Maximizing multiple influences and fair seed allocation on multilayer social networks.

The dissemination of information on networks involves many important practical issues, such as the spread and containment of rumors in social networks, the spread of infectious diseases among the population, commercial propaganda and promotion, the expansion of political influence and so on. One of the most important problems is the influence-maximization problem which is to find out k most influential nodes under a certain propagate mechanism. Since the problem was proposed in 2001, many works have focused on maximizing the influence in a single network. It is a NP-hard problem and the state-of-art algorithm IMM proposed by Youze Tang et al. achieves a ratio of 63.2% of the optimum with nearly linear time complexity. In recent years, there have been some works of maximizing influence on multilayer networks, either in the situation of single or multiple influences. But most of them study seed selection strategies to maximize their own influence from the perspective of participants. In fact, the problem from the perspective of network owners is also worthy of attention. Since network participants have not had access to all information of the network for reasons such as privacy protection and corporate interests, they may have access to only part of the social network. The owners of networks can get the whole picture of the networks, and they need not only to maximize the overall influence, but also to consider allocating seeds to their customers fairly, i.e., the Fair Seed Allocation (FSA) problem. As far as we know, FSA problem has been studied on a single network, but not on multilayer networks yet. From the perspective of network owners, we propose a multiple-influence diffusion model MMIC on multilayer networks and its FSA problem. Two solutions of FSA problem are given in this paper, and we prove theoretically that our seed allocation schemes are greedy. Subsequent experiments also validate the effectiveness of our approaches.