Given a graph G and a query vertex q, the topic of community search (CS), aiming to retrieve a dense subgraph of G containing q, has gained much attention. Most existing works focus on undirected graphs which overlooks the rich information carried by the edge directions. Recently, the problem of community search over directed graphs (or CSD problem) has been studied; it finds a connected subgraph containing q, where the in-degree and out-degree of each vertex within the subgraph are at least k and l, respectively. However, existing solutions are inefficient, especially on large graphs. To tackle this issue, in this paper, we propose a novel index called D-Forest, which allows a CSD query to be completed within the optimal time cost. We further propose efficient index construction methods. Extensive experiments on six real large graphs show that our index-based query algorithm is up to two orders of magnitude faster than existing solutions.

翻译：给定图G和查询顶点q，社区搜索（CS）问题旨在检索包含q的密集子图，该问题已引起广泛关注。现有工作大多聚焦于无向图，忽略了边方向所携带的丰富信息。近期，有向图上的社区搜索问题（即CSD问题）得到了研究；它寻找包含q的连通子图，其中子图内每个顶点的入度和出度分别至少为k和l。然而，现有解决方案效率较低，尤其是在大规模图上。为解决这一问题，本文提出了一种名为D-Forest的新颖索引，该索引使得CSD查询能在最优时间复杂度内完成。我们进一步提出了高效的索引构建方法。在六个真实大规模图上的大量实验表明，基于索引的查询算法比现有解决方案快两个数量级。