Computing the minimum cover of functional dependencies

doi:10.1016/0020-0190(86)90063-3

Information Processing Letters

Volume 22, Issue 3, 3 March 1986, Pages 157-159

https://doi.org/10.1016/0020-0190(86)90063-3 Get rights and content

Abstract

Let FD X → Y denote a functional dependency and let F denote a set of FDs. An FD X → Y is said to be closed if Y is the closure of X under F. A cover is closed if each FD is closed. The main theoretical results states that a closed, nonredundant cover is a minimum cover. A simple algorithm is presented to compute a minimum cover for F.

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It is well known that every closure system can be represented by an implicational base, or by the set of its meet-irreducible elements. In Horn logic, these are respectively known as the Horn expressions and the characteristic models. In this paper, we consider the problem of translating between the two representations in acyclic convex geometries. Quite surprisingly, we show that the problem in this context is already harder than the dualization in distributive lattices, a generalization of the well-known hypergraph dualization problem for which the existence of an output quasi-polynomial time algorithm is open. In light of this result, we consider a proper subclass of acyclic convex geometries, namely ranked convex geometries, as those that admit a ranked implicational base analogous to that of ranked posets. For this class, we provide output quasi-polynomial time algorithms based on hypergraph dualization for translating between the two representations.
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Computing the minimum cover of functional dependencies

Abstract

Inform. Systems

Computational problems related to the design of normal form relational schemas

ACM Trans. Database Systems

Synthesizing third normal form relations from functional dependencies

ACM Trans. Database Systems