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 Ri in the decomposed D or could be inferred from the dependencies that appear in some Ri.

Decomposition D = { R1 , R2, R3,,.., ,Rm} of R is said to be dependency-preserving with respect to F if the union of the projections of F on each Ri , in D is equivalent to F. In other words, R ⊂  join of R1, R1 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. 


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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