Social Networks Spread Rumors in Sublogarithmic Time

Doerr, Benjamin; Fouz, Mahmoud; Friedrich, Tobias

doi:10.1016/j.endm.2011.09.050

Cited by 66 publications

(77 citation statements)

References 14 publications

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“…(4) The triangulation and two-hop walks are both "memoryless" processes. It has been shown recently that the inclusion of memory in rumor-spreading can be beneficial in certain classes of graphs [21]. Can adding memory to the two processes we study have a similar effect?…”

Section: Resultsmentioning

confidence: 82%

Discovery through gossip

Haeupler

Pandurangan²,

Peleg

et al. 2012

Proceedings of the Twenty-Fourth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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We study randomized gossip-based processes in dynamic networks that are motivated by information discovery in large-scale distributed networks such as peer-to-peer and social networks. A well-studied problem in peer-to-peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self-stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying networknew edges are added to the network -and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. 566HAEUPLER ET AL.This paper studies and analyzes two natural gossip-based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., "pushes" their mutual information to each other). In the pull discovery process or the two-hop walk, each node repeatedly requests or "pulls" a random contact from a random neighbor and connects itself to this two-hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip.Our main result is an almost-tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n-node graph both processes take O(n log 2 n) rounds to connect every node to all other nodes with high probability, whereas (n log n) is a lower bound. We also study the two-hop walk in directed graphs, and show that it takes O(n 2 log n) time with high probability, and that the worst-case bound is tight for arbitrary directed graphs, whereas (n 2 ) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks.

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Section: Resultsmentioning

confidence: 82%

Discovery through gossip

Haeupler

Pandurangan²,

Peleg

et al. 2012

Proceedings of the Twenty-Fourth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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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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“…It is also known that push-pull is efficient on many classes of random graphs. For example, on classical preferential attachment graphs [3] it was shown in [13] that w.h.p. a rumor spreads in Θ(ln(n)) rounds.…”

Section: Related Workmentioning

confidence: 99%

Asynchronous Rumor Spreading on Random Graphs

Παναγιώτου¹,

Speidel²

2013

Algorithms and Computation

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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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Social Networks Spread Rumors in Sublogarithmic Time

Cited by 66 publications

References 14 publications

Discovery through gossip

Discovery through gossip

Distributed Algorithms as Combinatorial Structures

Asynchronous Rumor Spreading on Random Graphs

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