Normalization - DBMS - Computer science fundamentals tutorial

        Normalization in DBMS

Normalization is a process that “improves” a database design by generating relations that are of higher normal forms.

The objective of normalization: “to create relations where every dependency is on the key, the whole key, and nothing but the key”.

We discuss four normal forms: first, second, third, and Boyce-Codd normal forms

1NF, 2NF, 3NF, and BCNF

There is a sequence to normal forms:

1NF is considered the weakest,

2NF is stronger than 1NF,

3NF is stronger than 2NF, and

BCNF is considered the strongest

Also,

any relation that is in BCNF, is in 3NF;

any relation in 3NF is in 2NF; and

any relation in 2NF is in 1NF.

a relation in BCNF, is also in 3NF

a relation in 3NF is also in 2NF

a relation in 2NF is also in 1NF

We consider a relation in BCNF to be fully normalized. 

The benefit of higher normal forms is that update semantics for the affected data are simplified.

This means that applications required to maintain the database are simpler.

A design that has a lower normal form than another design has more redundancy. Uncontrolled redundancy can lead to data integrity problems.

First we introduce the concept of functional dependency

Functional Dependencies

We say an attribute, B, has a functional dependency on another attribute, A, if for any two records, which have

the same value for A, then the values for B in these two records must be the same. We illustrate this as:

A à B

Example: Suppose we keep track of employee email addresses, and we only track one email address for each employee. Suppose each employee is identified by their unique employee number. We say there is a functional dependency of email address on employee number:

employee number   à  email address

If EmpNum is the PK then the FDs:

         EmpNum  à EmpEmail

         EmpNum à EmpFname

         EmpNum à EmpLname

must exist.

EmpNum  à EmpEmail

EmpNum à EmpFname

 EmpNum à EmpLname

  

First Normal Form

We say a relation is in 1NF if all values stored in the relation are single-valued and atomic.

1NF places restrictions on the structure of relations. Values must be simple.                                                                             

The following in not in 1NF

EmpNum	Empphone	EmpDegrees
123	250-7853
233	250-1325	BA,BSC,PhD
976	250-2311	BSc,MSc

EmpDegrees is a multi-valued field:

employee 976has two degrees: BSc and MSc

employee 233 has three degrees: BA, BSc, PhD

EmpNum	EmpPhone	EmpDegrees
123	250-7853
233	250-1325	BA,BSC,PhD
976	250-2311	BSc,MSc

To obtain 1NF relations we must, without loss of information, replace the above with two relations are given below

Boyce-Codd Normal Form

BCNF is defined very simply:

a relation is in BCNF if it is in 1NF and if every determinant is a candidate key.

If our database will be used for OLTP (on line transaction processing), then BCNF is our target. Usually, we meet this objective. However, we might denormalize (3NF, 2NF, or 1NF) for performance reasons.

Second Normal Form

A relation is in 2NF if it is in 1NF, and every non-key attribute is fully dependent on each candidate key. (That is, we don’t have any partial functional dependency.)

•       2NF (and 3NF) both involve the concepts of key and non-key attributes.

•       A key attribute is any attribute that is part of a key; any attribute that is not a key attribute,

     is a non-key attribute.

•       Relations that are not in BCNF have data redundancies

•       A relation in 2NF will not have any partial dependencies

Consider this InvLine table (in 1NF):

InvNum

LineNum

ProdNum

Qty

InvDate

     
There are two

                                       candidate keys.

Qty is the only non-key attribute, and it is dependent on InvNum

                                            

InvNum  →  InvDate

Since there is a determinant that is not a candidate key, InvLine is not BCNF

InvLine is not 2NF since there is a partial dependency of InvDate on InvNum

InvLine

InvNum

LineNum

ProdNum

Qty

InvDate

The above relation has redundancies: the invoice date is repeated on each invoice line.

We can improve the database by decomposing the relation into two relations:

     

          

Third Normal Form

•      A relation is in 3NF if the relation is in 1NF and all determinants of non-key attributes are candidate keys That is, for any functional dependency: X ® Y, where Y is a non-key attribute (or a set of non-key attributes), X is a candidate key.

•      This definition of 3NF differs from BCNF only in the specification of non-key attributes - 3NF is weaker than BCNF. (BCNF requires all determinants to be candidate keys.)

•      A relation in 3NF will not have any transitive dependencies of non-key attribute on a candidate key through another non-key attribute.

Consider this Employee relation

EmpName, DeptNum, and DeptName are non-key attributes.

DeptNum determines DeptName, a non-key attribute, and DeptNum is not a candidate key.

Is the relation in 3NF? … no

Is the relation in 2NF? … yes

Is the relation in BCNF? … no

We correct the situation by decomposing the original relation into two 3NF relations. Note the decomposition is lossless.

Verify these two relations are in 3NF.