Multivalued Dependency

Synonyms

MVD

Definition

A multivalued dependency (MVD) over a relation schema R[U], is an expression of the form X ↠ Y, where X,Y ⊆ U. An instance I of R[U] satisfies X ↠ Y, denoted by I⊧X ↠ Y, if for every two tuples t₁, t₂ in I such that t₁[X] = t₂[X], there is another tuple t₃ in I such that t₃[X] = t₁[X] = t₂[X], t₃[Y ] = t₁[Y], and t₃[Z] = t₂[Z], where Z = U − XY (XY represents X ∪ Y). In other words, for every value of X, the value of attributes in Y is independent of the value of attributes in Z. A multivalued dependencyX ↠ Y is a special case of a join dependency expressed as ⋈[XY,X(U − XY)], which specifies that the decomposition of any instance I satisfying ⋈ [XY,X(U − XY)] into π _XY (I) and π _X(U−XY)(I) is lossless, i.e., I = π _XY (I) ⋈ π _X(U−XY)(I).

Key Points

Multivalued dependencies, like functional dependencies, can cause redundancy in relational databases. For instance, in the following table, each director of the movie The Matrixis recorded once per actor of the...