# Dependency-Preserving Decomposition

The **dependency preservation decomposition** is another property of decomposed relational database schema D in which each functional dependency X -> Y specified in F either appeared directly in one of the relation schemas R_{i} in the decomposed D or could be inferred from the dependencies that appear in some Ri.

Decomposition D = { R_{1} , R_{2}, R_{3},,.., ,R_{m}} of R is said to be dependency-preserving with respect to F if the union of the projections of F on each R_{i} , in D is equivalent to F. In other words, R ⊂ join of R_{1}, R_{1} over X. The dependencies are preserved because each dependency in F represents a constraint on the database. If decomposition is not dependency-preserving, some dependency is lost in the decomposition.

### Example:

Let a relation R(A,B,C,D) and set a FDs F = { A -> B , A -> C , C -> D} are given.

A relation R is decomposed into -

R_{1 }= (A, B, C) with FDs F_{1 }= {A -> B, A -> C}, and
R_{2}_{ }= (C, D) with FDs F_{2}_{ }= {C -> D}.
F' = F_{1 }∪ F_{2 }= {A -> B, A -> C, C -> D}
so, F' = F.
And so, F'^{+ }= F^{+}.

Thus, the decomposition is dependency preserving decomposition.

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