Targeted Activation Probability Maximization Problem in Online Social Networks

In the past decade, influence maximization becomes one of the fundamental problems in online social networks. It has popular applications such as viral marketing and rumor blocking. This problem asks for some influential users to maximize the expected followers. Unlike traditional influence maximization, we discuss the problem of influence towards a special target user in this paper. We define the targeted activation probability maximization problem, which aims at finding k intermediate users so that a given target user is more likely to be influenced by the start user. Motivated by the need for modeling the diffusion process from one user to another, we propose the Targeted Linear Threshold (TLT) model and Targeted Independent Cascade (TIC) model. We prove that the problem is NP-hard, computation of the objective function is #P-hard, and the objective functions are non-submodular. Moreover, the objective function in the TLT model is an upper bound of that in the TIC model. Based on the sandwich approximation strategy, we obtain their data-dependent approximate solutions. Finally, we use three real datasets to evaluate the effectiveness of our algorithms. The experimental results indicate that our methods can effectively increase the activation probability of the target user.