Efficient Size-Constrained (k, d)-Truss Community Search

Abstract

In recent years, finding a cohesive subgraph containing the user-given query vertices has been extensively explored as the community search problem. Most of the existing research ignores the size and diameter of the community and instead focuses only on how cohesive returned communities are. However, it has been a natural requirement for many applications that a community’s number of vertices or members fall within a given range. In this paper, therefore, we investigate the problem of searching maximal (k, d)-truss community with a size constraint (denoted by SkdC) in a social network G: Given a size lower constraint l, a size upper constraint s, a query distance constraint d, an integer k, and a query vertex q, SkdC search problem aims to find a maximal (k, d)-truss H that contains the query vertex q, the query distance of each vertex in H from the query vertex q does not exceed d, the size of H (i.e., the total number of vertices in H) is no less than l and no more than s, and no subgraph $H^{\prime }$ has a size bigger than that of H. We prove that the SkdC search problem is NP-hard. To the best of our knowledge, this is the first work to find a size-constrained maximal (k, d)-truss community in a large graph. To address this issue, first, a practically efficient SkdC search solution is proposed. Then, we explore an improved searching algorithm by updating blocks locally. Finally, we conduct comprehensive experimental studies on several real social networks to evaluate both the efficiency and effectiveness of our proposed searching algorithms.