Given a directed edge labeled graph G , to check whether vertex v is reachable from vertex u under a label set S is to know if there is a path from u to v whose edge labels across the path are a subset of S . Such a query is referred to as a label-constrained reachability ( LCR ) query. In this article, we present a new approach to store a compressed transitive closure of G in the form of intervals over spanning trees (forests). The basic idea is to associate each vertex v with two sequences of some other vertices: one is used to check reachability from v to any other vertex, by using intervals, while the other is used to check reachability to v from any other vertex. We will show that such sequences are in general much shorter than the number of vertices in G. Extensive experiments have been conducted, which demonstrates that our method is much better than all the previous methods for this problem in all the important aspects, including index construction times, index sizes, and query times.

中文翻译：

---

用于有效评估标签约束可达性查询的图索引

给定一个有向边标记图G, 检查是否有顶点v可以从顶点到达你在标签集下小号是知道是否有一条路径从你到v其路径上的边缘标签是小号. 这样的查询被称为标签约束可达性(LCR） 询问。在本文中，我们提出了一种存储压缩传递闭包的新方法G以跨越树木（森林）的间隔形式。基本思想是关联每个顶点v有两个其他顶点序列：一个用于检查可达性v到任何其他顶点，通过使用间隔，而另一个用于检查可达性v从任何其他顶点。我们将证明这样的序列通常比中的顶点数短得多G。已经进行了广泛的实验，这表明我们的方法在所有重要方面都比以前的所有方法都好得多，包括索引构建时间、索引大小和查询时间。