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Rumor Spreading with Bounded In-Degree [article]

Sebastian Daum, Fabian Kuhn, Yannic Maus
2015 arXiv   pre-print
by O(Δ / δ n), where Δ and δ are the largest and smallest degree of the network.  ...  If u knows the data (rumor) to be disseminated, it disperses it to v (known as PUSH) and if it does not, it requests it from v (known as PULL).  ...  Each neighboring leaf node in some L i has degree m + 1, i.e., requests the rumor from r with probability at most 1/m.  ... 
arXiv:1506.00828v2 fatcat:qgrdief7mrbnphrkrxrhpmegoi

How to Discreetly Spread a Rumor in a Crowd [article]

Mohsen Ghaffari, Calvin Newport
2016 arXiv   pre-print
In this paper, we study PUSH-PULL style rumor spreading algorithms in the mobile telephone model, a variant of the classical telephone model in which each node can participate in at most one connection  ...  spreading in this increasingly important setting.  ...  In particular, we prove that offline optimal rumor spreading terminates in O( ∆ δ·φ log n) rounds in graphs with conductance φ, maximum degree ∆, and minimum degree δ.  ... 
arXiv:1607.05697v1 fatcat:fvgrjwuhjbedjcic2ahosvv7z4

Randomized Rumor Spreading in Ad Hoc Networks with Buffers [article]

Dariusz R. Kowalski, Christopher Thraves Caro
2018 arXiv   pre-print
We develop upper and lower bounds for randomized rumor spreading time in the new framework, and compare the results with analogous in the old framework without buffers.  ...  The randomized rumor spreading problem generates a big interest in the area of distributed algorithms due to its simplicity, robustness and wide range of applications.  ...  Upper bounds For any network G, we denote by d u the degree of node u and by ∆ max the maximum degree in the network.  ... 
arXiv:1812.11903v1 fatcat:snzccs2wq5egrfxrbwc4cvwx24

Tight bounds for rumor spreading in graphs of a given conductance

George Giakkoupis, Marc Herbstritt
2011 Symposium on Theoretical Aspects of Computer Science  
We show that for any n-node graph with conductance φ, the classical PUSH-PULL algorithm distributes a rumor to all nodes of the graph in O(φ −1 log n) rounds with high probability.  ...  We study the connection between the rate at which a rumor spreads throughout a graph and the conductance of the graph-a standard measure of a graph's expansion properties.  ...  on the degrees also guarantees rumor spreading in O(φ −1 log n) rounds.  ... 
doi:10.4230/lipics.stacs.2011.57 dblp:conf/stacs/Giakkoupis11 fatcat:pcpcjhwsmjh73duqxnlmrthhkq

A Rumor Spreading Model considering the Cumulative Effects of Memory

Yi Zhang, Jiuping Xu
2015 Discrete Dynamics in Nature and Society  
Further, rumor spreading model simulations are conducted with different parameters in three artificial networks.  ...  This paper proposes a rumor spreading model which examines how the memory effects rate changes over time in artificial network and a real social network.  ...  Acknowledgments We appreciated all support in finance and in spirit.  ... 
doi:10.1155/2015/204395 fatcat:oa2aozozmfbmfigejnzzgpaiqy

Randomized Rumor Spreading in Dynamic Graphs [chapter]

George Giakkoupis, Thomas Sauerwald, Alexandre Stauffer
2014 Lecture Notes in Computer Science  
Our first result is a bound on the rumor spreading time in terms of the conductance of those graphs.  ...  We consider the well-studied rumor spreading model in which nodes contact a random neighbor in each round in order to push or pull the rumor.  ...  that O(log(n) log(d)/α) rounds suffice w.h.p. to spread a rumor on any graph (even non-regular) with vertex expansion α and maximum degree d.  ... 
doi:10.1007/978-3-662-43951-7_42 fatcat:eiyxr7hokjf53ipynw2zy7s6ji

Tight Analysis of Asynchronous Rumor Spreading in Dynamic Networks [article]

Ali Pourmiri, Bernard Mans
2020 arXiv   pre-print
The asynchronous rumor algorithm spreading propagates a piece of information, the so-called rumor, in a network.  ...  Starting with a single informed node, each node is associated with an exponential time clock with rate 1 and calls a random neighbor in order to possibly exchange the rumor.  ...  Suppose that a node of G (0) is aware of a rumor and the algorithm starts spreading the rumor through G(n, ρ). Then, with high probability, the rumor spreads in Ω(n/(ρ · k)) time.  ... 
arXiv:2005.07859v1 fatcat:bh3guh6h5zhstop6xopi4beooy

Experimental Analysis of Rumor Spreading in Social Networks [chapter]

