  This survey presents the main results achieved for the influence maximization
problem in social networks. This problem is well studied in the literature and,
thanks to its recent applications, some of which currently deployed on the
field, it is receiving more and more attention in the scientific community. The
problem can be formulated as follows: given a graph, with each node having a
certain probability of influencing its neighbors, select a subset of vertices
so that the number of nodes in the network that are influenced is maximized.
Starting from this model, we introduce the main theoretical developments and
computational results that have been achieved, taking into account different
diffusion models describing how the information spreads throughout the network,
various ways in which the sources of information could be placed, and how to
tackle the problem in the presence of uncertainties affecting the network.
Finally, we present one of the main application that has been developed and
deployed exploiting tools and techniques previously discussed.
