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Experimental Analysis of Rumor Spreading in Social Networks
"... Abstract Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks. Most interesting from the algorithm design point of view was the observation that the asymptotic runtime drops when memory is used to avoid recontactin ..."
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Abstract Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks. Most interesting from the algorithm design point of view was the observation that the asymptotic runtime drops when memory is used to avoid recontacting neighbors within a small number of rounds. In this experimental investigation, we confirm that a small amount of memory indeed reduces the runtime of the protocol even for small network sizes. We observe that one memory cell per node suffices to reduce the runtime significantly; more memory helps comparably little. Aside from extremely sparse graphs, preferential attachment graphs perform faster than all other graph classes examined. This holds independent of the amount of memory, but preferential attachment graphs benefit the most from the use of memory. We also analyze the influence of the network density and the size of the memory. For the asynchronous version of the rumor spreading protocol, we observe that the theoretically predicted asymptotic advantage of preferential attachment graphs is smaller than expected. There are other topologies which benefit even more from asynchrony. We complement our findings on artificial network models by the corresponding experiments on crawls of popular online social networks, where again we observe extremely rapid information dissemination and a sizable benefit from using memory and asynchrony. 1
Plurality Consensus in the Gossip Model
 In Proc. of the 26th Ann. ACMSIAM Symp. on Discrete Algorithms (SODA’15
, 2015
"... We study Plurality Consensus in the GOSSIP Model over a network of n anonymous agents. Each agent supports an initial opinion or color. We assume that at the onset, the number of agents supporting the plurality color exceeds that of the agents supporting any other color by a sufficientlylarge bias, ..."
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We study Plurality Consensus in the GOSSIP Model over a network of n anonymous agents. Each agent supports an initial opinion or color. We assume that at the onset, the number of agents supporting the plurality color exceeds that of the agents supporting any other color by a sufficientlylarge bias, though the initial plurality itself might be very far from absolute majority. The goal is to provide a protocol that, with high probability, brings the system into the configuration in which all agents support the (initial) plurality color. We consider the UndecidedState Dynamics, a wellknown protocol which uses just one more state (the undecided one) than those necessary to store colors. We show that the speed of convergence of this protocol depends on the initial color configuration as a whole, not just on the gap between the plurality and the second largest color community. This dependence is best captured by a novel notion we introduce, namely, the monochromatic distance md(c̄) which measures the distance of the initial color configuration c ̄ from the closest monochromatic one. In the complete graph, we prove that, for a wide range of the input parameters, this dynamics converges within O(md(c̄) log n) rounds. We prove that this upper bound is almost tight in the strong sense: Starting from any color configuration c̄, the convergence time is Ω(md(c̄)). Finally, we adapt the UndecidedState Dynamics to obtain a fast, random walkbased protocol for plurality consensus on regular expanders. This protocol converges in O(md(c̄) polylog(n)) rounds using only polylog(n) local memory. A keyingredient to achieve the above bounds is a new analysis of the maximum node congestion that results from performing n parallel random walks on regular expanders. All our bounds hold with high probability.
Simple, Fast and Deterministic Gossip and Rumor Spreading
"... We study gossip algorithms for the rumor spreading problem which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple and robust solutions to the rumo ..."
