This content originally appeared on DEV Community and was authored by hebaShakeel
A minimal cover is a simplified and reduced version of the given set of functional dependencies.
Since it is a reduced version, it is also called as Irreducible set.
It is also called as Canonical Cover.
Steps to Find Minimal Cover
1) Split the right-hand attributes of all FDs.
Example
A->XY => A->X, A->Y
2) Remove all redundant FDs.
Example
{ A->B, B->C, A->C }
Here A->C is redundant since it can already be achieved using the Transitivity Property.
3) Find the Extraneous attribute and remove it.
Example
AB->C, either A or B or none can be extraneous.
If A closure contains B then B is extraneous and it can be removed.
If B closure contains A then A is extraneous and it can be removed.
Example 1
Minimize {A->C, AC->D, E->H, E->AD}
Step 1: {A->C, AC->D, E->H, E->A, E->D}
Step 2: {A->C, AC->D, E->H, E->A}
Here Redundant FD : {E->D}
Step 3: {AC->D}
{A}+ = {A,C}
Therefore C is extraneous and is removed.
{A->D}
Minimal Cover = {A->C, A->D, E->H, E->A}
Example 2
Minimize {AB->C, D->E, AB->E, E->C}
Step 1: {AB->C, D->E, AB->E, E->C}
Step 2: {D->E, AB->E, E->C}
Here Redundant FD = {AB->C}
Step 3: {AB->E}
{A}+ = {A}
{B}+ = {B}
There is no extraneous attribute.
Therefore, Minimal cover = {D->E, AB->E, E->C}
This content originally appeared on DEV Community and was authored by hebaShakeel
hebaShakeel | Sciencx (2021-06-13T15:56:31+00:00) Minimal Cover. Retrieved from https://www.scien.cx/2021/06/13/minimal-cover/
Please log in to upload a file.
There are no updates yet.
Click the Upload button above to add an update.