Maximizing the influence with -grouping constraint.

Recently, a new business model called online group buying is emerging into our daily lives. For example, the online business platforms provide people group-discount coupons which will be issued for at least k buyers grouping for a purchase. With the coupon link widely shared over the social platforms, they hope to promote people into groups to facilitate more purchases. Inspired by aforementioned real-world scenario with grouping constraint of a given minimum number of group members (rc-grouping constraint), in this paper, we analyze and model the diffusion-group behavior, and propose the rc-grouping joining influence maximization (rc-GJIM) problem. Our problem aims to choose budgeted seeds to maximize the number of rc-grouping joiners by social influence, where a rc-grouping joiner is a person who can group with at least rc -1 (rc >= 2) like-mind partners. We prove that this problem is NP-hard. We also prove that the computation of objective is #P-hard and then propose an efficient method to estimate the objective. We show that rc-GJIM is a non-submodular optimization problem, and then design two algorithms to solve it. At last, the experiments based on real-world datasets show that our methods provide good strategies for maximizing the influence with rc-grouping constraint.