Influence maximization with limit cost in social network

Social networking service (SNS) applications are changing the way information spreads in online communities. As real social relationships are projected into SNS applications, word of mouth has been an important factor in the information spreading processes of those applications. By assuming each user needs a cost to accept some specific information, this paper studies the initial "seed user" selection strategy to maximize information spreading in a social network with a cost budget. The main contributions of this paper are: 1) proposing a graphic SEIR model (gSEIR) by extending the epidemic compartmental model to simulate the dynamic information spreading process between individuals in the social network; 2) proposing a formal definition for the influence maximization problem with limit cost (IMLC) in social networks, and proving that this problem can be transformed to the weighted set-cover problem (WSCP) and thus is NP-Complete; 3) providing four different greedy algorithms to solve the IMLC problem; 4) proposing a heuristic algorithm based on the method of Lagrange multipliers (HILR) for the same problem; 5) providing two parts of experiments to test the proposed models and algorithms in this paper. In the first part, we verify that gSEIR can generate similar macro-behavior as an SIR model for the information spreading process in an online community by combining the micro-behaviors of all the users in that community, and that gSEIR can also simulate the dynamic change process of the statuses of all the individuals in the corresponding social networks during the information spreading process. In the second part, by applying the simulation result from gSEIR as the prediction of information spreading in the given social network, we test the effectiveness and efficiency of all provided algorithms to solve the influence maximization problem with cost limit. The result show that the heuristic algorithm HILR is the best for the IMLC problem.