Database normalization

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Database normalization is the process of structuring a database, usually a relational database, in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by Edgar F. Codd as part of his relational model.

Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of synthesis (creating a new database design) or decomposition (improving an existing database design).

Objectives[edit]

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.[1] (SQL is an example of such a data sub-language, albeit one that Codd regarded as seriously flawed.[2])

The objectives of normalisation 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 Normalisation of the Data Base Relational Model"[3]
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 or her details cannot be recorded.
A deletion anomaly. All information about Dr. Giddens is lost if he or she temporarily ceases to be assigned to any courses.

When an attempt is made to modify (update, insert into, or delete from) a relation, the following undesirable side-effects may arise in relations that have not been sufficiently normalized:

  • Update anomaly. The same information can be expressed on multiple rows; therefore updates to the relation may result in logical inconsistencies. For example, each record in an "Employees' Skills" relation might contain an Employee ID, Employee Address, and Skill; thus a change of address for a particular employee may need to be applied to multiple records (one for each skill). If the update is only partially successful – the employee's address is updated on some records but not others – then the relation is left in an inconsistent state. Specifically, the relation provides conflicting answers to the question of what this particular employee's address is. This phenomenon is known as an update anomaly.
  • Insertion anomaly. There are circumstances in which certain facts cannot be recorded at all. For example, each record in a "Faculty and Their Courses" relation might contain a Faculty ID, Faculty Name, Faculty Hire Date, and Course Code. Therefore, the details of any faculty member who teaches at least one course can be recorded, but a newly hired faculty member who has not yet been assigned to teach any courses cannot be recorded, except by setting the Course Code to null. This phenomenon is known as an insertion anomaly.
  • Deletion anomaly. Under certain circumstances, deletion of data representing certain facts necessitates deletion of data representing completely different facts. The "Faculty and Their Courses" relation described in the previous example suffers from this type of anomaly, for if a faculty member temporarily ceases to be assigned to any courses, the last of the records on which that faculty member appears must be deleted, effectively also deleting the faculty member, unless the Course Code field is set to null. This phenomenon is known as a deletion anomaly.

Minimize redesign when extending the database structure[edit]

A fully normalized database allows its structure to be extended to accommodate new types of data without changing existing structure too much. As a result, applications interacting with the database are minimally affected.

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

Normal forms[edit]

Codd introduced the concept of normalization and what is now known as the first normal form (1NF) in 1970.[4] Codd went on to define the second normal form (2NF) and third normal form (3NF) in 1971,[5] and Codd and Raymond F. Boyce defined the Boyce–Codd normal form (BCNF) in 1974.[6]

Informally, a relational database relation is often described as "normalized" if it meets third normal form.[7] Most 3NF relations are free of insertion, updation, and deletion anomalies.

The normal forms (from least normalized to most normalized) are:

UNF
(1970)
1NF
(1970)
2NF
(1971)
3NF
(1971)
EKNF
(1982)
BCNF
(1974)
4NF
(1977)
ETNF
(2012)
5NF
(1979)
DKNF
(1981)
6NF
(2003)
Primary key (no duplicate tuples)[4] Maybe Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Atomic columns (cells cannot have tables as values)[5] No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
Every non-trivial functional dependency either does not begin with a proper subset of a candidate key or ends with a prime attribute (no partial functional dependencies of non-prime attributes on candidate keys)[5] No No Yes Yes Yes Yes Yes Yes Yes Yes Yes
Every non-trivial functional dependency either begins with a superkey or ends with a prime attribute (no transitive functional dependencies of non-prime attributes on candidate keys)[5] No No No Yes Yes Yes Yes Yes Yes Yes Yes
Every non-trivial functional dependency either begins with a superkey or ends with an elementary prime attribute No No No No Yes Yes Yes Yes Yes Yes N/A
Every non-trivial functional dependency begins with a superkey No No No No No Yes Yes Yes Yes Yes N/A
Every non-trivial multivalued dependency begins with a superkey No No No No No No Yes Yes Yes Yes N/A
Every join dependency has a superkey component[8] No No No No No No No Yes Yes Yes N/A
Every join dependency has only superkey components No No No No No No No No Yes Yes N/A
Every constraint is a consequence of domain constraints and key constraints No No No No No No No No No Yes No
Every join dependency is trivial No No No No No No No No No No Yes

Example of a step by step normalization[edit]

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]

Please note that the data in the following example were intentionally designed to contradict most of the normal forms. In real life, it's quite possible to be able to skip some of the normalization steps because the table doesn't contain anything contradicting the given normal form. It also commonly occurs that fixing a violation of one normal form also fixes a violation of a higher normal form in the process. Also one table has been chosen for normalization at each step, meaning that at the end of this example process, there might still be some tables not satisfying the highest normal form.

