Forming external behaviors by leveraging internal opinions

People make decisions and express their opinions according to their communities. A natural idea for controlling the diffusion of a behavior is to find influential people, and employ them to spread a desired behavior. We investigate an influencing problem when individuals´ behaviors are affected by their friends in an opinion formation process. Our goal is to design efficient algorithms for finding opinion leaders such that changing their opinions has a great impact on the overall external behaviors in the society. We study directed social networks and define a set of problems like maximizing the sum of individuals´ behaviors or maximizing the number of individuals whose external behaviors are above a threshold. We discuss the complexity of the defined problems and design polynomial-time optimum algorithms for the non NP-hard variants of them. We also propose polynomial-time approximation algorithms with guaranteed performances and prove inapproximability results for the NP-hard variants of these problems. Furthermore, we run simulations on real-world social networks and show our proposed algorithm outperforms the classical algorithms such as degree-based algorithm, closeness-based algorithm, and pagerank-based algorithm.