Database normalization

Database normalization is the process of organizing the fields and tables of a relational database to minimize redundancy. Normalization usually involves dividing large tables into smaller (and less redundant) tables and defining relationships between them. The objective is to isolate data so that additions, deletions, and modifications of a field can be made in just one table and then propagated through the rest of the database using the defined relationships.

Edgar F. Codd, the inventor of the relational model, introduced the concept of normalization and what we now know as the First Normal Form (1NF) in 1970. Codd went on to define the Second Normal Form (2NF) and Third Normal Form (3NF) in 1971, and Codd and Raymond F. Boyce defined the Boyce-Codd Normal Form (BCNF) in 1974. Informally, a relational database table is often described as "normalized" if it is in the Third Normal Form. Most 3NF tables are free of insertion, update, and deletion anomalies.

A standard piece of database design guidance is that the designer should first create a fully normalized design; then selective denormalization can be performed for performance reasons.

A typical example of normalization is that a unique ID is stored everywhere in the system but its name is held in only one table. The name can be updated more easily in one row of one table. A typical update in such an example would be the RIM company changing its name to BlackBerry. That update would be done in one place and immediately the correct "BlackBerry" name would be displayed throughout the system.

Objectives

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 logic. (SQL is an example of such a data sub-language, albeit one that Codd regarded as seriously flawed.)

The objectives of normalization beyond 1NF (First Normal Form) 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.

— E.F. Codd, "Further Normalization of the Data Base Relational Model"

The sections below give details of each of these objectives.

Free the database of modification anomalies

An update anomaly. Employee 519 is shown as having different addresses on different records.

An insertion anomaly. Until the new faculty member, Dr. Newsome, is assigned to teach at least one course, his details cannot be recorded.

A deletion anomaly. All information about Dr. Giddens is lost if 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 skill). 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 except by setting the Course Code to null. This phenomenon is known as an insertion anomaly.
• Under certain circumstances, deletion of data representing certain facts necessitates 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, effectively also deleting the faculty member, unless we set the Course Code to null in the record itself. This phenomenon is known as a deletion anomaly.

Minimize 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.

For example, consider an online bookseller whose customers maintain wishlists of books they'd like to have. For the obvious, anticipated query—what books does this customer want?—it's enough to store the customer's wishlist in the table as, say, a homogeneous string of authors and titles.

With this design, though, the database can answer only that one single query. It cannot by itself answer interesting but unanticipated queries: What is the most-wished-for book? Which customers are interested in WWII espionage? How does Lord Byron stack up against his contemporary poets? Answers to these questions must come from special adaptive tools completely separate from the database. One tool might be software written especially to handle such queries. This special adaptive software has just one single purpose: in effect to normalize the non-normalized field.

Unforeseen queries can be answered trivially, and entirely within the database framework, with a normalized table.

Example

Querying and manipulating the data within a data structure which is not normalized, such as the following non-1NF representation of customers' credit card transactions, involves more complexity than is really necessary:

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

To each customer 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	Cust. ID
Jones	1
Wilkins	2
Stevens	3

Cust. ID	Tr. ID	Date	Amount
1	12890	14-Oct-2003	−87
1	12904	15-Oct-2003	−50
2	12898	14-Oct-2003	−21
3	12907	15-Oct-2003	−18
3	14920	20-Nov-2003	−70
3	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. The data structure places all of the values on an equal footing, exposing each to the DBMS directly, so each can potentially participate directly 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 normalized version also allows the user to change the customer name in one place and guards against errors that arise if the customer name is misspelled on some records.

Background to normalization: definitions

'{{{1}}}'

Functional dependency

In a given table, an attribute Y is said to have a functional dependency on a set of attributes X (written X → Y) if and only if each X value is associated with precisely one Y value. For example, in an "Employee" table that includes the attributes "Employee ID" and "Employee Date of Birth", the functional dependency {Employee ID} → {Employee Date of Birth} would hold. It follows from the previous two sentences that each {Employee ID} is associated with precisely one {Employee Date of Birth}.

