  Core decomposition is a fundamental operator in network analysis. In this
paper, we study the 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 $h$-degree.
The $h$-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 $h$-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 $h$-degree updating
technique. Instead of recomputing the $h$-degrees, our algorithm can
dynamically maintain the $h$-degrees for all vertices via exploring a very
small subgraph, after peeling a vertex. We show that such an $h$-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 $h\ge 3$, our exact and sampling-based
algorithms can achieve up to $10\times$ and $100\times$ speedup over the
state-of-the-art algorithm, respectively.
