A general method of active friending in different diffusion models in social networks

Active friending is a problem in social networks that is to assist a user to build a relationship to a target user by sending invitations to a set of intermediate users; the goal is to maximize the acceptance probability at the target node taking advantage of the social influence through the network formed by the intermediate nodes. In this paper, we convert the original formulated active friending problem of nonsubmodular maximization subject to cardinality constraint into a submodular cost submodular knapsack problem in the IC model, and we show that the two problems are equivalent. We similarly make the conversion on the active friending in the LT model. Then we give a general combinatorial optimization algorithm to solve active friending problems in both the IC model and the LT model with a guaranteed approximation. We analyze the computational complexity of the problem and the algorithm performance. The effectiveness of the generalized method is verified on real data sets.