Advanced Database Management System - Tutorials and Notes: Finding Extraneous Attribute in DBMS

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Friday, 29 August 2014

Finding Extraneous Attribute in DBMS


Finding Extraneous Attributes in DBMS / How to find extraneous attributes in the process of Normalization? / Finding Extraneous Attributes Examples / Extraneous attribute finding as part of finding Canonical cover



Extraneous Attribute

If we are able to remove an attribute from a functional dependency without changing the closure of the set of functional dependencies, that attribute is called as Extraneous Attribute.
[Dictionary meaning of ‘Extraneous’ is ‘irrelevant’, ‘inappropriate’, or ‘unconnected’]
Assume a set of functional dependencies F, and the closure of set of functional dependencies F+. Also, assume that we remove an attribute from any of the FDs under F and find the closure of new set of functional dependencies. Let us mention the new closure of set of functional dependencies as F1+.  If F+ equals the newly constituted closure F1+, then the attribute which has been removed is called as Extraneous Attribute. In other words, that attribute does not violate any of the functional dependencies.

Example 1:

Let us consider a relation R with schema R(A, B, C) and set of functional dependencies F = { AB C, A C }. The closure for F is F+ = { AB C, A C }.
In AB C, B is extraneous attribute. The reason is, there is another FD A C, which means when A alone can determine C, the use of B is unnecessary (redundant).
Now, we can find the closure for the new set of functional dependencies, which is same as F+. Hence, we can declare that B is extraneous.

Example 2:

Let us consider a relation R with schema R(A, B, C, D) and a set of functional dependencies F = { A BC, B C, AB → D }. What extraneous attributes are present in FDs of F?
C is extraneous in the RHS (Right Hand Side) of A BC. Because, A can determine B (A BC), B can determine C (B C). Hence, A can determine C also (Transitivity rule). Hence, it is inappropriate to repeat or check an attribute many times.
B is extraneous in the LHS of AB D. The reason is, from A BC, it is clear that A determines B. it would indirectly mean that if you know A and B then you know D also.

Formal definition of Extraneous Attribute

In a set of functional dependencies F, consider a functional dependency α → β.
Attribute A is extraneous in α, if A α, and F logically implies (F − {α β}) {(α − A) β}.
Attribute A is extraneous in β, if A β, and the set of functional dependencies
(F − {α β}) (β − A)} logically implies F.

For example, suppose F contains AB CD, A E, and E C. To check if C is extraneous in AB CD, we compute the attribute closure of AB under F’ = {AB D, A E, and E C}. The closure is ABCDE, which includes CD, so we infer that C is extraneous.
[Source: Database System Concepts – Korth]






What is extraneous attributes?

Role of extraneous attributes in normalization process

How to find extraneous attributes in database normalization

Why do we need to find extraneous attributes in finding closures?

Closure of functional dependencies and extraneous attributes

Relationship between extraneous attributes and canonical cover


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