Minimum-sized Positive Influential Node Set Selection for Social Networks: Considering Both Positive and Negative Influences

Social networks are important mediums for spreading information, ideas, and influences among individuals. Most of existing research work focus on understanding the characteristics of social networks, investigating spreading information through the "word of mouth" effect of social networks, or exploring social influences among individuals and groups. However, most of existing work ignore negative influences among individuals or groups. Motivated by alleviating social problems, such as drinking, smoking, gambling, and influence spreading problems (e. g., promoting new products), we take both positive and negative influences into consideration and propose a new optimization problem, named the Minimum-sized Positive Influential Node Set (MPINS) selection problem, to identify the minimum set of influential nodes, such that every node in the network can be positively influenced by these selected nodes no less than a threshold e. Our contributions are threefold. First, we propose a new optimization problem MPINS, which is investigated under the independent cascade model considering both positive and negative influences. Moreover, we claim that MPIMS is NP-hard. Subsequently, we present a greedy approximation algorithm to address the MPINS selection problem. Finally, to validate the proposed greedy algorithm, extensive simulations are conducted on random Graphs representing small and large size networks.