Some Remarks on Relational Database Schemes Having Few Minimal Keys
Relational database schemes comprise semantic constraints to formally capture at least part of the “real-world” semantics of an application. Functional dependencies constitute a basic and widely studied class of such constraints. Accordingly, many properties of this class are known, including the insight that the number of minimal keys – as determined by a declared set of functional dependencies – might vary extensively, from just one to exponentially many (in the number of the underlying attributes). The case of just one minimal key is known to be characterized by the set of extremal attributes forming a minimal key. Starting from this result, the present work studies schemes having only a few minimal keys. In particular, we consider the cases of schemes having two and three minimal keys, and then suggest some research for dealing with the more general case of n minimal keys. Furthermore we study the impact of additionally requiring the schemes to be in Boyce-Codd normal form or Third normal form.
KeywordsBoyce-Codd normal form computational complexity extremal attribute functional dependency functional relationship implicational closure logical implication minimal key minimal-key equivalence NP-completeness object normal form prime attribute relational database relation scheme semantic modeling Sperner system superprime attribute Third normal form
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