Minimizing Seed Set Selection with Probabilistic Coverage Guarantee in a Social Network - Zhang, Peng; Chen, Wei; Sun, Xiaoming; Wang, Yajun; Zhang, Jialin (Proceedings of 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD'2014), 2014)
A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task of selecting initial seed users of a topic with minimum size so that with a guaranteed probability the number of users discussing the topic would reach a given threshold. We formulate the task as an optimization problem called seed minimization with probabilistic coverage guarantee (SM-PCG). This problem departs from the previous studies on social inﬂuence maximization or seed minimization because it considers inﬂuence coverage with probabilistic guarantees instead of guarantees on expected inﬂuence coverage. We show that the problem is not submodular, and thus is harder than previously studied problems based on submodular function optimization. We provide an approximation algorithm and show that it approximates the optimal solution with both a multiplicative ratio and an additive error. The multiplicative ratio is tight while the additive error would be small if inﬂuence coverage distributions of certain seed sets are well concentrated. For one-way bipartite graphs we analytically prove the concentration condition and obtain an approximation algorithm with an O(log n) multiplicative ratio and an O(√n) additive error, where n is the total number of nodes in the social graph. Moreover, we empirically verify the concentration condition in real-world networks and experimentally demonstrate the eﬀectiveness of our proposed algorithm comparing to commonly adopted benchmark algorithms.