Mass Media Influence Spreading in Social Networks with Community Structure

We study an extension of Axelrod's model for social influence, in which cultural drift is represented as random perturbations, while mass media are introduced by means of an external field. In this scenario, we investigate how the modular structure of social networks affects the propagation of mass media messages across the society. The community structure of social networks is represented by coupled random networks, in which two random graphs are connected by intercommunity links. Considering inhomogeneous mass media fields, we study the conditions for successful message spreading and find a novel phase diagram in the multidimensional parameter space. These findings show that social modularity effects are of paramount importance in order to design successful, cost-effective advertising campaigns.Comment: 21 pages, 9 figures. To appear in JSTA

On the Role of Mobility for Multi-message Gossip

We consider information dissemination in a large $n$-user wireless network in which $k$ users wish to share a unique message with all other users. Each of the $n$ users only has knowledge of its own contents and state information; this corresponds to a one-sided push-only scenario. The goal is to disseminate all messages efficiently, hopefully achieving an order-optimal spreading rate over unicast wireless random networks. First, we show that a random-push strategy -- where a user sends its own or a received packet at random -- is order-wise suboptimal in a random geometric graph: specifically, $\Omega(\sqrt{n})$ times slower than optimal spreading. It is known that this gap can be closed if each user has "full" mobility, since this effectively creates a complete graph. We instead consider velocity-constrained mobility where at each time slot the user moves locally using a discrete random walk with velocity $v(n)$ that is much lower than full mobility. We propose a simple two-stage dissemination strategy that alternates between individual message flooding ("self promotion") and random gossiping. We prove that this scheme achieves a close to optimal spreading rate (within only a logarithmic gap) as long as the velocity is at least $v(n)=\omega(\sqrt{\log n/k})$. The key insight is that the mixing property introduced by the partial mobility helps users to spread in space within a relatively short period compared to the optimal spreading time, which macroscopically mimics message dissemination over a complete graph.Comment: accepted to IEEE Transactions on Information Theory, 201

Global Computation in a Poorly Connected World: Fast Rumor Spreading with No Dependence on Conductance

In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the widely studied GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In this paper, we give an algorithm that solves the information dissemination problem in at most $O(D+\text{polylog}{(n)})$ rounds in a network of diameter $D$, withno dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of $D$, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires $T$ rounds in the LOCAL model can be simulated in $O(T +\mathrm{polylog}(n))$ rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent

On Fast and Robust Information Spreading in the Vertex-Congest Model

This paper initiates the study of the impact of failures on the fundamental problem of \emph{information spreading} in the Vertex-Congest model, in which in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message to all of its neighbors. Our contribution to coping with failures is twofold. First, we prove that the randomized algorithm which chooses uniformly at random the next message to forward is slow, requiring $\Omega(n/\sqrt{k})$ rounds on some graphs, which we denote by $G_{n,k}$, where $k$ is the vertex-connectivity. Second, we design a randomized algorithm that makes dynamic message choices, with probabilities that change over the execution. We prove that for $G_{n,k}$ it requires only a near-optimal number of $O(n\log^3{n}/k)$ rounds, despite a rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing probabilities that change according to the execution is of independent interest.Comment: Appears in SIROCCO 2015 conferenc