Embedded join dependencies as a tool for decomposing full join dependencies
Marc Gyssens · 1985
In [lo] a method is proposed for decomposing join dependencies (jds) in a relational database, nsing the notiofi of a hinge.Decompositions of jds can be used to make integrity-checking more efficient.Therefore it is important for a given jd to Bnd the "best possible" decomposition.In [12] it is shown that decompositions obtained by the method mentioned above minimize the number of components of their *largest" element.However it is still possible to further "simplify" out decompositions.Thusfar, we always restricted our attention to full jds: indeed, the decomposition methodology introduced in [lo] an< subsequently studied in [ll] and [12] generates only full jds.This restriction however seems unnatural.In this paper we slightly modify the decomposition methodology of [lo] .In order to remove this restriction.It turns out that in doing SO, and hence allowing embedded jds in our decompositions, a certain redundancy is eliminated.This leads to a minimality criterion of which we show that it is satisfied by the decompositions obtained using the modified methodology.We also generalize the notion of hinge, introduced in [lo].Surprisingly, generalised hinges turn out to be a very natural tool for characterking when an arbitrary (possibly embedded) jd is logically implied by a given jd.This result generalizes the well known characterization for a full jd to be a consequence of a given full jd.