Scaling up Distance-generalized Core Decomposition

Core decomposition is a fundamental operator in network analysis. In this paper, we study a problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed (k, h)-core, is a maximal subgraph in which every vertex has at least k other vertices at distance no larger than h. The state-of-the-art algorithm for solving this problem is based on a peeling technique which iteratively removes the vertex (denoted by v) from the graph that has the smallest h-hop degree. The h-hop degree of a vertex v denotes the number of other vertices that are reachable from v within h hops. Such a peeling algorithm, however, needs to frequently recompute the h-hop degrees of v's neighbors after deleting v, which is typically very costly for a large h. To overcome this limitation, we propose an efficient peeling algorithm based on a novel h-hop degree updating technique. Instead of recomputing the h-hop degrees, our algorithm can dynamically maintain the h-hop degrees for all vertices via exploring a very small subgraph, after peeling a vertex. We show that such an h-hop degree updating procedure can be efficiently implemented by an elegant bitmap technique. In addition, we also propose a sampling-based algorithm and a parallelization technique to further improve the efficiency. Finally, we conduct extensive experiments on 12 real-world graphs to evaluate our algorithms. The results show that, when h≥3, our exact and sampling-based algorithms can achieve up to 10x and 100x speedup over the state-of-the-art algorithm, respectively.