Influence maximization (IM) has been widely studied in recent years. Given fixed number of seed users and certain diffusion models, the IM problem aims to select proper seed users in a social networks such that they can achieve the maximal spread of influence. Most previous work assumes that there are only positive relationships between users, and thus users spread influence positively. However, negative relationships also universally exist in various social networks and are complementary to positive relationships in information diffusion. In this paper, the influence maximization problem is addressed in signed social networks that contain both positive and negative relationships. We propose a novel diffusion model called LT-S and two influence spread functions. The proposed LT-S model extends the classical linear threshold model with opinion formation that incorporates both positive and negative opinions and simulates information diffusion in real-world social networks. The influence spread functions under the LT-S model are neither monotone nor submodular which bring challenges to maximization. The RLP algorithm is proposed to tackle the issue, which is improved from R-Greedy algorithm by incorporating two proposed accelerating techniques, the live-edge based and propagation-path based techniques. The results of the extensive experiments on public real signed social network datasets demonstrate that our algorithm outperforms the baseline algorithms in terms of both efficiency and effectiveness.

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