A Sublinear Time Algorithm for Opinion Optimization in Directed Social Networks via Edge Recommendation

In this paper, we study the opinion maximization problem for the leader-follower DeGroot model of opinion dynamics in a social network modelled by a directed graph with n nodes, where a small number of nodes are competing leader nodes with binary opposing opinions 0 or 1, and the rest are follower nodes. We address the problem of maximizing the overall opinion by adding k ⇐ n new edges, where each edge is incident to a 1-leader and a follower. We prove that the objective function is monotone and submodular, and then propose a deterministic greedy algorithm with an approximation ratio (1-1 over e) and O(n3) running time. We then develop a fast sampling algorithm based on l-truncated absorbing random walks and sample-materialization techniques, which has sublinear time complexity O(kn1/2 log3/2 n/ε3) for any error parameter ε > 0. We provide extensive experiments on real networks to evaluate the performance of our algorithms. The results show that for undirected graphs our fast sampling algorithm outperforms the state-of-the-art method in terms of efficiency and effectiveness. While for directed graphs our fast sampling algorithm is as effective as our deterministic greedy algorithm, both of which are much better than the baseline strategies. Moreover, our fast algorithm is scalable to large directed graphs with over 41 million nodes.