Fundamentals of Order Dependencies

TL;DR

This paper introduces the concept of order dependencies in databases, formalizes their axioms, and demonstrates their application in query optimization, showing they generalize functional dependencies.

Contribution

It formally defines order dependencies, presents a complete set of inference rules, and proves their applicability and superiority over functional dependencies in database optimization.

Findings

Order dependencies subsume functional dependencies.

A set of sound and complete axioms for order dependencies.

Query rewrites based on order dependencies improve optimization.

Abstract

Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We introduce formally the concept of order dependency and present a set of axioms (inference rules) for them. We show how query rewrites based on these axioms can be used for query optimization. We present several interesting theorems that can be derived using the inference rules. We prove that functional dependencies are subsumed by order dependencies and that our set of axioms for order dependencies is sound and complete.