Minimum-sized influential node set selection for social networks under the independent cascade model

Social networks are important mediums for communication,information dissemination, and influence spreading. Most of existing works focus on understanding the characteristics of social networks or spreading information through the 'word of mouth' effect of social networks. However, motivated by applications of alleviating social problems, such as drinking, smoking, addicting to gaming, and influence spreading problems, such as promoting new products, we propose a new optimization problem named the Minimum-sized Influential Node Set (MINS) selection problem, which is to identify the minimum-sized set of influential nodes, such that every node in the network could be influenced by these selected nodes no less than a threshold. Our contributions are threefold. First, we prove that, under the independent cascade model, MINS is NP-hard. Subsequently, we present a greedy approximation algorithm to address the MINS selection problem. Moreover, the performance ratio of the greedy algorithm is analyzed. Finally, to validate the proposed greedy algorithm, extensive experiments and simulations are conducted both on real world coauthor data sets and random graphs.