Dependency Preservation and Lossless Design

DEPENDENCY PRESERVATION AND LOSSLESS DECOMPOSITION

Dependency preserving decomposition- Dependency preserving decomposition of a relation R is R1, R2, R3...Rn concerning the set of Functional Dependencies FD if,

 (FD1 U FD2 U ... U FDn)+ = FD+

where,

• FD1, FD2, FD3…...FDn Sets of Functional dependencies of relations R1, R2, R3 ...Rn.
• (FD1 U FD2 U FD3 U … U FDn)+ -> Closure of Union of all sets of functional dependencies.
• FD+ -> Closure of set of functional dependency FD of R. 

With FD (FD1) R is decomposed or divided into R1 and with FD(FD2) into R2, then the possibility of three cases arise,

FD1 U FD2 = FD -> Decomposition is dependency preserving.

FD1 U FD2 is a subset of FD -> Not Dependency preserving.

FD1 U FD2 is a superset of FD -> This case is not possible. 

Lossless dependency preserving decomposition- In this closure of the set of functional dependencies of discrete relations R1, R2, R3 ...Rn should be equal to the set of functional dependencies of the main relation R before decomposition. For the general case of decomposition of multiple schemas at once, the test for lossless decomposition is complicated.

Dependency preservation and Normalization process, both concepts works on some similarity. As in the Normalization process, to change the form of a relationship into a higher normal form, the solution is by decomposing the relation into two or more relations, which is done by using the set of functional dependencies associated in the lower normal form state.