Abstract

Functional dependencies and Normalization play an important role in relational database design. Functional dependencies are key to establishing the relationship between key and non-key attributes in a relation. Normalization process works towards removing anomalies in a relation and prevents data redundancy. This paper, intended to be a graduate research paper, establishes the definitions of these concepts. The paper introduces Functional Dependency and explains its inference rules. The paper also introduces Normalization and various normal forms 1NF thru 5NF including the BCNF. The paper also explains how Functional Dependencies and Normalization are related, why they are important with regards to relational databases, and advantages of designing a normalized database.

Relational Databases: Functional Dependency and Normalization

Definitions and Concepts

Functional Dependency

A functional dependency is a constraint between two sets of attributes from the database. A functional dependency, represented by X → Y, between two sets of attributes X and Y that are subsets of a relation R specifies a constraint that, for any two tuples t1 and t2 in R that have t1[X] = t2[X],they must also have t1[Y] = t2[Y].

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This means the values of the set of attributes Y of a tuple in R are determined by the set of attributes X. In other words, the values of the set of attributes X functionally determine the values of the set of attributes Y. We can also say that Y is functionally dependent on Y.

The set of attributes X on the left-hand side of the functional dependency is called determinant and the set of attributes Y on the right-hand side of the functional dependency is called dependent. Despite the mathematical definition a functional dependency cannot be determined automatically. It is a property of the semantics of attributes – the database designers will have to understand how the attributes are related to each other to specify a functional dependency. (Elmasri, Ramez and Shamkant B. Navathe. 2006)

Example

Consider the example of an SSN (Social Security Number) database. Every individual has a unique SSN. So, the other attributes of the relation, like name, address etc. can be determined using the SSN. That makes SSN a determinant, and name, address, the dependents – thus establishing the functional dependencies:

SSN  name

SSN  address