In the real world, a large number of social systems can be modeled as signed social networks including both positive and negative relationships. Influence maximization in signed social networks is an interesting and significant research direction, which has gained some attention. All of existing studies mainly focused on positive influence maximization (PIM) problem. The goal of the PIM problem is to select the seed set with maximum positive influence in signed social networks. However, the selected seed set with maximum positive influence may also has a large amount of negative influence, which will cause bad effects in the real applications. Therefore, maximizing purely positive influence is not the final and best goal in signed social networks. In this paper, we introduce the concept of net positive influence and propose the net positive influence maximization (NPIM) problem for signed social networks, to select the seed set with as much positive influence as possible and as less negative influence as possible. Additionally, we prove that the objective function of NPIM problem under polarity-related independent cascade model is non-monotone and non-submodular, which means the traditional greedy algorithm is not applicable to the NPIM problem. Thus, we propose an improved R-Greedy algorithm to solve the NPIM problem. Extensive experiments on two Epinions and Slashdot datasets indicate the differences between positive influence and net positive influence, and also demonstrate that our proposed solution performs better than the state-of-the-art methods in terms of promoting net positive influence diffusion in less running time.
Influence maximization in signed networks by enhancing the negative influence