Asynchronous Rumor Spreading on Random Graphs

Παναγιώτου, Κωνσταντίνος; Speidel, Leo

doi:10.1007/978-3-642-45030-3_40

Cited by 11 publications

(9 citation statements)

References 24 publications

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“…Theorem 2 above is a corrected version of Theorem 2 in the conference version of this paper [26]. The bound on T (G n,p ) is slightly worse in the corrected version, however it is still independent of p. To quantify this robustness we performed numerical simulations in Section 7.…”

Section: Resultsmentioning

confidence: 99%

Asynchronous Rumor Spreading on Random Graphs

Παναγιώτου¹,

Speidel

2016

Algorithmica

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We perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erdős-Rényi random graphs G n,p , for any p > c ln(n)/n with c > 1. In particular, we provide a simple strategy for analyzing the asynchronous push-pull protocol on arbitrary graph topologies and apply this strategy to G n,p . We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous pushpull protocol is asymptotically almost unaffected by the average degree of the graph. Similarly tight bounds for Erdős-Rényi random graphs have previously only been obtained for the synchronous push protocol, where it has been observed that the total running time increases significantly for sparse random graphs. Finally, we quantify the robustness of the protocol with respect to transmission and node failures. Our analysis suggests that the asynchronous protocols are particularly robust with respect to these failures compared to their synchronous counterparts.

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Section: Resultsmentioning

confidence: 99%

Asynchronous Rumor Spreading on Random Graphs

Παναγιώτου¹,

Speidel

2016

Algorithmica

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“…Furthermore, several variants of push,pull and push&pull were studied. These include vertices being restricted to answer only one pull request per round [7], vertices being allowed to contact multiple neighbours per round [25,11], vertices not calling the same neighbour twice [10] and asynchronous versions [4,26,1,2]. Finally, besides [11], robustness of these rumor spreading algorithms with respect to message transmission failures was also studied by Elsässer and Sauerwald in [13].…”

Section: :3mentioning

confidence: 99%

Robustness of randomized rumour spreading

Daknama

Παναγιώτου

Reisser

2020

Combinator. Probab. Comp.

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In this work we consider three well-studied broadcast protocols: push, pull and push&pull. A key property of all these models, which is also an important reason for their popularity, is that they are presumed to be very robust, since they are simple, randomized and, crucially, do not utilize explicitly the global structure of the underlying graph. While sporadic results exist, there has been no systematic theoretical treatment quantifying the robustness of these models. Here we investigate this question with respect to two orthogonal aspects: (adversarial) modifications of the underlying graph and message transmission failures. We explore in particular the following notion of local resilience: beginning with a graph, we investigate up to which fraction of the edges an adversary may delete at each vertex, so that the protocols need significantly more rounds to broadcast the information. Our main findings establish a separation among the three models. On one hand, pull is robust with respect to all parameters that we consider. On the other hand, push may slow down significantly, even if the adversary may modify the degrees of the vertices by an arbitrarily small positive fraction only. Finally, push&pull is robust when no message transmission failures are considered, otherwise it may be slowed down. On the technical side, we develop two novel methods for the analysis of randomized rumour-spreading protocols. First, we exploit the notion of self-bounding functions to facilitate significantly the round-based analysis: we show that for any graph the variance of the growth of informed vertices is bounded by its expectation, so that concentration results follow immediately. Second, in order to control adversarial modifications of the graph we make use of a powerful tool from extremal graph theory, namely Szemerédi’s Regularity Lemma.

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“…See [42] for a more detailed discussion of these algorithms. In addition, these algorithmic results concern the spreading time of a rumor on a P2P network with respect to the underlying graphical topology of the peers [11,17,18,20,36,41,42]. As above, these papers assume that all content (rumors) to be spread exists in the network at time 0; our work incorporates exogenous arrivals to study block propagation on P2P networks in blockchain-like systems.…”

Section: Related Workmentioning

confidence: 99%

Stability and Scalability of Blockchain Systems

Gopalan,

Sankararaman,

Walid

et al. 2020

Preprint

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The blockchain paradigm provides a mechanism for content dissemination and distributed consensus on Peer-to-Peer (P2P) networks. While this paradigm has been widely adopted in industry, it has not been carefully analyzed in terms of its network scaling with respect to the number of peers. Applications for blockchain systems, such as cryptocurrencies and IoT, require this form of network scaling.In this paper, we propose a new stochastic network model for a blockchain system. We identify a structural property called one-endedness, which is desirable in any blockchain system. We prove that whenever the blockchain network model is stochastically stable, then a blockchain is one-ended. We further establish that our model is monotone separable and use this result to establish upper and lower bounds on the stability region. The bounds on stability depend on the conductance of the P2P network and allow us to analyze the scalability of blockchain systems on large P2P networks. We verify our theoretical insights using both synthetic data and real data from the Bitcoin network.

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Asynchronous Rumor Spreading on Random Graphs

Cited by 11 publications

References 24 publications

Asynchronous Rumor Spreading on Random Graphs

Asynchronous Rumor Spreading on Random Graphs

Robustness of randomized rumour spreading

Stability and Scalability of Blockchain Systems

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