ULBRF: A Framework for Maximizing Influence in Dynamic Networks Based on Upper and Lower Bounds of Propagation

The influence maximization problem that selects a set of seed nodes to maximize the influence spread has been becoming a hot research topic. The classical algorithms select the seed nodes at the initial moment based on the topological properties in static networks, which are not suitable for solving the problem in dynamic networks. In this paper, we propose the Upper and Lower Bound Radix Forward framework to solve this problem in the dynamic network. First, we propose the upper bound of the influence spread and derive the corresponding lower bound to find the seed nodes. When extending the classical IM to the dynamic network, we find the problem that the final influence spreads increase logarithmically with the linear expansion of the initial seed sets. Therefore, the Dynamic Network Path Dispersion is proposed to solve the problem by measuring the heterogeneity of the snaphots on the dynamic network. The Upper and Lower Bound Radix Forward (ULBRF) is tested and applied in two real dynamic networks and two synthetic networks. Experimental results show that the ULBRF is better than the widely recognized improved greedy algorithms. The Dynamic Network Path Dispersion (DNPD) and the strategy based on the heterogeneities also expand the final influence spread by $35\% \sim 45\%$.