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Sunday, 14 February 2016

Dependency preserving decomposition - solved exercises 1

Dependency preserving decomposition - Dependency preserving decomposition solved exercises - How to verify that a decomposition is dependency preserving? - Steps to find dependency preserving decomposition - Dependency preserving decomposition examples


Dependency preserving decomposition
Consider a relation R (A, B, C, D) with the following set of functional dependencies;
F = {A B, B C, and C D}.
Is the decomposition of R (A, B, C, D) into R1 (A, B, C) and R2 (C, D) a dependency preserving decomposition?

Solution:

The above said decomposition of R into R1 and R2 is a dependency preserving decomposition if (F1 U F2)+ = F+, where F1 is set of FDs hold by R1, F2 is set of FDs hold by R2, and F is the set of FDs hold by R.

Step 1: for R1, the derivable non-trivial functional dependencies are, A B, and B C. Hence, F1 = {A B, B C}

Step 2: for R2, the derivable non-trivial functional dependency is, C D. Hence, F2 = {C D}

(F1 U F2) = ({A B, B C} U {C D}) = {A B, B C, C D} = F.

F1 U F2 and F both have same set of functional dependencies. Hence, the decomposition of R (A, B, C, D) into R1 (A, B, C) and R2 (C, D) a dependency preserving decomposition.


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