Motif-oriented influence maximization for viral marketing in large-scale social networks

The influence maximization (IM) problem aims to identify a budgeted set of nodes with the highest potential to influence the largest number of users in a cascade model, a key challenge in viral marketing. Traditional IM approaches consider each user/node independently as a potential target customer. However, in many scenarios, the target customers comprise motifs, where activating only one or a few users within a motif is insufficient for effective viral marketing, which, nevertheless, receives little attention. For instance, if a motif of three friends planning to dine together, targeting all three simultaneously is crucial for a restaurant advertisement to succeed. In this paper, we address the motif-oriented influence maximization problem under the linear threshold model. We prove that the motif-oriented IM problem is NP-hard and that the influence function is neither supermodular nor submodular, in contrast to the classical IM setting. To simplify the problem, we establish the submodular upper and lower bounds for the influence function. By leveraging the submodular property, we propose a natural greedy strategy that simultaneously maximizes both bounds.