Influence maximization in a social network in the presence of multiple influences and acceptances

In the real-world, people would acquire or accept the same item, which can be a product, a service, or an event, multiple times. Meanwhile, an individual in a social network may influence others again and again. To address this phenomenon, we propose MIMA, a novel influence propagation model that describes the Multiple Influences and Multiple Acceptances of an individual on some item in a social network. MIMA models two important behaviors of influence and adoption: the marginal increase of a person's influence ability on others diminishes as he or she owns more that item, and the desire of a person to accept one more item will decrease as he or she already owns some. With the MIMA model, we study a new influence maximization problem in a social network where a person may accept the item multiple times: to select k initial promoters such that the final total acceptance volume of all people in the network is maximum. We prove this problem is NP-hard and propose greedy and heuristic algorithms. Experimental results show that the greedy algorithm achieves the best influence spread when compared to the existing algorithms. The influence spread of the heuristic algorithm is only slightly worse than that of the greedy algorithm but can save significant computation time.