# Dependency Preservation in DBMS

### About Dependency Preserving Decomposition in DBMS

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 Ri in the decomposed D.

## Dependency Preserving Decomposition in DBMS

• `Decomposition` of a relation in relational model is done to convert it into appropriate normal form
• A relation R is decomposed into two or more only if the decomposition is both lossless join and dependency preserving.

### Dependency Preserving Decomposition

• If we decompose a relation R into relations R1 and R2, all dependencies of R must be part of either R1 or R2 or must be derivable from combination of functional dependencies(FD) of R1 and R2
• Suppose a relation R(A,B,C,D) with FD set {A->BC} is decomposed into R1(ABC) and R2(AD) which is dependency preserving because FD A->BC is a part of R1(ABC).

### Theory

Consider a schema R(A,B,C,D) and functional dependencies A->B and C->D which is decomposed into R1(AB) and R2(CD)

This decomposition is dependency preserving decompostion because

• A->B can be ensured in R1(AB)
• C->D can be ensured in R2(CD)

### 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 –

```R1 = (A, B, C) with FDs F1 = {A -> B, A -> C}, and
R2 = (C, D) with FDs F2 = {C -> D}.
F' = F1 ∪ F2 = {A -> B, A -> C, C -> D}
so, F' = F.
And so, F'+ = F+.
```

Thus, the decomposition is dependency preserving decomposition.

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