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 t ₁,t ₂ in I such that t ₁[X] = t ₂[X], there is another tuple t ₃ in I such that t ₃[X] = t ₁[X] = t ₂[X], t ₃[Y ] = t ₁[Y], and t ₃[Z] = t ₂[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...