Mahmoud Fouz

Why rumors spread so quickly in social networks

A few hubs with many connections share with many individuals with few connections.

Social Networks Spread Rumors in Sublogarithmic Time

Abstract It has been observed that information spreads extremely fast in social networks. We model social networks with the preferential attachment model of Barabasi and Albert (Science 1999) and information spreading with the random phone call model of Karp et al. (FOCS 2000). In a recent paper (STOC 2011), we prove the following two results. (i) The random phone call model delivers a message to all nodes of graphs in the preferential attachment model within Θ ( log n ) rounds with high probability. The best known bound so far was O ( log 2 n ) . (ii) If we slightly modify the protocol so that contacts are chosen uniformly from all neighbors but the one 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 run-time to a smaller order of magnitude.

Social networks spread rumors in sublogarithmic time

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 well-known random phone call model of Karp et al. (FOCS 2000) is a push-pull strategy where in each round, each vertex chooses a random neighbor and exchanges information with it. We prove the following. - The push-pull strategy delivers a message to all nodes within Θ(log n) rounds with high probability. The best known bound so far was O(log2 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 double-contacts reduces the run-time to a smaller order of magnitude.

Sharp bounds by probability-generating functions and variable drift

We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al. (GECCO~2010) in several respects. First, the upper bound on the expected running time of the most successful quasirandom evolutionary algorithm for the OneMax function is improved from 1.28n ln n to 0.982n ln n, which breaks the barrier of n ln n posed by coupon-collector processes. Compared to the classical 1+1-EA, whose runtime will for the first time be analyzed with respect to terms of lower order, this represents a speedup by more than a factor of e=2.71...

Quasirandom evolutionary algorithms

Motivated by recent successful applications of the concept of quasirandomness, we investigate to what extent such ideas can be used in evolutionary computation. To this aim, we propose different variations of the classical (1+1) evolutionary algorithm, all imitating the property that the (1+1) EA over intervals of time touches all bits roughly the same number of times. We prove bounds on the optimization time of these algorithms for the simple OneMax function. Surprisingly, none of the algorithms achieves the seemingly obvious reduction of the runtime from Θ(n log n) to O(n). On the contrary, one may even need Ω(n2) time. However, we also find that quasirandom ideas, if implemented correctly, can yield an over 50% speed-up.

Asymptotically optimal randomized rumor spreading

We propose a new protocol for the fundamental problem of disseminating a piece of information to all members of a group of n players. It builds upon the classical randomized rumor spreading protocol and several extensions. The main achievements are the following: Our protocol spreads a rumor from one node to all other nodes in the asymptotically optimal time of (1 + o(1)) log2 n. The whole process can be implemented in a way such that only O(nf(n)) calls are made, where f(n) = ω(1) can be arbitrary. In spite of these quantities being close to the theoretical optima, the protocol remains relatively robust against failures; for random node failures, our algorithm again comes arbitrarily close to the theoretical optima. The protocol can be extended to also deal with adversarial node failures. The price for that is only a constant factor increase in the run-time, where the constant factor depends on the fraction of failing nodes the protocol is supposed to cope with. It can easily be implemented such that only O(n) calls to properly working nodes are made. In contrast to the push-pull protocol by Karp et al. [FOCS 2000], our algorithm only uses push operations, i.e., only informed nodes take active actions in the network. On the other hand, we discard address-obliviousness. To the best of our knowledge, this is the first randomized push algorithm that achieves an asymptotically optimal running time.

Asynchronous rumor spreading in preferential attachment graphs

We show that the asynchronous push-pull protocol spreads rumors in preferential attachment graphs (as defined by Barabasi and Albert) in time

Experimental analysis of rumor spreading in social networks

O(\sqrt{\log n})

Truthful mechanisms for exhibitions

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(logn/loglogn).

On Smoothed Analysis of Quicksort and Hoare’s Find

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.