Approaches of influence maximization in social networks with positive and negative opinions

In viral marketing, considering the phenomenon that negative opinions may emerge and propagate in social networks, based on the fundamental linear threshold model (LT), a new model - linear threshold model with negative opinions (LTN) was proposed in this study. Subsequently, some properties of the LTN model, such as monotonicity and submodularity have been shown. With these properties, a greedy approximate algorithm with a ratio of (1-1/e) for influence maximization on the LTN model was proposed. To overcome the inefficiency of the greedy algorithm, three improved algorithms-LTN_NewGreedy (NewGreedy algorithm on LTN), LTN_CELF(CELF algorithm on LTN) and LTN_MixedGreedy (MixedGreedy algorithm on LTN) have been provided in this work. The experimental results on two synthetic datasets showed that the influence spread of these improved algorithms was close to that of those benchmark algorithms, but they were faster than those benchmark algorithms.