In recent years, motivated by many practical applications such as viral marketing, researchers have paid significant attention to the circulation of information on social networks. The influential nodes that can influence the largest part of social networks are an essential topic in social network analysis. Most present solutions address the issue of discovering the influential nodes that could maximize influence effectiveness rather than minimize the cost of the information diffusion. In this paper, we investigate the circulation of emergency information, such as timely production promotion or disaster information, through a social network. These are real-life problems that have a significant effect in a very short time. We focus on how to minimize the total cost for all users in a specific social network to receive such information. We propose an efficient k-best social disseminator discovering algorithm in which the total diffusion cost on spreading timely information for each user in this social network is minimized.