An improved division operator for relational algebra

摘要

Since the introduction of the relational data model, relational algebra has been used to gauge the completeness of relational query languages. As a concise language for formulating queries against relational databases, relational algebra is unmatched. Furthermore, human factor studies have shown that for difficult queries, users perform better using the procedurally-oriented relational algebra than using a non-procedural, specification-based, language such as SQL. Still, the current implementations of relational algebra in database management systems are not “friendly” when it comes to formulation of queries involving universal quantification. The algebraic operation of division normally used for this purpose is difficult for most users to comprehend and work with and is incapable of expressing queries that demand the comparison of sets of values associated with matching groups of tuples in two relations. This paper introduces a new algebraic operation, called grouped generalized division (GGD), which overcomes such shortcomings. We also show how the GGD operation can be expressed in terms of the other more “primitive” algebraic operations. As such, the implementors of algebraic languages can support the GGD operation at the user interface with minimal effort.