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）旨在检索包含 q 的稠密子图，该课题已引起广泛关注。现有研究大多关注无向图，忽略了边方向所携带的丰富信息。近年来，有向图上的社区搜索问题（即 CSD 问题）已被研究，该问题寻找一个包含 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，现有解决方案效率低下，尤其是在大规模图上。为解决这一问题，本文提出一种名为 D-Forest 的新型索引，使得 CSD 查询能够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广泛实验表明，基于索引的查询算法比现有解决方案快两个数量级。