# On the Precision of Social and Information Networks

## Reza Bosagh Zadeh, Ashish Goel, Kamesh Munagala, Aneesh Sharma

Abstract: The diffusion of information on online social and information networks has been a popular topic of study in recent years, but attention has typically focused on speed of dissemination and recall (i.e. the fraction of users getting a piece of information). In this paper, we study the complementary notion of the precision of information diffusion. Our model of information dissemination is \broadcast-based”, i.e., one where every message (original or forwarded) from a user goes to a fixed set of recipients, often called the user’s “friends” or “followers”, as in Facebook and Twitter. The precision of the diffusion process is then defined as the fraction of received messages that a user finds interesting.
On first glance, it seems that broadcast-based information diffusion is a “blunt” targeting mechanism, and must necessarily suffer from low precision. Somewhat surprisingly, we present preliminary experimental and analytical evidence to the contrary: it is possible to simultaneously have high precision (i.e. is bounded below by a constant), high recall, and low diameter!
We start by presenting a set of conditions on the structure of user interests, and analytically show the necessity of each of these conditions for obtaining high precision. We also present preliminary experimental evidence from Twitter verifying that these conditions are satisfied. We then prove that the Kronecker-graph based generative model of Leskovec et al. satisfies these conditions given an appropriate and natural definition of user interests. Further, we show that this model also has high precision, high recall, and low diameter. We finally present preliminary experimental evidence showing Twitter has high precision, validating our conclusion. This is perhaps a first step towards a formal understanding of the immense popularity of online social networks as an information dissemination mechanism.

Guest: Aneesh Sharma
Host: Yvonne-Anne Pignolet

# Information Dissemination via Random Walks in d-Dimensional Space

## Henry Lam, Zhenming Liu, Michael Mitzenmacher, Xiaorui Sun and Yajun Wan

Abstract:
We study a natural information dissemination problem for multiple mobile agents in a bounded Euclidean space. Agents are placed uniformly at random in the d-dimensional space {-n, …, n}^d at time zero, and one of the agents holds a piece of information to be disseminated. All the agents then perform independent random walks over the space, and the information is transmitted from one agent to another if the two agents are sufficiently close. We wish to bound the total time before all agents receive the information (with high probability). Our work extends Pettarin et al’s work [10], which solved the problem for d = 2. We present tight bounds up to polylogarithmic factors for the case d = 3. (While our results extend to higher dimensions, for space and readability considerations we provide only the case d = 3 here.) Our results show the behavior when d >= 3 is qualitatively different from the case d = 2. In particular, as the ratio between the volume of the space and the number of agents varies, we show an interesting phase transition for three dimensions that does not occur in one or two dimensions.

Guest: Henry Lam
Host: Chen Avin