How Could a Boy Influence a Girl?

A boy wants to make friends with a pretty girl. He feels that he may get rejected if he invites her directly. In this situation, what he could do is to influence the girl´s friends. Similar situations may occur in social activities. Based on this background, we formulate a new optimization problem, the Target Influence Maximization (TIM) problem and show that this problem can be solved in polynomial-time in networks with no directed cycles. Motivated by this, we study a special strategy to construct solutions for TIM, i.e., The Target Influence Maximization through Sub graph without Directed Cycle (TIMSDC). Two polynomial-time approximation algorithms are designed for TIMSDC. Through extensive experiments on real-world data sets, we demonstrate that our algorithms work efficiently and outperform existing methods.