Nested Intervals with Farey Fractions

Abstract

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.