Example of a step-by-step normalization
Normalization is a database design technique, which is used to design a relational database table up to higher normal form. [9] The process is progressive, and a higher level of database normalization cannot be achieved unless the previous levels have been satisfied. [10]
That means that, having data in unnormalized form (the least normalized) and aiming to achieve the highest level of normalization, the first step would be to ensure compliance to first normal form, the second step would be to ensure second normal form is satisfied, and so forth in order mentioned above, until the data conform to sixth normal form.
However, it is worth noting that normal forms beyond 4NF are mainly of academic interest, as the problems they exist to solve rarely appear in practice. [11]
The data in the following example were intentionally designed to contradict most of the normal forms. In practice it is often possible to skip some of the normalization steps because the data is already normalized to some extent. Fixing a violation of one normal form also often fixes a violation of a higher normal form. In the example, one table has been chosen for normalization at each step, meaning that at the end, some tables might not be sufficiently normalized.
Initial data
Let a database table exist with the following structure: [10]
| Title | Author | Author Nationality | Format | Price | Subject | Pages | Thickness | Publisher | Publisher Country | Genre ID | Genre Name |
|---|
| Beginning MySQL Database Design and Optimization | Chad Russell | American | Hardcover | 49.99 | | 520 | Thick | Apress | USA | 1 | Tutorial |
For this example it is assumed that each book has only one author.
A table that conforms to the relational model has a primary key which uniquely identifies a row. In our example, the primary key is a composite key of {Title, Format} (indicated by the underlining):
| Title | Author | Author Nationality | Format | Price | Subject | Pages | Thickness | Publisher | Publisher Country | Genre ID | Genre Name |
|---|
| Beginning MySQL Database Design and Optimization | Chad Russell | American | Hardcover | 49.99 | | 520 | Thick | Apress | USA | 1 | Tutorial |
Satisfying 1NF
In the first normal form each field contains a single value. A field may not contain a set of values or a nested record.
Subject contains a set of subject values, meaning it does not comply.
To solve the problem, the subjects are extracted into a separate Subject table: [10]
Book| Title | Author | Author Nationality | Format | Price | Pages | Thickness | Publisher | Publisher Country | Genre ID | Genre Name |
|---|
| Beginning MySQL Database Design and Optimization | Chad Russell | American | Hardcover | 49.99 | 520 | Thick | Apress | USA | 1 | Tutorial |
Title - Subject| Title | Subject name |
|---|
| Beginning MySQL Database Design and Optimization | MySQL |
| Beginning MySQL Database Design and Optimization | Database |
| Beginning MySQL Database Design and Optimization | Design |
Instead of one table in unnormalized form, there are now two tables conforming to the 1NF.
Satisfying 2NF
Recall that the Book table below has a composite key of {Title, Format}, which will not satisfy 2NF if some subset of that key is a determinant. At this point in our design the key is not finalised as the primary key, so it is called a candidate key. Consider the following table:
Book| Title | Format | Author | Author Nationality | Price | Pages | Thickness | Publisher | Publisher Country | Genre ID | Genre Name |
|---|
| Beginning MySQL Database Design and Optimization | Hardcover | Chad Russell | American | 49.99 | 520 | Thick | Apress | USA | 1 | Tutorial |
| Beginning MySQL Database Design and Optimization | E-book | Chad Russell | American | 22.34 | 520 | Thick | Apress | USA | 1 | Tutorial |
| The Relational Model for Database Management: Version 2 | E-book | E.F.Codd | British | 13.88 | 538 | Thick | Addison-Wesley | USA | 2 | Popular science |
| The Relational Model for Database Management: Version 2 | Paperback | E.F.Codd | British | 39.99 | 538 | Thick | Addison-Wesley | USA | 2 | Popular science |
All of the attributes that are not part of the candidate key depend on Title, but only Price also depends on Format. To conform to 2NF and remove duplicates, every non-candidate-key attribute must depend on the whole candidate key, not just part of it.
