Influence optimization in networks: New formulations and valid inequalities

Influence propagation has been the subject of extensive study due to its important role in social networks, epidemiology, and many other areas. Understanding propagation mechanisms is critical to control the spread of fake news or epidemics. In this work, we study the problem of detecting the smallest group of users whose conversion achieves, through propagation, a certain influence level over the network, therefore giving valuable information on the propagation behavior in this network. We develop mixed integer programming algorithms to solve this problem. The core of our algorithm is based on new valid inequalities, cutting planes, and separation algorithms embedded into a branch-and-cut algorithm. We additionally introduce a light formulation relying on fewer variables than the literature formulations. Through extensive computational experiments, we observe that the proposed methods can optimally solve many previously-open benchmark instances, and otherwise achieve small optimality gaps. These experiments also provide various insights into the benefits of different mathematical formulations.