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2012 Lecture Notes in Computer Science  
Randomized rumor spreading was recently shown to be a very efficient mechanism to spread information in preferential attachment networks.  ...  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.  ...  Moreover, on average such a pull operation transfers the rumor from a high degree node (with degree 66 on average) to a node with low degree (with degree 3 on average).  ... 
doi:10.1007/978-3-642-34862-4_12 fatcat:qlozimt5srdr5m7on4adeactpa

Tight Bounds for Rumor Spreading with Vertex Expansion [chapter]

George Giakkoupis
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show that O(log 2 (n)/α) rounds suffice with high probability to spread a rumor from a single node to all n nodes, in any graph with vertex expansion at least α.  ...  We establish a bound for the classic PUSH-PULL rumor spreading protocol on arbitrary graphs, in terms of the vertex expansion of the graph.  ...  Combining this with Claim 5, which bounds τ by O(log n) with probability 1 − n −β , and applying the union bound gives that the rumor spreads from u to at least one v ∈ S in O(log n) rounds with probability  ... 
doi:10.1137/1.9781611973402.59 dblp:conf/soda/Giakkoupis14 fatcat:tut3ixhtljbozin3otf4f3wleq

Asynchronous Rumor Spreading in Preferential Attachment Graphs [chapter]

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2012 Lecture Notes in Computer Science  
We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs (as defined by Barabási and Albert) in time O( √ log n) to all but a lower order fraction of the nodes  ...  with high probability.  ...  In this paper, we revisit the rumor spreading problem in PA graphs, i.e., the spread of one piece of information in a graph. The classical rumor spreading process is modeled on a discrete time line.  ... 
doi:10.1007/978-3-642-31155-0_27 fatcat:tzyy5mhx7zhxthdrk475qxaace

Rumor Spreading in Social Networks [chapter]

Flavio Chierichetti, Silvio Lattanzi, Alessandro Panconesi
2009 Lecture Notes in Computer Science  
If m = 1 the graph is disconnected with high probability, so no rumor spreading strategy can work.)  ...  In this paper, we study the performance of rumor spreading in the classic preferential attachment model of Bollobás et al. which is considered to be a valuable model for social networks.  ...  Their work implies that if the conductance (or the edge expansion) of a graph is Ω(1) then rumor spreading ends in O(∆ log 2 n) many rounds -this, while being a good bound for constant-degree graphs, is  ... 
doi:10.1007/978-3-642-02930-1_31 fatcat:iptgmssjiffh7k6htlv2xa55qu

Why rumors spread so quickly in social networks

Benjamin Doer, Mahmoud Fouz, Tobias Friedrich
2012 Communications of the ACM  
In [17] , we obtain a mathematical proof that rumors in such networks spread much faster than in many other network topologies-even faster than in networks having a communication link between any two nodes  ...  It is quite remarkable that social networks spread news so fast. Both the structure of social networks and the process that distributes the news are not designed with this purpose in mind.  ...  This result improves the previous best bound for rumor spreading in preferential attachment graphs [14] , which is of order log(n) 2 .  ... 
doi:10.1145/2184319.2184338 fatcat:4v7imawtbnd2hla7uz3jns6g3e

Rumor Spreading and Vertex Expansion [chapter]

George Giakkoupis, Thomas Sauerwald
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
For any n-node graph with vertex expansion α, we show that this protocol spreads a rumor from a single node to all other nodes in O(α −1 log 2 n √ log n) rounds with high probability.  ...  We consider the standard rumor spreading protocol where every node chooses a random neighbor in each round and the two nodes exchange the rumors they know.  ...  bound the progress of the rumor spreading process (in Claim 3.2).  ... 
doi:10.1137/1.9781611973099.129 dblp:conf/soda/GiakkoupisS12 fatcat:yo4p47ntwfbkln6ma3nyjhmjue

Social networks spread rumors in sublogarithmic time

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
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.  ...  (FOCS 2000) is a push-pull strategy where in each round, each vertex chooses a random neighbor and exchanges information with it.  ...  Consider a fixed graph G and a run of our rumor spreading protocol started with the rumor in some node u. Let v = u be a node of degree exactly m.  ... 
doi:10.1145/1993636.1993640 dblp:conf/stoc/DoerrFF11 fatcat:jv56bakusrhf7ffbkk3cjz4miy

Social Networks Spread Rumors in Sublogarithmic Time

Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
2011 Electronic Notes in Discrete Mathematics  
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.  ...  (FOCS 2000) is a push-pull strategy where in each round, each vertex chooses a random neighbor and exchanges information with it.  ...  Consider a fixed graph G and a run of our rumor spreading protocol started with the rumor in some node u. Let v = u be a node of degree exactly m.  ... 
doi:10.1016/j.endm.2011.09.050 fatcat:vm4tmbutnzboxgy3r5lnoczmpe
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