To normalize this table, make {Title} a (simple) candidate key (the primary key) so that every non-candidate-key attribute depends on the whole candidate key, and remove Price into a separate table so that its dependency on Format can be preserved:
Book| Title | Author | Author Nationality | Pages | Thickness | Publisher | Publisher Country | Genre ID | Genre Name |
|---|
| Beginning MySQL Database Design and Optimization | Chad Russell | American | 520 | Thick | Apress | USA | 1 | Tutorial |
| The Relational Model for Database Management: Version 2 | E.F.Codd | British | 538 | Thick | Addison-Wesley | USA | 2 | Popular science |
Price| Title | Format | Price |
|---|
| Beginning MySQL Database Design and Optimization | Hardcover | 49.99 |
| Beginning MySQL Database Design and Optimization | E-book | 22.34 |
| The Relational Model for Database Management: Version 2 | E-book | 13.88 |
| The Relational Model for Database Management: Version 2 | Paperback | 39.99 |
Now, both the Book and Price tables conform to 2NF.
Satisfying 3NF
The Book table still has a transitive functional dependency ({Author Nationality} is dependent on {Author}, which is dependent on {Title}). Similar violations exist for publisher ({Publisher Country} is dependent on {Publisher}, which is dependent on {Title}) and for genre ({Genre Name} is dependent on {Genre ID}, which is dependent on {Title}). Hence, the Book table is not in 3NF. To resolve this, we can place {Author Nationality}, {Publisher Country}, and {Genre Name} in their own respective tables, thereby eliminating the transitive functional dependencies:
Book| Title | Author | Pages | Thickness | Publisher | Genre ID |
|---|
| Beginning MySQL Database Design and Optimization | Chad Russell | 520 | Thick | Apress | 1 |
| The Relational Model for Database Management: Version 2 | E.F.Codd | 538 | Thick | Addison-Wesley | 2 |
Price| Title | Format | Price |
|---|
| Beginning MySQL Database Design and Optimization | Hardcover | 49.99 | | Beginning MySQL Database Design and Optimization | E-book | 22.34 | | The Relational Model for Database Management: Version 2 | E-book | 13.88 | | The Relational Model for Database Management: Version 2 | Paperback | 39.99 | |
Author| Author | Author Nationality |
|---|
| Chad Russell | American |
| E.F.Codd | British |
Publisher| Publisher | Country |
|---|
| Apress | USA |
| Addison-Wesley | USA |
Genre| Genre ID | Name |
|---|
| 1 | Tutorial |
| 2 | Popular science |
Satisfying EKNF
The elementary key normal form (EKNF) falls strictly between 3NF and BCNF and is not much discussed in the literature. It is intended "to capture the salient qualities of both 3NF and BCNF" while avoiding the problems of both (namely, that 3NF is "too forgiving" and BCNF is "prone to computational complexity"). Since it is rarely mentioned in literature, it is not included in this example.
Satisfying 4NF
Assume the database is owned by a book retailer franchise that has several franchisees that own shops in different locations. And therefore the retailer decided to add a table that contains data about availability of the books at different locations:
Franchisee - Book - Location| Franchisee ID | Title | Location |
|---|
| 1 | Beginning MySQL Database Design and Optimization | California |
| 1 | Beginning MySQL Database Design and Optimization | Florida |
| 1 | Beginning MySQL Database Design and Optimization | Texas |
| 1 | The Relational Model for Database Management: Version 2 | California |
| 1 | The Relational Model for Database Management: Version 2 | Florida |
| 1 | The Relational Model for Database Management: Version 2 | Texas |
| 2 | Beginning MySQL Database Design and Optimization | California |
| 2 | Beginning MySQL Database Design and Optimization | Florida |
| 2 | Beginning MySQL Database Design and Optimization | Texas |
| 2 | The Relational Model for Database Management: Version 2 | California |
| 2 | The Relational Model for Database Management: Version 2 | Florida |
| 2 | The Relational Model for Database Management: Version 2 | Texas |
| 3 | Beginning MySQL Database Design and Optimization | Texas |
|
As this table structure consists of a compound primary key, it doesn't contain any non-key attributes and it's already in BCNF (and therefore also satisfies all the previous normal forms). However, assuming that all available books are offered in each area, the Title is not unambiguously bound to a certain Location and therefore the table doesn't satisfy 4NF.
That means that, to satisfy the fourth normal form, this table needs to be decomposed as well:
Franchisee - Book| Franchisee ID | Title |
|---|
| 1 | Beginning MySQL Database Design and Optimization | | 1 | The Relational Model for Database Management: Version 2 | | 2 | Beginning MySQL Database Design and Optimization | | 2 | The Relational Model for Database Management: Version 2 | | 3 | Beginning MySQL Database Design and Optimization | |
| Franchisee - Location| Franchisee ID | Location |
|---|
| 1 | California | | 1 | Florida | | 1 | Texas | | 2 | California | | 2 | Florida | | 2 | Texas | | 3 | Texas | |
|
Now, every record is unambiguously identified by a superkey, therefore 4NF is satisfied.
