Maximizing rumor containment in social networks with constrained time

The spread of rumor or misinformation in social networks may cause bad effects among the public. Thus, it is necessary to find effective strategies to control the spread of rumor. Specifically, in our paper, we consider such a setting: initially, a subset of nodes is chosen as the set of protectors, and the influence of protector diffuses competitively with the diffusion of rumor. However, in real world, we generally have limited budget (limited number of protectors) and time to fight with rumor. Therefore, we study the problem of maximizing rumor containment within a fixed number of initial protectors and a given time deadline. Generalizing two seminal models in the fieldthe Independent Cascade (IC) model and the Linear Threshold (LT) model-we propose two new models of competitive influence diffusion in social networks with the following three factors: a time deadline for information diffusion, random time delay of information exchange and personal interests regarding the acceptance of information. Under these two models, we show that the optimization problems are NP-hard. Furthermore, we prove that the objective functions are submodular. As a result, the greedy algorithm is used as constant-factor approximation algorithms with performance guarantee 1 - 1/e for the two optimization problems.