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Rumour spreading and graph conductance
 IN PROCEEDINGS OF THE 21ST ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA
, 2010
"... We show that if a connected graph with n nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log 4 n/φ 6) many steps, with high probability, using the PUSHPULL strategy. An interesting feature of our approach is that it draws ..."
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Cited by 21 (2 self)
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We show that if a connected graph with n nodes has conductance φ then rumour spreading, also known as randomized broadcast, successfully broadcasts a message within O(log 4 n/φ 6) many steps, with high probability, using the PUSHPULL strategy. An interesting feature of our approach is that it draws a connection between rumour spreading and the spectral sparsification procedure of Spielman and Teng [23].
Diffusion without False Rumors: On Propagating Updates in a Byzantine Environment
 Theoretical Computer Science
, 2003
"... We study how to efficiently diffuse updates to a large distributed system of data replicas, some of which may exhibit arbitrary (Byzantine) failures. We assume that strictly fewer than t replicas fail, and that each update is initially received by at least t correct replicas. The goal is to diffus ..."
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Cited by 20 (2 self)
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We study how to efficiently diffuse updates to a large distributed system of data replicas, some of which may exhibit arbitrary (Byzantine) failures. We assume that strictly fewer than t replicas fail, and that each update is initially received by at least t correct replicas. The goal is to diffuse each update to all correct replicas while ensuring that correct replicas accept no updates generated spuriously by faulty replicas. To achieve this, each correct replica further propagates an update only after receiving it from at least t others. In this way, no correct replica will ever propagate or accept an update that only faulty replicas introduce, since it will receive that update from only the t 1 faulty replicas.
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 18 (6 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)).
Information Dissemination via Gossip: Applications to Averaging and Coding”. available at http:// www.arXiv.org /cs.NI/0504029
"... We study distributed algorithms, also known as gossip algorithms, for information dissemination in an arbitrary connected network of nodes. Distributed algorithms have applications to peertopeer, sensor, and ad hoc networks, in which nodes operate under limited computational, communication, and en ..."
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Cited by 16 (4 self)
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We study distributed algorithms, also known as gossip algorithms, for information dissemination in an arbitrary connected network of nodes. Distributed algorithms have applications to peertopeer, sensor, and ad hoc networks, in which nodes operate under limited computational, communication, and energy resources. These constraints naturally give rise to “gossip” algorithms: schemes in which nodes repeatedly communicate with randomly chosen neighbors, thus distributing the computational burden across all the nodes in the network. We analyze the information dissemination problem under the gossip constraint for arbitrary networks, and find that the information dissemination time of a gossip algorithm is strongly related to the isoperimetric properties of the underlying graph. This characterization allows us to formulate the problem of finding the fastest information dissemination algorithm as a concave maximization problem over the convex set of graphconformant doubly stochastic matrices. Next, we use these results for two seemingly unrelated important questions: distributed averaging and coding based information dissemination. For averaging, we analyze an algorithm based on a classic result of Flajolet and Martin [7]. Information dissemination based on coding was introduced by Deb and Médard [6]. They showed the virtue of coding by analyzing a coding algorithm for a complete graph. Although their scheme generalizes to arbitrary graphs, the analysis does not. We present an analysis of this algorithm for arbitrary graphs, which suggests that for a large class of graphs, such as gridlike graphs, codingbased algorithms do not seem to improve performance. Finally, we apply our results to several classes of graphs: complete graphs, expander graphs, and grid graphs. 1
On the runtime and robustness of randomized broadcasting
 In Proc. of ISAAC’ 06
, 2006
"... Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. I ..."
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Cited by 15 (5 self)
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Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. In this work, we develop tight bounds on the runtime of the algorithm described above, and analyze its robustness. First, it is shown that on Δregular graphs this algorithm requires at least log2 − 1 N +log Δ
Social networks spread rumors in sublogarithmic time
 IN STOC
, 2011
"... With the prevalence of social networks, it has become increasingly important to understand their features and limitations. It has been observed that information spreads extremely fast in social networks. We study the performance of randomized rumor spreading protocols on graphs in the preferential a ..."
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Cited by 14 (5 self)
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With the prevalence of social networks, it has become increasingly important to understand their features and limitations. It has been observed that information spreads extremely fast in social networks. We study the performance of randomized rumor spreading protocols on graphs in the preferential attachment model. The wellknown random phone call model of Karp et al. (FOCS 2000) is a pushpull strategy where in each round, each vertex chooses a random neighbor and exchanges information with it. We prove the following. • The pushpull strategy delivers a message to all nodes within Θ(log n) rounds with high probability. The best known bound so far was O(log 2 n). • If we slightly modify the protocol so that contacts are chosen uniformly from all neighbors but the one contacted in the previous round, then this time reduces to Θ(log n / log log n), which is the diameter of the graph. This is the first time that a sublogarithmic broadcast time is proven for a natural setting. Also, this is the first time that avoiding doublecontacts reduces the runtime to a smaller order of magnitude.
