Influence maximization modeling and analyzing is a critical issue in social network analysis in a complex network environment, and it can be significantly beneficial to both theory and real life. Given a fixed number k, how to find the set size k which has the greatest influencing scope is a combinatory optimization problem that has been proved to be NP-hard by Kempe et al. (2003). State-of-the-art random algorithm, although it is computation efficient, yields the worst performance; on the contrary, the well-studied greedy algorithms can achieve approximately optimal performance but its computing complexity is prohibitive for large social network; meanwhile, these algorithms should first acquire the global information (topology) of the network which is impractical for the colossal and forever changing network. We propose a new algorithm for influence maximization computing-RMDN and its improved version RMDN++. RMDN uses the information of a randomly chosen node and its nearest neighboring nodes which can avoid the procedure of knowing knowledge of the whole network. This can greatly accelerate the computing process, but its computing complexity is limited to the order of O(klog(n)). We use three different real-life datasets to test the effectiveness and efficiency of RMDN in IC model and LT model respectively. Result shows that RMDN has a comparable performance as the greedy algorithms, but obtains orders of magnitude faster according to different network; in the meantime, we have systematically and theoretically studied and proved the feasibility of our method. The wider applicability and stronger operability of RMDN may also shed light on the profound problem of influence maximization in social network.