In the field of relational database design, normalization is a systematic way of ensuring that a database structure is suitable for general-purpose querying and free of certain undesirable characteristics—insertion, update, and deletion anomalies—that could lead to a loss of data integrity. E.F. Codd, the inventor of the relational model, introduced the concept of normalization and what we now know as the first normal form in 1970. Codd went on to define the second and third normal forms in 1971; and Codd and Raymond F. Boyce defined the Boyce-Codd normal form in 1974 . Higher normal forms were defined by other theorists in subsequent years, the most recent being the sixth normal form introduced by Chris Date, Hugh Darwen, and Nikos Lorentzos in 2002.

Informally, a relational database table $(the computerized representation of a relation) is often described as “normalized” if it is in the third normal form (3NF). Most 3NF tables are free of insertion, update, and deletion anomalies, i.e. in most cases 3NF tables adhere to BCNF, 4NF, and 5NF (but typically not 6NF).

A standard piece of database design guidance is that the designer should begin by fully normalizing the design, and selectively denormalize only in places where doing so is absolutely necessary to address performance issues However, some modeling disciplines, such as the dimensional modeling approach to data warehouse design, explicitly recommend non-normalized designs, i.e. designs that in large part do not adhere to 3NF.

Objective of normalization

A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a “universal data sub-language” grounded in first-order logi^[(SQL is an example of such a data sub-language, albeit one that Codd regarded as seriously flawed. Querying and manipulating the data within an unnormalized data structure, such as the following non-1NF representation of customers' credit card transactions, involves more complexity than is really necessary:

Customer	Transactions __Tr. ID____Date______Amt._
Jones	12890 14-Oct-2003 -87 12904 15-Oct-2003 -50
Wilkins	12898 14-Oct-2003 -21
Stevens	12907 15-Oct-2003 -18 14920 20-Nov-2003 -70 15003 27-Nov-2003 -60

To each customer there corresponds a repeating group of transactions. The automated evaluation of any query relating to customers' transactions therefore would broadly involve two stages:

1. Unpacking one or more customers' groups of transactions allowing the individual transactions in a group to be examined, and
2. Deriving a query result based on the results of the first stage

For example, in order to find out the monetary sum of all transactions that occurred in October 2003 for all customers, the system would have to know that it must first unpack the Transactions group of each customer, then sum the Amounts of all transactions thus obtained where the Date of the transaction falls in October 2003.

One of Codd's important insights was that this structural complexity could always be removed completely, leading to much greater power and flexibility in the way queries could be formulated (by users and applications) and evaluated (by the DBMS). The normalized equivalent of the structure above would look like this:

Customer	Tr. ID	Date	Amount
Jones	12890	14-Oct-2003	-87
Jones	12904	15-Oct-2003	-50
Wilkins	12898	14-Oct-2003	-21
Stevens	12907	15-Oct-2003	-18
Stevens	14920	20-Nov-2003	-70
Stevens	15003	27-Nov-2003	-60

Now each row represents an individual credit card transaction, and the DBMS can obtain the answer of interest, simply by finding all rows with a Date falling in October, and summing their Amounts. All of the values in the data structure are on an equal footing: they are all exposed to the DBMS directly, and can directly participate in queries, whereas in the previous situation some values were embedded in lower-level structures that had to be handled specially. Accordingly, the normalized design lends itself to general-purpose query processing, whereas the unnormalized design does not.

The objectives of normalization beyond 1NF were stated as follows by Codd:

1. To free the collection of relations from undesirable insertion, update and deletion dependencies;

2. To reduce the need for restructuring the collection of relations as new types of data are introduced, and thus increase the life span of application programs;

3. To make the relational model more informative to users;

4. To make the collection of relations neutral to the query statistics, where these statistics are liable to change as time goes by.

a deletion anomaly. All information about Dr. Giddens is lost when he temporarily ceases to be assigned to any courses.

