Group Influence Maximization Problem in Social Networks

Group plays an important role in social society. Much of the world’s decision or work is done by groups and teams. A group’s decision should be made based on most of the members in the group that reach agreement on a concerned topic. If we want to spread a topic and maximize the total number of activated groups in a social network, which seed users should we choose. In this article, we will study a new influence maximization (IM) problem which focuses on the number of groups activated by some concerned topic or information. A group is said to be <italic>activated</italic> if <inline-formula> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> percent of users in this group are activated. Group IM (GIM) aims to select <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> seed users such that the number of eventually activated groups is maximized. We first analyze the complexity and approximability of GIM, which is NP-hard, and the objective function presented in this article is proven to be neither submodular nor supermodular. We develop an upper bound problem and a lower bound problem whose objective functions are submodular. Then, an algorithm based on group coverage will be proposed, and the Sandwich framework is formulated with theoretical analysis to solve GIM. Our experiments verify the effectiveness of our method, as well as the advantage of our method against the other heuristic methods.