Satisfying ETNF
Suppose the franchisees can also order books from different suppliers. Let the relation also be subject to the following constraint:
- If a certain supplier supplies a certain title
- and the title is supplied to the franchisee
- and the franchisee is being supplied by the supplier,
- then the supplier supplies the title to the franchisee. [12]
Supplier - Book - Franchisee| Supplier ID | Title | Franchisee ID |
|---|
| 1 | Beginning MySQL Database Design and Optimization | 1 |
| 2 | The Relational Model for Database Management: Version 2 | 2 |
| 3 | Learning SQL | 3 |
This table is in 4NF, but the Supplier ID is equal to the join of its projections: {{Supplier ID, Title}, {Title, Franchisee ID}, {Franchisee ID, Supplier ID}}. No component of that join dependency is a superkey (the sole superkey being the entire heading), so the table does not satisfy the ETNF and can be further decomposed: [12]
Supplier - Book| Supplier ID | Title |
|---|
| 1 | Beginning MySQL Database Design and Optimization | | 2 | The Relational Model for Database Management: Version 2 | | 3 | Learning SQL | | Book - Franchisee| Title | Franchisee ID |
|---|
| Beginning MySQL Database Design and Optimization | 1 | | The Relational Model for Database Management: Version 2 | 2 | | Learning SQL | 3 | | Franchisee - Supplier| Supplier ID | Franchisee ID |
|---|
| 1 | 1 | | 2 | 2 | | 3 | 3 | |
The decomposition produces ETNF compliance.
Satisfying 5NF
To spot a table not satisfying the 5NF, it is usually necessary to examine the data thoroughly. Suppose the table from 4NF example with a little modification in data and let's examine if it satisfies 5NF:
Franchisee - Book - Location| Franchisee ID | Title | Location |
|---|
| 1 | Beginning MySQL Database Design and Optimization | California |
| 1 | Learning SQL | California |
| 1 | The Relational Model for Database Management: Version 2 | Texas |
| 2 | The Relational Model for Database Management: Version 2 | California |
|
Decomposing this table lowers redundancies, resulting in the following two tables:
Franchisee - Book| Franchisee ID | Title |
|---|
| 1 | Beginning MySQL Database Design and Optimization | | 1 | Learning SQL | | 1 | The Relational Model for Database Management: Version 2 | | 2 | The Relational Model for Database Management: Version 2 | |
| Franchisee - Location| Franchisee ID | Location |
|---|
| 1 | California | | 1 | Texas | | 2 | California | |
|
The query joining these tables would return the following data:
Franchisee - Book - Location JOINed| Franchisee ID | Title | Location |
|---|
| 1 | Beginning MySQL Database Design and Optimization | California |
| 1 | Learning SQL | California |
| 1 | The Relational Model for Database Management: Version 2 | California |
| 1 | The Relational Model for Database Management: Version 2 | Texas |
| 1 | Learning SQL | Texas |
| 1 | Beginning MySQL Database Design and Optimization | Texas |
| 2 | The Relational Model for Database Management: Version 2 | California |
|
The JOIN returns three more rows than it should; adding another table to clarify the relation results in three separate tables:
Franchisee - Book| Franchisee ID | Title |
|---|
| 1 | Beginning MySQL Database Design and Optimization | | 1 | Learning SQL | | 1 | The Relational Model for Database Management: Version 2 | | 2 | The Relational Model for Database Management: Version 2 | |
| Franchisee - Location| Franchisee ID | Location |
|---|
| 1 | California | | 1 | Texas | | 2 | California | |
| Location - Book| Location | Title |
|---|
| California | Beginning MySQL Database Design and Optimization | | California | Learning SQL | | California | The Relational Model for Database Management: Version 2 | | Texas | The Relational Model for Database Management: Version 2 | |
|
What will the JOIN return now? It actually is not possible to join these three tables. That means it wasn't possible to decompose the Franchisee - Book - Location without data loss, therefore the table already satisfies 5NF.