Buffer Management in Probabilistic PeertoPeer Communication Protocols
 In Proceedings of the 22nd Symposium on Reliable Distributed Systems (SRDS ’03
, 2003
"... In multipeer communication decentralised probabilistic protocols have received a lot of attention because of their robustness against faults in the communication traffic and their potential to provide scalability for large groups. These protocols provide a probabilistic guarantee for a propagated ev ..."
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Cited by 13 (3 self)
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In multipeer communication decentralised probabilistic protocols have received a lot of attention because of their robustness against faults in the communication traffic and their potential to provide scalability for large groups. These protocols provide a probabilistic guarantee for a propagated event to reach every group member. Recent work aims to improve the scalability of such protocols by reducing memory requirements. In saving memory resources, the history buffer, which is used to "remember" received events and to prevent multiple deliveries of events to the application, plays a very significant role. We examine how the buffer size should be chosen to challenge the multiple delivery problem. Further, we propose and evaluate several methods of organising the dissemination of events in order to provide high reliability and reduce the number of multiple deliveries at the same time.
Broadcasting vs. mixing and information dissemination on Cayley graphs
 In 24th Int. Symp. on Theor. Aspects of Computer Science (STACS
, 2007
"... Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succe ..."
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Cited by 13 (6 self)
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Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. First, we consider the relationship between randomized broadcasting and random walks on graphs. In particular, we prove that the runtime of the algorithm described above is upper bounded by the corresponding mixing time, up to a logarithmic factor. One key ingredient of our proofs is the analysis of a continuoustype version of the afore mentioned algorithm, which might be of independent interest. Then, we introduce a general class of Cayley graphs, including (among others) Star graphs, Transposition graphs, and Pancake graphs. We show that randomized broadcasting has optimal runtime on all graphs belonging to this class. Finally, we develop a new proof technique by combining martingale tail estimates with combinatorial methods. Using this approach, we show the optimality of our algorithm on another Cayley graph and obtain new knowledge about the runtime distribution on several Cayley graphs. 1
Random Walk Based Node Sampling in SelfOrganizing Networks
"... Random walk is a means of network node sampling that requires little index maintenance and can function on almost all connected network topologies. With careful guidance, node samples following a desired probability distribution can be generated with the only requirement that the sampling probabilit ..."
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Cited by 12 (0 self)
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Random walk is a means of network node sampling that requires little index maintenance and can function on almost all connected network topologies. With careful guidance, node samples following a desired probability distribution can be generated with the only requirement that the sampling probabilities of each visited node and its direct neighbors are known at each walk step. This paper describes a broad range of network applications that can benefit from such guided random walks in dynamic and decentralized settings. This paper also examines several key issues for implementing random walks in selforganizing networks, including the convergence time of random walks, impact of dynamic network changes and particularly resulted walker losses, and the difficulty of pacing walk steps without synchronized clocks between network nodes. Our result suggests that with proper management, these issues do not cause significant problems under many realistic network environments. 1.
Information spreading in stationary markovian evolving graphs
 In Proc. of the 23rd IEEE International Parallel and Distributed Processing Symposium (IPDPS
, 2009
"... Markovian evolving graphs [2] are dynamicgraph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamicnetwork scenarios. We study the speed of information spreading in the ..."
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Cited by 12 (3 self)
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Markovian evolving graphs [2] are dynamicgraph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamicnetwork scenarios. We study the speed of information spreading in the stationary phase by analyzing the completion time of the flooding mechanism. We prove a general theorem that establishes an upper bound on flooding time in any stationary Markovian evolving graph in terms of its nodeexpansion properties. We apply our theorem in two natural and relevant cases of such dynamic graphs: edgeMarkovian evolving graphs [24, 7] where the probability of existence of any edge at time t depends on the existence (or not) of the same edge at time t − 1; geometric Markovian evolving graphs [4, 10, 9] where the Markovian behaviour is yielded by n mobile radio stations, with fixed transmission radius, that perform n independent random walks over a square region of the plane. In both cases, the obtained upper bounds are shown to be nearly tight and, in fact, they turn out to be tight for a large range of the values of the input parameters. 1