Section: Overall Objectives

Information dissemination over social networks

While we have been studying information dissemination in practical settings (such as WhatsUp in Gossple ), modeling such dynamic systems is still in its infancy. We plan to complement our practical work on gossip algorithms and information dissemination along the following axes:

Rumour spreading is a family of simple randomized algorithms for information dissemination, in which nodes contact (uniformly) random neighbours to exchange information with them. Despite their simplicity these protocols have proved very efficient for various network topologies. We are interested in studying their properties in specific topologies such as social networks be they implicit (interest-based as in Gossple ) or explicit (where users choose their friends as in Facebook). Recently, there has been some work on bounding the speed of rumour spreading in terms of abstract properties of the network graph, especially the graph's expansion properties of conductance and vertex expansion. It has been shown that high values for either of these guarantees fast rumour spreading—this should be related to empirical observations that social networks have high expansion. Some works established increasingly tighter upper bounds for rumour spreading in term of conductance or vertex expansion, but these bounds are not tight.

Our objective is to prove the missing tight upper bound for rumour spreading with vertex expansion. It is known that neither conductance nor vertex expansion are enough by themselves to completely characterize the speed of rumour spreading: are there graphs with bad expansion in which rumours spread fast?

Overcoming the dependence on expansion: Rumour spreading algorithms have very nice properties such as their simplicity, good performances for many networks but they may have very poor performance for some networks, even though these networks have small diameter, and thus it is possible to achieve fast information dissemination with more sophisticated protocols. Typically nodes may choose the neighbours to contact with some non-uniform probabilities that are determined based on information accumulated by each node during the run of the algorithm. These algorithms achieve information dissemination in time that is close to the diameter of the network. These algorithms, however, do not meet some of the other nice properties of rumour spreading, most importantly, robustness against failures. We are investigating algorithms that combine the good runtime of these latest protocols with the robustness of rumour spreading.

Competing rumours: Suppose now that two, or more, conflicting rumours (or opinions) spread in the network, and whenever a node receives different rumours it keeps only one of them. Which rumour prevails, and how long does it take until this happens? Similar questions have been studied in other contexts but not in the context of rumour spreading. The voter model is a well studied graph process that can be viewed as a competing rumour process that follows the classic PULL rumour spreading algorithm. However, research has only recently started to address the question of how long it takes until a rumour prevails. An interesting variant of the problem that has not been considered before is when different rumours are associated with different weights (some rumours are more convincing than others). We plan to study the above models and variations of them, and investigate their connection to the standard rumour spreading algorithms. This is clearly related to the dissemination of news and personalization in social networks.