Initial data[edit]

Let a database table exist with the following structure:[10]

Title Author Author Nationality Format Price Subject Pages Thickness Publisher Publisher Country Publication Type Genre ID Genre Name
Beginning MySQL Database Design and Optimization Chad Russell American Hardcover 49.99
MySQL
Database
Design
520 Thick Apress USA E-book 1 Tutorial

For this example, it is assumed that each book has only one author.

As a prerequisite to conform to the relational model, a table must have a primary key, which uniquely identifies a row. Two books could have the same title, but an ISBN number uniquely identifies a book, so it can be used as the primary key:

ISBN# Title Author Author Nationality Format Price Subject Pages Thickness Publisher Publisher Country Publication Type Genre ID Genre Name
1590593324 Beginning MySQL Database Design and Optimization Chad Russell American Hardcover 49.99
MySQL
Database
Design
520 Thick Apress USA E-book 1 Tutorial

Satisfying 1NF[edit]

To satisfy First normal form, each column of a table must have a single value. Columns which contain sets of values or nested records are not allowed.

In the initial table, 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
ISBN# Title Format Author Author Nationality Price Pages Thickness Publisher Publisher country Genre ID Genre Name
1590593324 Beginning MySQL Database Design and Optimization Hardcover Chad Russell American 49.99 520 Thick Apress USA 1 Tutorial
Subject
ISBN# Subject name
1590593324 MySQL
1590593324 Database
1590593324 Design

A foreign key column to the Subject-table is added, which refers to the primary key of the row from which the subject was extracted. The same information is therefore represented but without the use of non-simple domains.

Instead of one table in unnormalized form, there are now two tables conforming to the 1NF.

Satisfying 2NF[edit]

The Book table has one candidate key (which is therefore the primary key), the composite key {Title, Format}.[12] Consider the following table fragment:

Book
Title Format Author Author Nationality Price Pages Thickness Genre ID Genre Name Publisher ID
Beginning MySQL Database Design and Optimization Hardcover Chad Russell American 49.99 520 Thick 1 Tutorial 1
Beginning MySQL Database Design and Optimization E-book Chad Russell American 22.34 520 Thick 1 Tutorial 1
The Relational Model for Database Management: Version 2 E-book E.F.Codd British 13.88 538 Thick 2 Popular science 2
The Relational Model for Database Management: Version 2 Paperback E.F.Codd British 39.99 538 Thick 2 Popular science 2

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 duplicities, 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 Genre ID Genre Name Publisher ID
Beginning MySQL Database Design and Optimization Chad Russell American 520 Thick 1 Tutorial 1
The Relational Model for Database Management: Version 2 E.F.Codd British 538 Thick 2 Popular science 2
Format - 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, the Book table conforms to 2NF.

Satisfying 3NF[edit]

The Book table still has a transitive functional dependency ({Author Nationality} is dependent on {Author}, which is dependent on {Title}). A similar violation exists for genre ({Genre Name} is dependent on {Genre ID}, which is dependent on {Title}). Hence, the Book table is not in 3NF. To make it in 3NF, let's use the following table structure, thereby eliminating the transitive functional dependencies by placing {Author Nationality} and {Genre Name} in their own respective tables:

Book
Title Author Pages Thickness Genre ID Publisher ID
Beginning MySQL Database Design and Optimization Chad Russell 520 Thick 1 1
The Relational Model for Database Management: Version 2 E.F.Codd 538 Thick 2 2
Format - 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
Genre
Genre ID Genre Name
1 Tutorial
2 Popular science

Satisfying EKNF[edit]

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.[13]

Satisfying 4NF[edit]

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.[14]

Satisfying ETNF[edit]

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.[15]
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, Book}, {Book, 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:[15]

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[edit]

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.[14]

C.J. Date has argued that only a database in 5NF is truly "normalized".[16]

Satisfying DKNF[edit]

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[edit]

