Sort sets in the relational model

Abstract

The notion of sort set is introduced here to formalize the fact that certain database relations can be sorted so that two or more columns are simultaneously listed in order. This notion is shown to be applicable in several ways to enhance the efficiency of an implemented database. A characterization of when order dependency implies the existence of sort sets in a database is presented, along with several corollaries concerning complexity, Armstrong relations, and cliques of certain graphs. Sort-set dependencies are then introduced. A (finite) sound and complete set of inference rules for sort-set dependencies is presented, as well as a proof that there is no such set for functional and sort-set dependencies taken together. Deciding logical implication for sort-set dependencies is proved to be polynomial, but if functional dependencies are included the problem is co-NP-complete. Each set of sort-set and functional dependencies is shown to have an Armstrong relation. A natural generalization of Armstrong relation, here called separator , is given and then used to study the relationship between order and sort-set dependencies.