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We study gossip algorithms for the rumor spreading problem which asks each node to deliver a rumor to all nodes in an unknown network. Gossip algorithms allow nodes only to call one neighbor per round and have recently attracted attention as message efficient, simple and robust solutions to the rumor spreading problem. A long series of papers analyzed the performance of uniform random gossip in which nodes repeatedly call a random neighbor to exchange all rumors with. A main result of this investigation was that uniform gossip comlog n pletes in O( Φ) rounds where Φ is the conductance of the network. More recently, nonuniform random gossip schemes were devised to allow efficient rumor spreading in networks with bottlenecks. In particular, [CensorHillel et al., STOC’12] gave an O(log 3 n) algorithm to solve the 1local broadcast problem in which each node wants to exchange rumors locally with its 1neighborhood. By repeatedly applying this protocol one can solve the global rumor spreading quickly for all networks with small diameter, independently of the conductance. All these algorithms are inherently randomized in their design and analysis. A parallel research direction has been to reduce and determine the amount of randomness needed for efficient rumor spreading. This has been done via lower bounds for restricted models and by designing gossip algorithms with a reduced need for randomness, e.g., by using pseudorandom generators with short random seeds. The general intuition and consensus of these results has been that randomization plays a important role in effectively spreading rumors and that at least a polylogarithmic number of random bit are crucially needed. In this paper we improves over this state of the art in several ways by presenting a deterministic gossip algorithm that solves the the klocal broadcast problem in 2(k + log n) log n rounds1. Besides being the first efficient deterministic solution to the rumor spreading problem this algorithm is interesting in many aspects: It is simpler, more natural, more robust and faster than
Breathe Before Speaking: Efficient Information Dissemination Despite Noisy, Limited and Anonymous Communication
 In Proc. of the ACM Symp. on Principles of Distributed Computing (PODC ’14
, 2014
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Randomized rumor spreading in poorly connected smallworld networks
 Distributed Computing (DISC ’14), volume 8784 of Lecture Notes in Computer Science
, 2014
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RandomnessEfficient Rumor Spreading
, 1304
"... We study the classical rumor spreading problem, which is used to spread information in an unknown network with n nodes. We present the first protocol for any expander graph G with n nodes and minimum degree Θ(n) such that, the protocol informs every node in O(logn) rounds with high probability, and ..."
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We study the classical rumor spreading problem, which is used to spread information in an unknown network with n nodes. We present the first protocol for any expander graph G with n nodes and minimum degree Θ(n) such that, the protocol informs every node in O(logn) rounds with high probability, and uses O(lognloglogn) random bits in total. The runtime of our protocol is tight, and the randomness requirement of O(lognloglogn) random bits almost matches the lower bound of Ω(logn) random bits. We further study rumor spreading protocols for more general graphs, and for several graph topologies our protocols are as fast as the classical protocol and use Õ(logn) random bits in total, in contrast to O(nlog 2 n) random bits used in the wellknown rumor spreading push protocol. These results together give us almost full understanding of the randomness requirement for this basic epidemic process. Ourprotocolsrelyonanovelreductionbetweenrumorspreadingprocessesandbranching programs, and this reduction provides a general framework to derandomize these complex and distributed epidemic processes. Interestingly, one cannot simply apply PRGs for branching programs as rumor spreading process is not characterized by smallspace computation. Our protocols require the composition of several pseudorandom objects, e.g. pseudorandom generators, and pairwise independent generators. Besides designing rumor spreading protocols, the techniques developed here may have applications in studying the randomness complexity of distributed algorithms.
Associate Team acronym: RADCON Principal investigator (Inria):
"... Over recent years, computing systems have seen a massive increase in parallelism and interconnectivity. Peertopeer systems, adhoc networks, sensor networks, or the “cloud ” are based on highly connected and volatile networks. Individual nodes such as cell phones, desktop computers or high perfor ..."
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Over recent years, computing systems have seen a massive increase in parallelism and interconnectivity. Peertopeer systems, adhoc networks, sensor networks, or the “cloud ” are based on highly connected and volatile networks. Individual nodes such as cell phones, desktop computers or high performance computing systems rely on parallel processing power achieved through multiple processing units. To exploit the power of massive networks or multiple processors, algorithms must cope with the scale and asynchrony of these systems, and their inherent instability, e.g., due to node, link, or processor failures. In this research project we explore randomized algorithms for largescale networks of distributed systems, and for shared memory multiprocessor systems. For largescale networks, decentralized gossip protocols have emerged as a standard approach to achieving faulttolerant communication between nodes with simple and scalable algorithms. We will devise new gossip protocols for various complex distributed tasks, and we will explore the power and limits of gossip protocols in various settings. For shared memory systems, randomized algorithms have proved extremely useful to deal with asynchrony and failures. Sometimes probabilistic algorithms provide the only solution to a problem; sometimes they are more efficient; sometimes they are simply easier to implement. We will devise efficient algorithms for some of the fundamental problems of shared memory computing, such as mutual exclusion, renaming, and consensus.