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18
Quasirandom Rumor Spreading
- In Proc. of SODA’08
, 2008
"... We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Mat ..."
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Cited by 37 (12 self)
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We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Math. 1985) show that this simple protocol succeeds in spreading a rumor from one node of a complete graph to all others within O(log n) rounds. For the network being a hypercube or a random graph G(n, p) with p ≥ (1+ε)(log n)/n, also O(log n) rounds suffice (Feige, Peleg, Raghavan, and Upfal, Random Struct. Algorithms 1990). In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show a O(log n) bound for sparsely connected random graphs G(n, p) with p = (log n+f(n))/n, where f(n) → ∞ and f(n) = O(log log n). Here, the classical model needs Θ(log 2 (n)) rounds. Hence the quasirandom model achieves similar or better broadcasting times with a greatly reduced use of random bits.
Asynchronous rumor spreading in preferential attachment graphs
- In Proc. 13th Scandinavian Workshop Algorithm Theory (SWAT
, 2012
"... Abstract. We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs in time O( √ log n) to all but a lower order fraction of the nodes with high probability. This is significantly faster than what synchronized protocols can achieve; an obvious lower bound for ..."
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Cited by 6 (1 self)
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Abstract. We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs in time O( √ log n) to all but a lower order fraction of the nodes with high probability. This is significantly faster than what synchronized protocols can achieve; an obvious lower bound for these is the average distance, which is known to be Θ(log n/ log log n) for preferential attachment graphs.
Flooding in weighted sparse random graphs
, 2013
"... In this paper, we study the impact of edge weights on distances in sparse random graphs. We interpret these weights as delays and take them as independent and identically distributed exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all ..."
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Cited by 6 (2 self)
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In this paper, we study the impact of edge weights on distances in sparse random graphs. We interpret these weights as delays and take them as independent and identically distributed exponential random variables. We analyze the weighted flooding time defined as the minimum time needed to reach all nodes from one uniformly chosen node and the weighted diameter corresponding to the largest distance between any pair of vertices. Under some standard regularity conditions on the degree sequence of the random graph, we show that these quantities grow as the logarithm of n when the size of the graph n tends to infinity. We also derive the exact value for the prefactor. These results allow us to analyze an asynchronous randomized broadcast algorithm for random regular graphs. Our results show that the asynchronous version of the algorithm performs better than its synchronized version: in the large size limit of the graph, it will reach the whole network faster even if the local dynamics are similar on average.
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 run-time drops when memory is used to avoid re-contactin ..."
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Cited by 3 (0 self)
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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 run-time drops when memory is used to avoid re-contacting neighbors within a small number of rounds. In this experimental investigation, we confirm that a small amount of memory indeed reduces the run-time of the protocol even for small network sizes. We observe that one memory cell per node suffices to reduce the run-time 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
Rumor Spreading in Random Evolving Graphs
"... In this paper, we aim at analyzing the classical information spreading Push protocol in dynamic networks. We consider the edge-Markovian evolving graph model which captures natural temporal dependencies between the structure of the network at time t, and the one at time t + 1. Precisely, a non-edg ..."
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Cited by 2 (1 self)
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In this paper, we aim at analyzing the classical information spreading Push protocol in dynamic networks. We consider the edge-Markovian evolving graph model which captures natural temporal dependencies between the structure of the network at time t, and the one at time t + 1. Precisely, a non-edge appears with probability p, while an existing edge dies with probability q. In order to fit with real-world traces, we mostly concentrate our study on the case where p = Ω ( 1 n) and q is constant. We prove that, in this realistic scenario, the Push protocol does perform well, completing information spreading in O(log n) time steps, w.h.p., even when the network is, w.h.p., disconnected at every log n n time step (e.g., when p ≪). The bound is tight. We also address other ranges of parameters p and q (e.g., p+q = 1 with arbitrary p and q, and p = Θ () 1 with arbitrary q). Although they do not precisely fit with n the measures performed on real-world traces, they can be of independent interest for other settings. The results in these cases confirm the positive impact of dynamism.
Online myopic network covering
- CoRR
"... Efficient marketing or awareness-raising campaigns seek to recruit n influential individuals – where n is the campaign budget – that are able to cover a large target audience through their social connections. So far most of the re-lated literature on maximizing this network cover assumes that the so ..."
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Cited by 2 (1 self)
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Efficient marketing or awareness-raising campaigns seek to recruit n influential individuals – where n is the campaign budget – that are able to cover a large target audience through their social connections. So far most of the re-lated literature on maximizing this network cover assumes that the social network topology is known. Even in such a case the optimal solution is NP-hard. In practice, how-ever, the network topology is generally unknown and needs to be discovered on-the-fly. In this work we consider an un-known topology where recruited individuals disclose their social connections (a feature known as one-hop lookahead). The goal of this work is to provide an efficient greedy online algorithm that recruits individuals as to maximize the size of target audience covered by the campaign. We propose a new greedy online algorithm, Maximum Ex-pected d-Excess Degree (MEED), and provide, to the best of our knowledge, the first detailed theoretical analysis of the cover size of a variety of well known network sampling algo-rithms on finite networks. Our proposed algorithm greedily maximizes the expected size of the cover. For a class of ran-dom power law networks we show that MEED simplifies into a straightforward procedure, which we denote MOD (Max-imum Observed Degree). We substantiate our analytical results with extensive simulations and show that MOD sig-nificantly outperforms all analyzed myopic algorithms. We note that performance may be further improved if the node degree distribution is known or can be estimated online dur-ing the campaign. 1.
Randomized rumor spreading in poorly connected small-world networks
- Distributed Computing (DISC ’14), volume 8784 of Lecture Notes in Computer Science
, 2014
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Asynchronous rumour spreading in social and signed topologies. arXiv, 1310.6119v3 [cs.SI
, 2015
"... In this paper, we present an experimental analysis of the asynchronous push & pull rumour spreading proto-col. This protocol is, to date, the best-performing rumour spreading protocol for simple, scalable, and robust infor-mation dissemination in distributed systems. We analyse the effect that m ..."
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Cited by 1 (0 self)
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In this paper, we present an experimental analysis of the asynchronous push & pull rumour spreading proto-col. This protocol is, to date, the best-performing rumour spreading protocol for simple, scalable, and robust infor-mation dissemination in distributed systems. We analyse the effect that multiple parameters have on the protocol’s performance, such as varying the rate at which nodes propagate rumours, using memory to avoid contacting the same neighbor twice in a row, varying the stopping criteria used by nodes to decide when to stop spreading the rumour, and others. Prior work has focused on either providing theoreti-cal upper bounds regarding the number of rounds needed to spread the rumour to all nodes, or, proposes improve-ments by adjusting isolated parameters. To our knowl-edge, our work is the first to study how multiple param-eters affect system behaviour both in isolation and com-bination and under a wide range of values. Our analysis is based on experimental simulations us-ing real-world social network datasets, thus complement-ing prior theoretical work to shed light on how the pro-tocol behaves in practical, real-world systems. We also study the behaviour of the protocol on a special type of social graph, called signed networks (e.g., Slashdot and Epinions), whose links indicate stronger trust relation-ships. Finally, through our detailed analysis, we demon-strate how a few simple additions to the protocol can im-prove the total time required to inform 100 % of the nodes by up to 92.49%. 1
