ARIS: Efficient Admitted Influence Maximizing in Large-Scale Networks Based on Valid Path Reverse Influence Sampling

Xiaojuan Yang, Jiaxing Shang, Qinghong Hu, Dajiang Liu

Abstract: Influence maximization problem has been extensively studied in recent years. It aims at finding a seed set consisting of $k$ vertices from a network, so that their collective influence spread can be maximized. However, existing works have neglected the user admission behavior where the successfully influenced individuals do not always disseminate the messages to their neighbors, and we show that ignoring admission behavior may incur significant bias to existing methods. Based on this observation, a new admitted influence maximization (AIM) problem is proposed by taking the admission behavior into consideration. Specifically, we first propose two new diffusion models, i.e., AIC and ALT, by extending traditional independent cascade and linear threshold models. Then, a novel edge coloring scheme is proposed to theoretically prove the NP-hardness of the AIM problem and the submodularity of its objective function. Based on the theoretical findings, a greedy algorithm is given to find a $(1-1/e-\epsilon)$ approximate solution. To further improve the algorithm efficiency and handle large-scale networks, an efficient algorithm ARIS based on valid path reverse influence sampling is proposed, which could also ensure a $(1-1/e-\epsilon)$ approximate solution. Experimental results on several large-scale real networks exhibit the effectiveness and efficiency of our proposed algorithm.