Influence-based Community Partition with Sandwich Method for Social Networks

Community partition is an important problem in many areas such as biology network, social network. The objective of this problem is to analyse the relationships among data via the network topology. In this paper, we consider the community partition problem under IC model in social networks. We formulate the problem as a combinatorial optimization problem which aims at partitioning a given social network into disjoint M communities. The objective is to maximize the sum of influence propagation of a social network through maximizing it within each community. The existing work shows the influence maximization for community partition problem (IMCPP) to be NP hard. We first prove that the objective function of IMCPP under IC model is neither submodular nor supermodular. Then both supermodular upper bound and submodular lower bound are constructed and proved so that the sandwich framework can be applied. A continuous greedy algorithm and a discrete implementation are designed for upper bound and lower bound problems and the algorithm for both of the two problems gets a 1-1/e approximation ratio. We also devise a simply greedy to solve the original objective function and apply the sandwich approximation framework to it to guarantee a data dependent approximation factor. Finally, our algorithms are evaluated on two real data sets, which clearly verifies the effectiveness of our method in community partition problem, as well as the advantage of our method against the other methods.