使用有理数对嵌套集进行键控
Using rational numbers to key nested sets
摘要：
此报表详细说明了在单个关系数据库表中生成和使用树节点排序键。每个节点的键都是从其父节点的键中计算出来的，排序顺序将树中的每个节点放在所有后代之前，并在所有具有较低索引的兄弟节点之后。从父键到子键的计算是简单的，并且在某种意义上是可逆的，即节点的每个祖先的键可以从该节点的键计算而不必咨询数据库。提供了密钥编码过程的上述性质及其与有限连分数形式的对应性的证明。
英文摘要：
This report details the generation and use of tree node ordering keys in a single relational database table. The keys for each node are calculated from the keys of its parent, in such a way that the sort order places every node in the tree before all of its descendants and after all siblings having a lower index. The calculation from parent keys to child keys is simple, and reversible in the sense that the keys of every ancestor of a node can be calculated from that node's keys without having to consult the database. Proofs of the above properties of the key encoding process and of its correspondence to a finite continued fraction form are provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
