node congestion that results from performing n parallel random walks on regular expanders.All our bounds hold with high probability.

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Section: Md(c)mentioning

confidence: 99%

Section: Md(c)mentioning

confidence: 99%

Plurality Consensus in the Gossip Model

Becchetti¹,

Clementi²,

Natale³

et al. 2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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show abstract

“…Hence, the monitoring algorithm should run from time to time which imposes huge message overhead. Recently, few works [14][15][16][17] have been proposed where the majority vote can be obtained with high probability if initial votes of nodes are sufficiently biased to the majority vote or the network size is large enough. However, these solutions also need a monitoring algorithm to detect convergence.…”

Section: Introductionmentioning

confidence: 99%

Distributed binary majority voting via exponential distribution

Salehkaleybar¹,

Golestani²

2016

IET signal process.

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In the binary majority voting problem, each node initially chooses between two alternative choices. The goal is to design a distributed algorithm that informs nodes which choice is in majority. In this study, the authors formulate this problem as a hypothesis testing problem and propose fixed-size and sequential solutions using classical and Bayesian approaches. In the sequential version, the proposed mechanism enables nodes to test which choice is in majority, successively in time. Hence, termination of the algorithm is embedded within it, contrary to the existing approaches which require a monitoring algorithm to indicate the termination. This property makes the algorithm more efficient in terms of message complexity. Furthermore, the authors show that the proposed solution is resilient to Byzantine attacks if network connectivity is F + 1 in the presence of F adversarial nodes. Thus, the proposed algorithm is more robust compared with the previous works which are vulnerable to the existence of adversarial nodes.

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Distributed Binary Consensus in Dynamic Networks

Babaee

Draief

2013

Information Sciences and Systems 2013

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Distributed Multivalued Consensus

Cited by 7 publications

References 4 publications

Plurality Consensus in the Gossip Model

Plurality Consensus in the Gossip Model

Distributed binary majority voting via exponential distribution

Distributed Binary Consensus in Dynamic Networks

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