C.J. Date has argued that only a database in 5NF is truly "normalized". [13]
Satisfying DKNF
Let's have a look at the Book table from previous examples and see if it satisfies the domain-key normal form:
Book| Title | Pages | Thickness | Genre ID | Publisher ID |
|---|
| Beginning MySQL Database Design and Optimization | 520 | Thick | 1 | 1 |
| The Relational Model for Database Management: Version 2 | 538 | Thick | 2 | 2 |
| Learning SQL | 338 | Slim | 1 | 3 |
| SQL Cookbook | 636 | Thick | 1 | 3 |
Logically, Thickness is determined by number of pages. That means it depends on Pages which is not a key. Let's set an example convention saying a book up to 350 pages is considered "slim" and a book over 350 pages is considered "thick".
This convention is technically a constraint but it is neither a domain constraint nor a key constraint; therefore we cannot rely on domain constraints and key constraints to keep the data integrity.
In other words – nothing prevents us from putting, for example, "Thick" for a book with only 50 pages – and this makes the table violate DKNF.
To solve this, a table holding enumeration that defines the Thickness is created, and that column is removed from the original table:
Thickness Enum| Thickness | Min pages | Max pages |
|---|
| Slim | 1 | 350 | | Thick | 351 | 999,999,999,999 | | Book - Pages - Genre - Publisher| Title | Pages | Genre ID | Publisher ID |
|---|
| Beginning MySQL Database Design and Optimization | 520 | 1 | 1 | | The Relational Model for Database Management: Version 2 | 538 | 2 | 2 | | Learning SQL | 338 | 1 | 3 | | SQL Cookbook | 636 | 1 | 3 | |
That way, the domain integrity violation has been eliminated, and the table is in DKNF.
Satisfying 6NF
A simple and intuitive definition of the sixth normal form is that "a table is in 6NF when the row contains the Primary Key, and at most one other attribute". [14]
That means, for example, the Publisher table designed while creating the 1NF:
Publisher| Publisher ID | Name | Country |
|---|
| 1 | Apress | USA |
needs to be further decomposed into two tables:
Publisher| Publisher ID | Name |
|---|
| 1 | Apress | | Publisher country| Publisher ID | Country |
|---|
| 1 | USA | |
The obvious drawback of 6NF is the proliferation of tables required to represent the information on a single entity. If a table in 5NF has one primary key column and N attributes, representing the same information in 6NF will require N tables; multi-field updates to a single conceptual record will require updates to multiple tables; and inserts and deletes will similarly require operations across multiple tables. For this reason, in databases intended to serve online transaction processing (OLTP) needs, 6NF should not be used.
However, in data warehouses, which do not permit interactive updates and which are specialized for fast query on large data volumes, certain DBMSs use an internal 6NF representation – known as a columnar data store. In situations where the number of unique values of a column is far less than the number of rows in the table, column-oriented storage allow significant savings in space through data compression. Columnar storage also allows fast execution of range queries (e.g., show all records where a particular column is between X and Y, or less than X.)
In all these cases, however, the database designer does not have to perform 6NF normalization manually by creating separate tables. Some DBMSs that are specialized for warehousing, such as Sybase IQ, use columnar storage by default, but the designer still sees only a single multi-column table. Other DBMSs, such as Microsoft SQL Server 2012 and later, let you specify a "columnstore index" for a particular table. [15]
Denormalization is a strategy used on a previously-normalized database to increase performance. In computing, denormalization is the process of trying to improve the read performance of a database, at the expense of losing some write performance, by adding redundant copies of data or by grouping data. It is often motivated by performance or scalability in relational database software needing to carry out very large numbers of read operations. Denormalization differs from the unnormalized form in that denormalization benefits can only be fully realized on a data model that is otherwise normalized.
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970.
The relational model (RM) is an approach to managing data using a structure and language consistent with first-order predicate logic, first described in 1969 by English computer scientist Edgar F. Codd, where all data is represented in terms of tuples, grouped into relations. A database organized in terms of the relational model is a relational database.
First normal form (1NF) is a property of a relation in a relational database. A relation is in first normal form if and only if no attribute domain has relations as elements. Or more informally, that no table column can have tables as values. Database normalization is the process of representing a database in terms of relations in standard normal forms, where first normal is a minimal requirement. SQL-92 does not support creating or using table-valued columns, which means that using only the "traditional relational database features" most relational databases will be in first normal form by necessity. Database systems which do not require first normal form are often called NoSQL systems. Newer SQL standards like SQL:1999 have started to allow so called non-atomic types, which include composite types. Even newer versions like SQL:2016 allow JSON.
Second normal form (2NF), in database normalization, is a normal form. A relation is in the second normal form if it fulfills the following two requirements:
- It is in first normal form.
