Sunday, 14 February 2016

Dependency preserving decomposition - solved exercises 2

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, C, D) and R2 (B, C) 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. (F1 U F2)+ is the closure of (F1 U F2), and F+ is the closure of F.

Step 1: for R1, the derivable non-trivial functional dependency is, C D. Hence, F1 = {C D}
Step 2: for R2, the derivable non-trivial functional dependency is, B C. Hence, F2 = {B C}
(F1 U F2) = ({C D} U {B C}) = {C D, B C} ≠ F.
(F1 U F2)+ = {C D, B C, B D}
F+ = {A B, B C, C D, A C, A D, B D}
Hence, (F1 U F2)+ ≠ F+

The FD A B is not supported by (F1 U F2)+. Hence, the decomposition of R (A, B, C, D) into R1 (A, C, D) and R2 (B, C) is not a dependency preserving decomposition.







 




No comments:

Post a comment

Featured Content

Multiple choice questions in Natural Language Processing Home

MCQ in Natural Language Processing, Quiz questions with answers in NLP, Top interview questions in NLP with answers Multiple Choice Que...

All time most popular contents