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.

Go back to Dependency preserving decomposition - solved exercises/examples page.