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".[17]

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 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.[18]

See also[edit]

Notes and references[edit]

  1. ^ "The adoption of a relational model of data ... permits the development of a universal data sub-language based on an applied predicate calculus. A first-order predicate calculus suffices if the collection of relations is in first normal form. Such a language would provide a yardstick of linguistic power for all other proposed data languages, and would itself be a strong candidate for embedding (with appropriate syntactic modification) in a variety of host languages (programming, command- or problem-oriented)." Codd, "A Relational Model of Data for Large Shared Data Banks" Archived June 12, 2007, at the Wayback Machine, p. 381
  2. ^ Codd, E.F. Chapter 23, "Serious Flaws in SQL", in The Relational Model for Database Management: Version 2. Addison-Wesley (1990), pp. 371–389
  3. ^ Codd, E.F. "Further Normalisation of the Data Base Relational Model", p. 34
  4. ^ a b Codd, E. F. (June 1970). "A Relational Model of Data for Large Shared Data Banks". Communications of the ACM. 13 (6): 377–387. doi:10.1145/362384.362685. S2CID 207549016. Archived from the original on June 12, 2007. Retrieved August 25, 2005.
  5. ^ a b c d Codd, E. F. "Further Normalization of the Data Base Relational Model". (Presented at Courant Computer Science Symposia Series 6, "Data Base Systems", New York City, May 24–25, 1971.) IBM Research Report RJ909 (August 31, 1971). Republished in Randall J. Rustin (ed.), Data Base Systems: Courant Computer Science Symposia Series 6. Prentice-Hall, 1972.
  6. ^ Codd, E. F. "Recent Investigations into Relational Data Base Systems". IBM Research Report RJ1385 (April 23, 1974). Republished in Proc. 1974 Congress (Stockholm, Sweden, 1974), N.Y.: North-Holland (1974).
  7. ^ Date, C. J. (1999). An Introduction to Database Systems. Addison-Wesley. p. 290.
  8. ^ Darwen, Hugh; Date, C. J.; Fagin, Ronald (2012). "A Normal Form for Preventing Redundant Tuples in Relational Databases" (PDF). Proceedings of the 15th International Conference on Database Theory. EDBT/ICDT 2012 Joint Conference. ACM International Conference Proceeding Series. Association for Computing Machinery. p. 114. doi:10.1145/2274576.2274589. ISBN 978-1-4503-0791-8. OCLC 802369023. Retrieved May 22, 2018.
  9. ^ Kumar, Kunal; Azad, S. K. (October 2017). Database normalization design pattern. 2017 4th IEEE Uttar Pradesh Section International Conference on Electrical, Computer and Electronics (UPCON). IEEE. doi:10.1109/upcon.2017.8251067. ISBN 9781538630044. S2CID 24491594.
  10. ^ a b c "Database normalization in MySQL: Four quick and easy steps". ComputerWeekly.com. Archived from the original on August 30, 2017. Retrieved March 23, 2021.
  11. ^ "Database Normalization: 5th Normal Form and Beyond". MariaDB KnowledgeBase. Retrieved January 23, 2019.
  12. ^ The table fragment itself has several candidate keys (simple key {Price}, and compound keys of Format together with any column except Price or Thickness), but we assume that in the complete table only {Title, Format} will be unique.
  13. ^ "Additional Normal Forms - Database Design and Relational Theory - page 151". what-when-how.com. Retrieved January 22, 2019.
  14. ^ a b "Normalizace databáze", Wikipedie (in Czech), November 7, 2018, retrieved January 22, 2019
  15. ^ a b Date, C. J. (December 21, 2015). The New Relational Database Dictionary: Terms, Concepts, and Examples. "O'Reilly Media, Inc.". p. 138. ISBN 9781491951699.
  16. ^ Date, C. J. (December 21, 2015). The New Relational Database Dictionary: Terms, Concepts, and Examples. "O'Reilly Media, Inc.". p. 163. ISBN 9781491951699.
  17. ^ "normalization - Would like to Understand 6NF with an Example". Stack Overflow. Retrieved January 23, 2019.
  18. ^ Microsoft Corporation. Columnstore Indexes: Overview. https://docs.microsoft.com/en-us/sql/relational-databases/indexes/columnstore-indexes-overview . Accessed Mar 23, 2020.

Further reading[edit]

External links[edit]