Concomitant with the tremendous prevalence of online social media platforms, the interactions among individuals are unprecedentedly enhanced. People are free to interact with acquaintances, express and exchange their own opinions through commenting, liking, retweeting on online social media, leading to resistance, controversy and other important phenomena over controversial social issues, which have been the subject of many recent works. In this paper, we study the problem of minimizing risk of conflict in social networks by modifying the initial opinions of a small number of nodes. We show that the objective function of the combinatorial optimization problem is monotone and supermodular. We then propose a na\"{\i}ve greedy algorithm with a $(1-1/e)$ approximation ratio that solves the problem in cubic time. To overcome the computation challenge for large networks, we further integrate several effective approximation strategies to provide a nearly linear time algorithm with a $(1-1/e-\epsilon)$ approximation ratio for any error parameter $\epsilon>0$. Extensive experiments on various real-world datasets demonstrate both the efficiency and effectiveness of our algorithms. In particular, the fast one scales to large networks with more than two million nodes, and achieves up to $20\times$ speed-up over the state-of-the-art algorithm.

翻译：与在线社交媒体平台的巨大普及相联,个人之间的互动得到了空前的加强。人们可以自由地与熟人互动,通过在线社交媒体上的评论、欣赏、重写,表达和交流自己的意见,导致对有争议的社会问题的抵制、争议和其他重要现象,这些是最近许多工作的主题。在本文件中,我们研究如何通过修改少数节点的初步意见来尽量减少社交网络的冲突风险。我们显示组合优化问题的客观功能是单调和超模式的。然后我们提出一个包含1美元/e美元近似率的贪婪算法,在立方时间里解决问题。为了克服大型网络的计算挑战,我们进一步整合了若干有效的近似战略,以近线性算法提供近乎1美元/e-e-e-ebsilon 的近似比率,以任何错误参数 $\epslon>0 。关于各种现实世界数据集的广泛实验显示了我们的算法的效率和有效性。特别是快速至20万至更高速的大型网络速度。