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}. Even by the removal of {Skill} functional dependency still holds between {Employee Address} and {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.

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}.

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 a combination of attributes that can be used to uniquely identify a database record. A table might have many superkeys.

Candidate key

A candidate key is a special subset of superkeys that do not have any extraneous information in them: it is a minimal superkey.

Example: A table with the fields <Name>, <Age>, <SSN> and <Phone Extension> has many possible superkeys. Three of these are <SSN>, <Phone Extension, Name> and <SSN, Name>. Of those, only <SSN> is a candidate key as the others contain information not necessary to uniquely identify records ('SSN' here refers to Social Security Number, which is unique to each person).

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.

Prime attribute

A prime attribute, conversely, is an attribute that does occur in some candidate key.

Primary key

One candidate key in a relation may be designated the primary key. While that may be a common practice (or even a required one in some environments), it is strictly notational and has no bearing on normalization. With respect to normalization, all candidate keys have equal standing and are treated the same.

Normal forms

The normal forms (abbrev. NF) of relational database theory provide criteria for determining a table's degree of immunity against logical inconsistencies and anomalies. The higher the normal form applicable to a table, the less vulnerable it is. 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.

Newcomers to database design sometimes suppose that normalization proceeds in an iterative fashion, i.e. a 1NF design is first normalized to 2NF, then to 3NF, and so on. This is not an accurate description of how normalization typically works. A sensibly designed table is likely to be in 3NF on the first attempt; furthermore, if it is 3NF, it is overwhelmingly likely to have an HNF of 5NF. Achieving the "higher" normal forms (above 3NF) does not usually require an extra expenditure of effort on the part of the designer, because 3NF tables usually need no modification to meet the requirements of these higher normal forms.

The main normal forms are summarized below.

	Normal form	Defined by	In	Brief definition
1NF	First normal form	Two versions: E.F. Codd (1970), C.J. Date (2003)	1970 and 2003	The domain of each attribute contains only atomic values, and the value of each attribute contains only a single value from that domain.
2NF	Second normal form	E.F. Codd	1971	No non-prime attribute in the table is functionally dependent on a proper subset of any candidate key
3NF	Third normal form	Two versions: E.F. Codd (1971), C. Zaniolo (1982)	1971 and 1982	Every non-prime attribute is non-transitively dependent on every candidate key in the table. The attributes that do not contribute to the description of the primary key are removed from the table. In other words, no transitive dependency is allowed.
EKNF	Elementary Key Normal Form	C. Zaniolo	1982	Every non-trivial functional dependency in the table is either the dependency of an elementary key attribute or a dependency on a superkey
BCNF	Boyce–Codd normal form	Raymond F. Boyce and E.F. Codd	1974	Every non-trivial functional dependency in the table is a dependency on a superkey
4NF	Fourth normal form	Ronald Fagin	1977	Every non-trivial multivalued dependency in the table is a dependency on a superkey
5NF	Fifth normal form	Ronald Fagin	1979	Every non-trivial join dependency in the table is implied by the superkeys of the table
DKNF	Domain/key normal form	Ronald Fagin	1981	Every constraint on the table is a logical consequence of the table's domain constraints and key constraints
6NF	Sixth normal form	C.J. Date, Hugh Darwen, and Nikos Lorentzos	2002	Table features no non-trivial join dependencies at all (with reference to generalized join operator)

Denormalization

Main article: Denormalization

Databases intended for online transaction processing (OLTP) are typically more normalized than databases intended for online analytical processing (OLAP). OLTP applications are characterized by a high volume of small transactions such as updating a sales record at a supermarket checkout counter. The expectation is that each transaction will leave the database in a consistent state. By contrast, databases intended for OLAP operations are primarily "read mostly" databases. OLAP applications tend to extract historical data that has accumulated over a long period of time. For such databases, redundant or "denormalized" data may facilitate business intelligence applications. Specifically, dimensional tables in a star schema often contain denormalized data. The denormalized or redundant data must be carefully controlled during extract, transform, load (ETL) processing, and users should not be permitted to see the data until it is in a consistent state. The normalized alternative to the star schema is the snowflake schema. In many cases, the need for denormalization has waned as computers and RDBMS software have become more powerful, but since data volumes have generally increased along with hardware and software performance, OLAP databases often still use denormalized schemas.

