Dependency Preservation in DBMS

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)

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+.