## 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.