Efficient (α, β)-core Computation: an Index-based Approach

The problem of computing (α, β)-core in a bipartite graph for given α and β is a fundamental problem in bipartite graph analysis and can be used in many applications such as online group recommendation, fraudsters detection, etc. Existing solution to computing (α, β)-core needs to traverse the entire bipartite graph once. Considering the real bipartite graph can be very large and the requests to compute (α, β)-core can be issued frequently in real applications, the existing solution is too expensive to compute the (α, β)-core. In this paper, we present an efficient algorithm based on a novel index such that the algorithm runs in linear time regarding the result size (thus, the algorithm is optimal since it needs at least linear time to output the result). We prove that the index only requires O(m) space where m is the number of edges in the bipartite graph. Moreover, we devise an efficient algorithm with time complexity O(δ·m) for index construction where δ is bounded by √m and is much smaller than √m in practice. We also discuss efficient algorithms to maintain the index when the bipartite graph is dynamically updated and parallel implementation of the index construction algorithm. The experimental results on real and synthetic graphs (more than 1 billion edges) demonstrate that our algorithms achieve up to 5 orders of magnitude speedup for computing (α, β)-core and up to 3 orders of magnitude speedup for index construction, respectively, compared with existing techniques.