Efficient Community Search with Size Constraint

The studies of k-truss based community search demonstrated that it can find high-quality personalized com-munities with good properties such as high connectivity and bounded diameter. Motivated by natural restrictions from real applications, in this paper, we investigate the search of triangle-connected k-truss with size constraint (denoted by SCkT) in a graph G: given a size constraint s, an integer k, and query set Q, SCkT search aims to find a triangle-connected k-truss H containing the vertices in Q and with size (i.e., total number of vertices in H) not exceeding s. We prove that the SCkT search problem is NP-hard. To tame the hardness, we fully exploit the properties of triangle-connected k-truss subgraphs s.t. a practically-efficient exact solution for SCkT search is developed. A novel and effective lower bound is proposed to early terminate unpromising search branches and narrow down the search space. Two search strategies, expansion and shrinking, are investigated to tailor for efficient support of SCkT search. A hybrid search method is proposed combining the expansion and shrinking strategies, where a score function is used to guide the search order. Our extensive experiments on real-life and synthetic graphs demonstrate the effectiveness of the SCkT model and the efficiency of the proposed techniques.