Maximizing Influence in Social Networks: A Two-Stage Stochastic Programming Approach That Exploits Submodularity

We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. We propose a Benders decomposition algorithm to find the optimal solution to the problem with a finite number of samples. We show that the submodularity of the influence function can be exploited to develop strong optimality cuts that are more effective than the standard optimality cuts available in the literature. Furthermore, we give an extension of this algorithm to solve general two-stage stochastic programs where the second-stage value function is submodular. Finally, we report our computational experiments with large-scale real-world datasets for two fundamental influence maximization problems, independent cascade and linear threshold, and show that our proposed algorithm outperforms the greedy algorithm.