• Functional Dependency :
  • Let attributes X and Y are two subsets of attributes of relation R.
  • If the values of the X component of a tuple uniquely (or functionally) determine the values of the Y component, then, there is a functional dependency from x to Y.
  • Algorithm:

Input: Let F be a set of FDs for relation R.

Let f: A  B is a FD to be examined for redundancy.

     Steps:

  1. F’ = F – f
  2. T = A
  3. For each FD: xy in F’ Do
  • If X subsetT Then

T = T  Y

End if

                        End for

                     4. If B subsetT Then

                        f: A  B is redundant.

                        End if

  • Output: Decision whether a given FD f: A  B is redundant or not.
  • Once a set of FDs for any relation R is given, it may be possible that this set contains redundant FDs.
  • “ A FD in the set is redundant, if it can be derived from the other FDs in the set”.
  • This algorithm is known as membership algorithm.
  • A set of functional decencies F for relation R is called Minimal or Irreducible cover of asset of functional dependencies, if it does not have any redundant functional dependency.