Asynchronous Rumor Spreading in Preferential Attachment Graphs

Doerr, Benjamin; Fouz, Mahmoud; Friedrich, Tobias

doi:10.1007/978-3-642-31155-0_27

Cited by 24 publications

(22 citation statements)

References 28 publications

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“…Indeed, the connectivity of the graph has a great impact on the efficiency of the uniform random algorithm. Many papers analyzed the uniform random algorithm with respect to some notion of connectivity [10,37,23,44,24], and additional papers studied other algorithms for information spreading [9,15,16,18] and additional problems [31,32], as well as different families of graphs [13,14,19] or with respect to different graph parameters [17].…”

Section: The Gossip Model and Spannersmentioning

confidence: 99%

Distributed Algorithms as Combinatorial Structures

Censor-Hillel

2015

SIGACT News

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For many distributed computing problems there exists a characterizing combinatorial structure. In other words, the existence of an algorithm for solving the problem on any graph G in time T (G) implies the existence of the structure in G with some parameter related to T (G), and vice versa. Such relations go back to classic examples, such as synchronizers and sparse spanners, and continue to emerge in recent studies of gossip algorithms and multicast algorithms in different communication settings. In this article, we give an overview of both old and recent results that illustrate these connections. We discuss how finding distributed algorithms as well as proving lower bounds can be reduced to studying combinatorial graph structures.

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Section: The Gossip Model and Spannersmentioning

confidence: 99%

Distributed Algorithms as Combinatorial Structures

Censor-Hillel

2015

SIGACT News

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“…Distancebased bounds were given for nodes placed with uniform density in R d [30,31], which also address gossip-based solutions to specific problems such as resource location and minimum spanning tree. Doerr, Fouz, and Friedrich [12,13] have recently presented algorithms for fast information spreading in preferential attachment graphs, which model social networks. Spreading in social networks was also analyzed in [19].…”

Section: Related Workmentioning

confidence: 99%

Rumor Spreading with No Dependence on Conductance

Censor-Hillel¹,

Haeupler²,

Kelner³

et al. 2017

SIAM J. Comput.

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Abstract. In this paper, we study how a collection of interconnected nodes can efficiently perform a global computation in the GOSSIP model of communication. In this model nodes do not know the global topology of the network and may only initiate contact with a single neighbor in each round. This contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of Θ(φ −1 log n). In this paper, we give the first protocol that works efficiently on any topology. In particular we give an algorithm that solves the information dissemination problem in at most O(D +polylog(n)) rounds in a network of diameter D, with no dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of D. In fact, we prove that something stronger is true: any algorithm that requires T rounds in the LOCAL model can be simulated in O(T + polylog(n)) rounds in the GOSSIP model. We thus prove that these two models of distributed computation are equivalent up to an additive polylogarithmic term.

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“…For the asynchronous push-pull protocol there exists much less literature [14,18], mostly devoted to models for scale-free networks. In [14] it was shown that on preferential attachment graphs a rumor needs a time of O( ln(n)) w.h.p.…”

Section: Related Workmentioning

confidence: 99%

“…In [14] it was shown that on preferential attachment graphs a rumor needs a time of O( ln(n)) w.h.p. to spread to almost all nodes.…”

Section: Related Workmentioning

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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Asynchronous Rumor Spreading in Preferential Attachment Graphs

Cited by 24 publications

References 28 publications

Distributed Algorithms as Combinatorial Structures

Distributed Algorithms as Combinatorial Structures

Rumor Spreading with No Dependence on Conductance

Asynchronous Rumor Spreading on Random Graphs

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