When an attempt is made to modify (update, insert into, or delete from) a table, undesired side-effects may follow. Not all tables can suffer from these side-effects; rather, the side-effects can only arise in tables that have not been sufficiently normalized. An insufficiently normalized table might have one or more of the following characteristics:

• The same information can be expressed on multiple rows; therefore updates to the table may result in logical inconsistencies. For example, each record in an "Employees' Skills" table might contain an Employee ID, Employee Address, and Skill; thus a change of address for a particular employee will potentially need to be applied to multiple records (one for each of his skills). If the update is not carried through successfully—if, that is, the employee's address is updated on some records but not others—then the table is left in an inconsistent state. Specifically, the table provides conflicting answers to the question of what this particular employee's address is. This phenomenon is known as an update anomaly.
• There are circumstances in which certain facts cannot be recorded at all. For example, each record in a "Faculty and Their Courses" table might contain a Faculty ID, Faculty Name, Faculty Hire Date, and Course Code—thus we can record the details of any faculty member who teaches at least one course, but we cannot record the details of a newly-hired faculty member who has not yet been assigned to teach any courses. This phenomenon is known as an insertion anomaly.
• There are circumstances in which the deletion of data representing certain facts necessitates the deletion of data representing completely different facts. The "Faculty and Their Courses" table described in the previous example suffers from this type of anomaly, for if a faculty member temporarily ceases to be assigned to any courses, we must delete the last of the records on which that faculty member appears. This phenomenon is known as a deletion anomaly.

[inimize redesign when extending the database structure

When a fully normalized database structure is extended to allow it to accommodate new types of data, the pre-existing aspects of the database structure can remain largely or entirely unchanged. As a result, applications interacting with the database are minimally affected.

Make the data model more informative to users

Normalized tables, and the relationship between one normalized table and another, mirror real-world concepts and their interrelationships.

Avoid bias towards any particular pattern of querying

Normalized tables are suitable for general-purpose querying. This means any queries against these tables, including future queries whose details cannot be anticipated, are supported. In contrast, tables that are not normalized lend themselves to some types of queries, but not others.

Background to normalization: definitions

• Functional dependency: Attribute B has a functional dependency on attribute A (i.e., A → B) if, for each value of attribute A, there is exactly one value of attribute B. If value of A is repeating in tuples then value of B will also repeat. In our example, Employee Address has a functional dependency on Employee ID, because a particular Employee ID value corresponds to one and only one Employee Address value. (Note that the reverse need not be true: several employees could live at the same address and therefore one Employee Address value could correspond to more than one Employee ID. Employee ID is therefore not functionally dependent on Employee Address.) An attribute may be functionally dependent either on a single attribute or on a combination of attributes. It is not possible to determine the extent to which a design is normalized without understanding what functional dependencies apply to the attributes within its tables; understanding this, in turn, requires knowledge of the problem domain. For example, an Employer may require certain employees to split their time between two locations, such as New York City and London, and therefore want to allow Employees to have more than one Employee Address. In this case, Employee Address would no longer be functionally dependent on Employee ID.

Another way to look at the above is by reviewing basic mathematical functions:

Let F(x) be a mathematical function of one independent variable. The independent variable is analogous to the attribute A. The dependent variable (or the dependent attribute using the lingo above), and hence the term functional dependency, is the value of F(A); A is an independent attribute. As we know, mathematical functions can have only one output. Notationally speaking, it is common to express this relationship in mathematics as F(A) = B; or, B → F(A).

There are also functions of more than one independent variable—commonly, this is referred to as multivariable functions. This idea represents an attribute being functionally dependent on a combination of attributes. Hence, F(x,y,z) contains three independent variables, or independent attributes, and one dependent attribute, namely, F(x,y,z). In multivariable functions, there can only be one output, or one dependent variable, or attribute.

Trivial functional dependency

A trivial functional dependency is a functional dependency of an attribute on a superset of itself. {Employee ID, Employee Address} → {Employee Address} is trivial, as is {Employee Address} → {Employee Address}.

Full functional dependency

An attribute is fully functionally dependent on a set of attributes X if it is

functionally dependent on X, and

· not functionally dependent on any proper subset of X. {Employee Address} has a functional dependency on {Employee ID, Skill}, but not a full functional dependency, because it is also dependent on {Employee ID}.

Transitive dependency

A transitive dependency is an indirect functional dependency, one in which X→Z only by virtue of X→Y and Y→Z.

Multivalued dependency

A multivalued dependency is a constraint according to which the presence of certain rows in a table implies the presence of certain other rows.

Join dependency

A table T is subject to a join dependency if T can always be recreated by joining multiple tables each having a subset of the attributes of T.

