Influence Maximazation is the problem of finding a small subset of nodes(seed nodes) in  a social network to maximize the spread of  influence .

　　Domingos and Richardson are the first to study influence maximization as an algorithmic problem.Their methods are probabilistic,however.

　　Kempe,Kleinberg and Tardos are the first to formulate the problem as the following discrete optimization problem.

 

　　Problem Description:Given a social network graph,a specific influence cascade model,and a small number k,the influence maximization  problem is to find k vertices in the graph(refered to as seeds) such that under the influence sascade model,the expected number of vertices innfluenced by the k seeds (referred to as the influence spread in the paper ) is the largest possible.

 

　　Kempe et al. prove that the optimization problem is NP-hard,and present a grredy approximation algorithm applicable to all three models,which guarantees that the influence spread is within(1-1/e) of the optimal influence spread.