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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.
Quasirandom Rumor Spreading: Expanders, Push vs. Pull, and Robustness
"... Randomized rumor spreading is an efficient protocol to distribute information in networks. Recently, a quasirandom version has been proposed and proven to work equally well on many graphs and better for sparse random graphs. In this work we show three main results for the quasirandom rumor spreading ..."
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Cited by 27 (9 self)
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Randomized rumor spreading is an efficient protocol to distribute information in networks. Recently, a quasirandom version has been proposed and proven to work equally well on many graphs and better for sparse random graphs. In this work we show three main results for the quasirandom rumor spreading model. We exhibit a natural expansion property for networks which suffices to make quasirandom rumor spreading inform all nodes of the network in logarithmic time with high probability. This expansion property is satisfied, among others, by many expander graphs, random regular graphs, and ErdősRényi random graphs. For all network topologies, we show that if one of the push or pull model works well, so does the other. We also show that quasirandom rumor spreading is robust against transmission failures. If each message sent out gets lost with probability f, then the runtime increases only by a factor of O(1/(1 − f)).
The Cover Time of Deterministic Random Walks
, 2010
"... The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how quickly this “deterministic random walk ” covers all vertices (or all edges). We present general techniques to der ..."
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Cited by 11 (2 self)
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The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how quickly this “deterministic random walk ” covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several important graph classes. Depending on the topology, the deterministic random walk can be asymptotically faster, slower or equally fast as the classic random walk. We also examine the short term behavior of deterministic random walks, that is, the time to visit a fixed small number of vertices or edges.
On the Randomness Requirements of Rumor Spreading
, 2011
"... We investigate the randomness requirements of the classical rumor spreading problem on fully connected graphs with n vertices. In the standard random protocol, where each node that knows the rumor sends it to a randomly chosen neighbor in every round, each node needs O((log n) 2) random bits in orde ..."
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Cited by 10 (3 self)
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We investigate the randomness requirements of the classical rumor spreading problem on fully connected graphs with n vertices. In the standard random protocol, where each node that knows the rumor sends it to a randomly chosen neighbor in every round, each node needs O((log n) 2) random bits in order to spread the rumor in O(log n) rounds with high probability (w.h.p.). For the simple quasirandom rumor spreading protocol proposed by Doerr, Friedrich, and Sauerwald (2008), ⌈log n ⌉ random bits per node are sufficient. A lower bound by Doerr and Fouz (2009) shows that this is asymptotically tight for a slightly more general class of protocols, the socalled gatemodel. In this paper, we consider general rumor spreading protocols. We provide a simple pushprotocol that requires only a total of O(n log log n) random bits (i.e., on average O(log log n) bits per node) in order to spread the rumor in O(log n) rounds w.h.p. We also investigate the theoretical minimal randomness requirements of efficient rumor spreading. We prove the existence of a (nonuniform) pushprotocol for which a total of 2 log n + log log n + o(log log n) random bits suffice to spread the rumor in log n + ln n + O(1) rounds with probability 1−o(1). This is contrasted by a simple timerandomness tradeoff for the class of all rumor spreading protocols, according to which any protocol that uses log n − log log n − ω(1) random bits requires ω(log n) rounds to spread the rumor.
Levavi Strong robustness of randomized rumor spreading protocols Discrete Applied
 Mathematics
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Asynchronous rumor spreading in preferential attachment graphs
 In Proc. 13th Scandinavian Workshop Algorithm Theory (SWAT
, 2012
"... Abstract. We show that the asynchronous pushpull 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 pushpull 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.
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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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 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