带Farey分数的区间套
Nested Intervals with Farey Fractions
摘要：
关系数据库被普遍认为是其前身网络和层次模型的一个进步。它们在每个查询方面都很出色，但在建模传递依赖关系时却令人惊讶地不完整。几乎每隔几个月，comp.database.theory新闻组就会出现一个关于如何在数据库中建立树模型的问题。本文完成了探索嵌套区间模型的系列文章。以前的文章介绍了使用二进制有理数的树编码。然而，二进制编码在广度和深度上都呈指数级增长。在本文中，我们将利用Farey分数来克服这个问题。我们还将演示我们的实现扩展到具有1M个节点的树。
英文摘要：
Relational Databases are universally conceived as an advance over their predecessors Network and Hierarchical models. Superior in every querying respect, they turned out to be surprisingly incomplete when modeling transitive dependencies. Almost every couple of months a question how to model a tree in the database surfaces at comp.database.theory newsgroup. This article completes a series of articles exploring Nested Intervals Model. Previous articles introduced tree encoding with Binary Rational Numbers. However, binary encoding grows exponentially, both in breadth and in depth. In this article, we'll leverage Farey fractions in order to overcome this problem. We'll also demonstrate that our implementation scales to a tree with 1M nodes.
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。