- It does not have any non-prime attribute that is functionally dependent on any proper subset of any candidate key of the relation. A non-prime attribute of a relation is an attribute that is not a part of any candidate key of the relation.
Third normal form (3NF) is a database schema design approach for relational databases which uses normalizing principles to reduce the duplication of data, avoid data anomalies, ensure referential integrity, and simplify data management. It was defined in 1971 by Edgar F. Codd, an English computer scientist who invented the relational model for database management.
Fourth normal form (4NF) is a normal form used in database normalization. Introduced by Ronald Fagin in 1977, 4NF is the next level of normalization after Boyce–Codd normal form (BCNF). Whereas the second, third, and Boyce–Codd normal forms are concerned with functional dependencies, 4NF is concerned with a more general type of dependency known as a multivalued dependency. A table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies XY, {X, Y} is a superkey—that is, the combination of all attributes in X and Y is either a candidate key or a superset thereof.
In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation R and attribute sets , X is said to functionally determineY if each X value is associated with precisely one Y value. R is then said to satisfy the functional dependency X → Y. Equivalently, the projection is a function, that is, Y is a function of X. In simple words, if the values for the X attributes are known, then the values for the Y attributes corresponding to x can be determined by looking them up in any tuple of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a subset of X.
A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other relation, S; furthermore that those attributes must also be a candidate key in S.
Database design is the organization of data according to a database model. The designer determines what data must be stored and how the data elements interrelate. With this information, they can begin to fit the data to the database model. A database management system manages the data accordingly.
In the relational data model a superkey is any set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are functionally dependent on the superkey.
In SQL, null or NULL is a special marker used to indicate that a data value does not exist in the database. Introduced by the creator of the relational database model, E. F. Codd, SQL null serves to fulfill the requirement that all true relational database management systems (RDBMS) support a representation of "missing information and inapplicable information". Codd also introduced the use of the lowercase Greek omega (ω) symbol to represent null in database theory. In SQL, NULL is a reserved word used to identify this marker.
Boyce–Codd normal form is a normal form used in database normalization. It is a slightly stricter version of the third normal form (3NF). By using BCNF, a database will remove all redundancies based on functional dependencies.
Fifth normal form (5NF), also known as projection–join normal form (PJ/NF), is a level of database normalization designed to remove redundancy in relational databases recording multi-valued facts by isolating semantically related multiple relationships. A table is said to be in the 5NF if and only if every non-trivial join dependency in that table is implied by the candidate keys. It is the final normal form as far as removing redundancy is concerned.
Sixth normal form (6NF) is a normal form used in relational database normalization which extends the relational algebra and generalizes relational operators to support interval data, which can be useful in temporal databases.
In relational database management systems, a unique key is a candidate key. All the candidate keys of a relation can uniquely identify the records of the relation, but only one of them is used as the primary key of the relation. The remaining candidate keys are called unique keys because they can uniquely identify a record in a relation. Unique keys can consist of multiple columns. Unique keys are also called alternate keys. Unique keys are an alternative to the primary key of the relation. In SQL, the unique keys have a UNIQUE constraint assigned to them in order to prevent duplicates. Alternate keys may be used like the primary key when doing a single-table select or when filtering in a where clause, but are not typically used to join multiple tables.
A database model is a type of data model that determines the logical structure of a database. It fundamentally determines in which manner data can be stored, organized and manipulated. The most popular example of a database model is the relational model, which uses a table-based format.
In database theory, a relation, as originally defined by E. F. Codd, is a set of tuples (d1,d2,...,dn), where each element dj is a member of Dj, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation. Instead, each element is termed an attribute value. An attribute is a name paired with a domain. An attribute value is an attribute name paired with an element of that attribute's domain, and a tuple is a set of attribute values in which no two distinct elements have the same name. Thus, in some accounts, a tuple is described as a function, mapping names to values.
In database normalization, unnormalized form (UNF or 0NF), also known as an unnormalized relation or non-first normal form (N1NF or NF2), is a database data model (organization of data in a database) which does not meet any of the conditions of database normalization defined by the relational model. Database systems which support unnormalized data are sometimes called non-relational or NoSQL databases. In the relational model, unnormalized relations can be considered the starting point for a process of normalization.
Essential tuple normal form (ETNF) is a normal form used in database normalization. It lies strictly between fourth normal form (4NF) and fifth normal form (5NF). As per the original paper, ETNF, although strictly weaker than 5NF, is exactly as effective as 5NF in eliminating redundancy of tuples.
