On the Push&amp;Pull Protocol for Rumour Spreading

Acan, Hüseyin; Collevecchio, Andrea; Mehrabian, Abbas; Wormald, Nicholas C.

doi:10.1007/978-3-319-51753-7_1

Cited by 14 publications

(39 citation statements)

References 21 publications

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“…Assume that the discordant push protocol starts from an initial state on the n-cycle with m runs of each color, such that all the blue runs are singletons and all the red runs have length at least two. Then after i steps the ratio of discordant blue vertices and discordant vertices is at most 1 3 + i 3m . Proof.…”

Section: Winning Probabilities On the Cyclementioning

confidence: 99%

“…According to Lemma 9, in any of the first N steps of the process, the probability that a blue vertex is pushing is at most 1 3 + N Due to Proposition 3 and Theorem 7 it is however possible to estimate the desired probability up to an error term O(1/ √ n) by running the process for O(n 3/2 ) steps. This is a good trade-off as the expected time to reach a consensus from the worst initial case is n 2 /4 + O(n 3/2 ), and it is quadratic in general (cf.…”

Section: Winning Probabilities On the Cyclementioning

confidence: 99%

“…Models of voting in finite graphs have been studied intensively for decades, see e.g., [6,16,12,1,15,7]. Throughout this paper, a discrete-time voting protocol is defined by specifying a graph and a set of nondeterministic rules.…”

Section: Introductionmentioning

confidence: 99%

“…For more details, see [7,2]. The application of these randomized protocols in studying how rumor spreads in a society goes back to decades, and it is still an active area [9,12,1]. The same can be said about peer-to-peer networks, see e.g., [19,15,14].…”

Section: Introductionmentioning

confidence: 99%

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Discordant Voting Protocols for Cyclically Linked Agents

Pongrácz

2020

Electron. J. Combin.

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Voting protocols, such as the push and the pull protocol, model the behavior of people during an election. These processes have been studied in distributed computing in peer-to-peer networks, and to describe how viruses or rumors spread in a community. We determine the asymptotic behavior of the runtime of discordant linear protocols on the cycle graph and the probability for each consensus to win.

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Section: Winning Probabilities On the Cyclementioning

confidence: 99%

Section: Winning Probabilities On the Cyclementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discordant Voting Protocols for Cyclically Linked Agents

Pongrácz

2020

Electron. J. Combin.

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“…Several authors have recently dropped this assumption by considering an asynchronous model. In the discrete time case, Acan et al (2015) study the rumor spreading time for any graph topology. They show that both the average and guaranteed spreading time are Ω(n ln(n)), where n is the number of nodes in the network.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis of Rumor-Spreading Time

Mocquard

Séricola

Anceaume

2020

INFORMS Journal on Computing

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The context of this work is the well studied dissemination of information in large scale distributed networks through pairwise interactions. This problem, originally called rumor mongering, and then rumor spreading has mainly been investigated in the synchronous model. This model relies on the assumption that all the nodes of the network act in synchrony, that is, at each round of the protocol, each node is allowed to contact a random neighbor. In this paper, we drop this assumption under the argument that it is not realistic in large scale systems. We thus consider the asynchronous variant, where at random times, nodes successively interact by pairs exchanging their information on the rumor. In a previous paper, we performed a study of the total number of interactions needed for all the nodes of the network to discover the rumor. While most of the existing results involve huge constants that do not allow us to compare different protocols, we provided a thorough analysis of the distribution of this total number of interactions together with its asymptotic behavior. In this paper we extend this discrete time analysis by solving a conjecture proposed previously and we consider the continuous time case, where a Poisson process is associated to each node to determine the instants at which interactions occur. The rumor spreading time is thus more realistic since it is the real time needed for all the nodes of the network to discover the rumor. Once again, as most of the existing results involve huge constants, we provide tight bound and equivalent of the complementary distribution of the rumor spreading time. We also give the exact asymptotic behavior of the complementary distribution of the rumor spreading time around its expected value when the number of nodes tends to infinity.

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Stochastic Analysis of Rumor Spreading with Multiple Pull Operations in Presence of Non-cooperative Nodes

Kilian,

Anceaume,

Sericola

2023

Computer Performance Engineering and Stochastic Modelling

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The recent rise of interest in distributed applications has highlighted the importance of effective information dissemination. The challenge lies in the fact that nodes in a distributed system are not necessarily synchronized, and may fail at any time. This has led to the emergence of randomized rumor spreading protocols, such as push and pull protocols, which have been studied extensively. The k-pull operation, which allows an uninformed node to ask for the rumor from a fixed number of other nodes in parallel, has been proposed to improve the pull algorithm's effectiveness. This paper presents and studies the performance of the k-pull operation in the presence of a certain fraction f of non-cooperative nodes. Our goal is to understand the impact of k on the propagation of the rumor despite the presence of a fraction f of non-collaborative nodes.

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On the Push&Pull Protocol for Rumour Spreading

Cited by 14 publications

References 21 publications

Discordant Voting Protocols for Cyclically Linked Agents

Discordant Voting Protocols for Cyclically Linked Agents

Probabilistic Analysis of Rumor-Spreading Time

Stochastic Analysis of Rumor Spreading with Multiple Pull Operations in Presence of Non-cooperative Nodes

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