Denormalization is also used to improve performance on smaller computers as in computerized cash-registers and mobile devices, since these may use the data for look-up only (e.g. price lookups). Denormalization may also be used when no RDBMS exists for a platform (such as Palm), or no changes are to be made to the data and a swift response is crucial.

Non-first normal form (NF² or N1NF)

Denormalization is the opposite of normalization. In recognition that denormalization can be deliberate and useful, the non-first normal form is a definition of database designs which do not conform to first normal form, by allowing "sets and sets of sets to be attribute domains" (Schek 1982). The languages used to query and manipulate data in the model must be extended accordingly to support such values.

One way of looking at this is to consider such structured values as being specialized types of values (domains), with their own domain-specific languages. However, what is usually meant by non-1NF models is the approach in which the relational model and the languages used to query it are extended with a general mechanism for such structure; for instance, the nested relational model supports the use of relations as domain values, by adding two additional operators (nest and unnest) to the relational algebra that can create and flatten nested relations, respectively.

Consider the following table:

First Normal Form

Person	Favourite Colour
Bob	blue
Bob	red
Jane	green
Jane	yellow
Jane	red

Assume a person has several favourite colours. Obviously, favourite colours consist of a set of colours modeled by the given table. To transform a 1NF into an NF² table a "nest" operator is required which extends the relational algebra of the higher normal forms. Applying the "nest" operator to the 1NF table yields the following NF² table:

Non-First Normal Form

Person	Favourite Colours
Bob	Favourite Colour blue red
Jane	Favourite Colour green yellow red

To transform this NF² table back into a 1NF an "unnest" operator is required which extends the relational algebra of the higher normal forms. The unnest, in this case, would make "colours" into its own table.

Although "unnest" is the mathematical inverse to "nest", the operator "nest" is not always the mathematical inverse of "unnest". Another constraint required is for the operators to be bijective, which is covered by the Partitioned Normal Form (PNF).

Categorical Normal Form

A relational schema such that every table is either 1) unary or 2) a binary function between unary tables is a presentation of a freely generated category. An instance on such a schema is (a presentation of) a functor from the free category to the category of sets. If the schema further imposes path equivalence constraints, then the schema denotes a finitely presented category (which is intuitively the quotient of the underlying free category by the path equivalence constraints). A schema denoting a finitely presented category is said to be in categorical normal form (see Functorial Data Migration).

See also

• Aspect (computer programming)
• Business rule
• Canonical form
• Cross-cutting concern
• Database testing
• Optimization (computer science)
• Refactoring
• Universal relation assumption

Notes and references

• Paper: "Non First Normal Form Relations" by G. Jaeschke, H. -J Schek ; IBM Heidelberg Scientific Center. -> Paper studying normalization and denormalization operators nest and unnest as mildly described at the end of this wiki page.

Further reading

• Litt's Tips: Normalization
• Date, C. J. (1999), An Introduction to Database Systems (8th ed.). Addison-Wesley Longman. ISBN 0-321-19784-4.
• Kent, W. (1983) A Simple Guide to Five Normal Forms in Relational Database Theory, Communications of the ACM, vol. 26, pp. 120–125
• H.-J. Schek, P. Pistor Data Structures for an Integrated Data Base Management and Information Retrieval System

External links

• Database Normalization Basics by Mike Chapple (About.com)
• Database Normalization Intro, Part 2
• An Introduction to Database Normalization by Mike Hillyer.
• A tutorial on the first 3 normal forms by Fred Coulson
• DB Normalization Examples
• Description of the database normalization basics by Microsoft
• Database Normalization and Design Techniques by Barry Wise, recommended reading for the Harvard MIS.
• A Simple Guide to Five Normal Forms in Relational Database Theory