Superkey

A superkey is an attribute or set of attributes that uniquely identifies rows within a table; in other words, two distinct rows are always guaranteed to have distinct superkeys. {Employee ID, Employee Address, Skill} would be a superkey for the “Employees’ Skills” table; {Employee ID, Skill} would also be a superkey.

Candidate key

A candidate key is a minimal superkey, that is, a superkey for which we can say that no proper subset of it is also a superkey. {Employee Id, Skill} would be a candidate key for the “Employees’ Skills” table.

Non-prime attribute

A non-prime attribute is an attribute that does not occur in any candidate key. Employee Address would be a non-prime attribute in the “Employees’ Skills” table.

Primary key

Most DBMSs require a table to be defined as having a single unique key, rather than a number of possible unique keys. A primary key is a key which the database designer has designated for this purpose.

Normal forms

The normal forms (abbrew. NF) of relational database theory provide criteria for determining a table’s degree of vulnerability to logical inconsistencies and anomalies. The higher the normal form applicable to a table, the less vulnerable it is to inconsistencies and anomalies. Each table has a “highest normal form” (HNF): by definition, a table always meets the requirements of its HNF and of all normal forms lower than its HNF; also by definition, a table fails to meet the requirements of any normal form higher than its HNF.

The normal forms are applicable to individual tables; to say that an entire database is in normal form n is to say that all of its tables are in normal form n.

The Normal Forms

The database community has developed a series of guidelines for ensuring that databases are normalized. These are referred to as normal forms and are numbered from one (the lowest form of normalization, referred to as first normal form or 1NF) through five (fifth normal form or 5NF). In practical applications, you’ll often see 1NF, 2NF, and 3NF along with the occasional 4NF. Fifth normal form is very rarely seen and won’t be discussed in this article.

Before we begin our discussion of the normal forms, it’s important to point out that they are guidelines and guidelines only. Occasionally, it becomes necessary to stray from them to meet practical business requirements. However, when variations take place, it’s extremely important to evaluate any possible ramifications they could have on your system and account for possible inconsistencies. That said, let’s explore the normal forms.

First Normal Form (1NF)

First normal form (1NF) sets the very basic rules for an organized database:

• Eliminate duplicative columns from the same table.
• Create separate tables for each group of related data and identify each row with a unique column or set of columns (the primary key).

Second Normal Form (2NF)

Second normal form (2NF) further addresses the concept of removing duplicative data:

• Meet all the requirements of the first normal form.
• Remove subsets of data that apply to multiple rows of a table and place them in separate tables.
• Create relationships between these new tables and their predecessors through the use of foreign keys.

Third Normal Form (3NF)

Third normal form (3NF) goes one large step further:

• Meet all the requirements of the second normal form.
• Remove columns that are not dependent upon the primary key.

Fourth Normal Form (4NF)

Finally, fourth normal form (4NF) has one additional requirement:

• Meet all the requirements of the third normal form.
• A relation is in 4NF if it has no multi-valued dependencies.

Remember, these normalization guidelines are cumulative. For a database to be in 2NF, it must first fulfill all the criteria of a 1NF database.

Denormalization

One major premise of this tutorial is that you should learn to develop the “best” possible design—which really focuses on the database structure itself. By doing this, you should be able to avoid many of the problems, bugs, inconsistencies, and maintenance nightmares that frequently plague actual systems in use today.

• However, your database will always be part of a larger system, which will include at least a user interface and reporting structure, perhaps with a large amount of application code written in a language such as Java or C++. Your database could also be the back-end of a Web site, with both middle-tier business logic and front-end presentation code dependent on it. It is not uncommon for developers to “break the rules” of database design in order to accommodate other parts of a system.

• An example of denormalization, using our “phone book” problem, would be to store the city and state attributes in the basic contacts table, rather than making a separate zip codes table. At the cost of extra storage, this would save one join in a SELECT statement. Although this would certainly not be needed in such a simple system, imagine a Web site that supports thousands of “hits” per second, with much more complicated queries needed to produce the output. With today’s terabyte disk systems, it might be worth using extra storage space to keep Web viewers from waiting excessively while a page is being generated. On the other hand, similarly-increasing processor power makes it less likely that this tradeoff will actually have to be made in practice.

• The key to successful denormalization is to make sure that end users of the system never have to manually duplicate or maintain the redundant data. Possible techniques for doing this include using materialized views, writing triggers (code executed by the database itself—not available on all systems), or writing application code that takes care of it at data-entry time.