Ultra-Fast Rumor Spreading in Social Networks

Fountoulakis, Nikolaos; Παναγιώτου, Κωνσταντίνος; Sauerwald, Thomas

doi:10.1137/1.9781611973099.130

Cited by 63 publications

(70 citation statements)

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“…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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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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“…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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“…Feige et al [25] show that the push process completes in every undirected graph in O(n log n) steps, with high probability. Since then, the push protocol and its variants have been extensively analyzed both for special graphs, as well as for general graphs in terms of their expansion properties (see e.g., [10,11,12,30,29,27,26]). Again, though cobra walks and push-based rumor spreading share the property that multiple nodes are active in a given step, the two mechanisms differ significantly.…”

Section: Related Work and Comparisonmentioning

confidence: 99%

Coalescing-branching random walks on graphs

Dutta

Pandurangan

Rajaraman

et al. 2013

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

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We study a distributed randomized information propagation mechanism in networks we call the coalescing-branching random walk (cobra walk, for short). A cobra walk is a generalization of the well-studied "standard" random walk, and is useful in modeling and understanding the SusceptibleInfected-Susceptible (SIS)-type of epidemic processes in networks. It can also be helpful in performing light-weight information dissemination in resource-constrained networks. A cobra walk is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. (For instance, this could be a node that has a piece of data, rumor, or a virus.) In each step of a cobra walk, each active node chooses k random neighbors to become active for the next step ("branching"). A node is active for step t + 1 only if it is chosen by an active node in step t ("coalescing"). This results in a stochastic process in the underlying network with properties that are quite different from both the standard random walk (which is equivalent * Chinmoy ...$15.00.to the cobra walk with branching factor 1) as well as other gossip-based rumor spreading mechanisms.We focus on the cover time of the cobra walk, which is the number of steps for the walk to reach all the nodes, and derive almost-tight bounds for various graph classes. Our main technical result is an O(log 2 n) high probability bound for the cover time of cobra walks on expanders, if either the expansion factor or the branching factor is sufficiently large; we also obtain an O(log n) high probability bound for the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We show that the cobra walk takes O(n log n) steps on any n-node tree for k ≥ 2, andÕ(n 1/d ) steps on a d-dimensional grid for k ≥ 2, with high probability.

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Ultra-Fast Rumor Spreading in Social Networks

Cited by 63 publications

References 0 publications

Rumor Spreading with No Dependence on Conductance

Rumor Spreading with No Dependence on Conductance

Distributed Algorithms as Combinatorial Structures

Coalescing-branching random walks on graphs

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