论文标题
有效的标签，以达到挖掘的可及性
Efficient Labeling for Reachability in Digraphs
论文作者
论文摘要
我们考虑将有向图的节点标记以进行可及性查询。该图的可及性标记方案将一个称为标签的二进制字符串分配给每个节点。然后，鉴于节点$ u $和$ v $的标签，并且没有有关基础图的其他信息，应该可以确定是否存在从$ u $到$ v $的有向路径。通过简单的信息理论论点并调用部分订单的界限，在任何方案中，一些标签都需要由至少$ n/4 $位组成，其中$ n $是节点的数量。另一方面，设计具有由$ n/2+o（\ log n）$位组成的标签的方案并不难。在经典的集中设置中，Munro和Nicholson设计了一个数据结构，用于包含$ n^2/4+O（n^2）$位的可及性查询（最佳，直到较低阶段）。我们扩展了他们的方法，以获取包含$ n/3+o（n）$位的标签的计划。
We consider labeling nodes of a directed graph for reachability queries. A reachability labeling scheme for such a graph assigns a binary string, called a label, to each node. Then, given the labels of nodes $u$ and $v$ and no other information about the underlying graph, it should be possible to determine whether there exists a directed path from $u$ to $v$. By a simple information theoretical argument and invoking the bound on the number of partial orders, in any scheme some labels need to consist of at least $n/4$ bits, where $n$ is the number of nodes. On the other hand, it is not hard to design a scheme with labels consisting of $n/2+O(\log n)$ bits. In the classical centralised setting, Munro and Nicholson designed a data structure for reachability queries consisting of $n^2/4+o(n^2)$ bits (which is optimal, up to the lower order term). We extend their approach to obtain a scheme with labels consisting of $n/3+o(n)$ bits.
