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Unformatted text preview: Based on slides from Database System Concepts  5 th Edition Multivalued Dependencies ( Multivalued Dependencies ( MVDs MVDs ) ) ¡ Let R be a relation schema and let α ⊆ R and β ⊆ R. The multivalued dependency α →→ β holds on R if in any legal relation r(R), for all pairs for tuples t 1 and t 2 in r such that t 1 [ α ] = t 2 [ α ], there exist tuples t 3 and t 4 in r such that: t 1 [ α ] = t 2 [ α ] = t 3 [ α ] = t 4 [ α ] t 3 [ β ] = t 1 [ β ] t 3 [ R – β ] = t 2 [ R – β ] t 4 [ β ] = t 2 [ β ] t 4 [ R – β ] = t 1 [ R – β ] ¡ Remember that an fd α→β relates one value on α to one value on β ¡ Intuitively, a multivalued dependency defines a relationship in which a set of values on attributes β are determined by a single value on α Based on slides from Database System Concepts  5 th Edition MVD (Cont.) MVD (Cont.) ¡ Tabular representation of α →→ β t1, t2, t3, and t4 all agree on α t1 and t3 also agree on β t2 and t3 agree on the rest t2 and t4 agree on β t1 and t4 agree on the rest Based on slides from Database System Concepts  5 th Edition Example Example ¡ Suppose that R is a relation schema with a set of attributes that are partitioned into 3 nonempty subsets. Y, Z, W ¡ We say that Y →→ Z ( Y multidetermines Z ) if and only if for all possible relations r ( R ) if < y 1 , z 1 , w 1 > ∈ r and < y 2 , z 2 , w 2 > ∈ r then < y 1 , z 1 , w 2 > ∈ r and < y 2 , z 2 , w 1 > ∈ r ¡ Notice that since the behavior of Z and W are identical it follows that Y →→ Z if Y →→ W ¡ Also note: Y →→ Z holds if, for a given value set for attributes Y there is a set of 0 or more associated values for the set of attributes Z and the Z values depend only on Y values and have no dependence on the set of attributes W. Based on slides from Database System Concepts  5 th Edition Example (Cont.) Example (Cont.) ¡ In the example we saw of teachers, courses, and books: course →→ teacher course →→ book ¡ The above formal definition is supposed to formalize the notion that given a particular value of Y ( course ) it has associated with it a set of values of Z (teacher) and a set of values of W (book) , and these two sets are in some sense...
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This note was uploaded on 04/08/2008 for the course EE 468 taught by Professor Conry during the Spring '08 term at Clarkson University .
 Spring '08
 Conry

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