normalization

Database normalization is a technique for designing relational database tables to minimize duplication of information and, in so doing, to safeguard the database against certain types of logical or structural problems, namely data anomalies. For example, when multiple instances of a given piece of information occur in a table, the possibility exists that these instances will not be kept consistent when the data within the table is updated, leading to a loss of data integrity. A table that is sufficiently normalized is less vulnerable to problems of this kind, because its structure reflects the basic assumptions for when multiple instances of the same information should be represented by a single instance only.

Higher degrees of normalization typically involve more tables and create the need for a larger number of joins, which can reduce performance. Accordingly, more highly normalized tables are typically used in database applications involving many isolated transactions (e.g. an Automated teller machine), while less normalized tables tend to be used in database applications that do not need to map complex relationships between data entities and data attributes (e.g. a reporting application, or a full-text search application).

Database theory describes a table's degree of normalization in terms of normal forms of successively higher degrees of strictness. A table in third normal form (3NF), for example, is consequently in second normal form (2NF) as well; but the reverse is not always the case.

Although the normal forms are often defined informally in terms of the characteristics of tables, rigorous definitions of the normal forms are concerned with the characteristics of mathematical constructs known as relations. Whenever information is represented relationally, it is meaningful to consider the extent to which the representation is normalized.

Problems addressed by normalization

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

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

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

A table that is not sufficiently normalized can suffer from logical inconsistencies of various types, and from anomalies involving data operations. In such a table:

• The same information can be expressed on multiple records; 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.

Ideally, a relational database table should be designed in such a way as to exclude the possibility of update, insertion, and deletion anomalies. The normal forms of relational database theory provide guidelines for deciding whether a particular design will be vulnerable to such anomalies. It is possible to correct an unnormalized design so as to make it adhere to the demands of the normal forms: this is called normalization.

Normalization typically involves decomposing an unnormalized table into two or more tables that, were they to be combined (joined), would convey exactly the same information as the original table.

Background to normalization: definitions

• Functional dependency: Attribute B has a functional dependency on attribute A if, for each value of attribute A, there is exactly one value of attribute B. 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.
• 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 a) functionally dependent on X, and b) 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, for 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: see the Multivalued Dependency article for a rigorous definition.
• 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 candidate key which the database designer has designated for this purpose.

History

Edgar F. Codd first proposed the process of normalization and what came to be known as the 1st normal form:

There is, in fact, a very simple elimination^[1] procedure which we shall call normalization. Through decomposition non-simple domains are replaced by "domains whose elements are atomic (non-decomposable) values."

—Edgar F. Codd, A Relational Model of Data for Large Shared Data Banks^[2]

In his paper, Edgar F. Codd used the term "non-simple" domains to describe a heterogeneous data structure, but later researchers would refer to such a structure as an abstract data type.

Normal forms

The normal forms (abbrev. 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 such 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.

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.

Edgar F. Codd originally defined the first three normal forms (1NF, 2NF, and 3NF). These normal forms have been summarized as requiring that all non-key attributes be dependent on "the key, the whole key and nothing but the key". The fourth and fifth normal forms (4NF and 5NF) deal specifically with the representation of many-to-many and one-to-many relationships among attributes. Sixth normal form (6NF) incorporates considerations relevant to temporal databases.

First normal form

Main article: First normal form

A table is in first normal form (1NF) if and only if it faithfully represents a relation.^[3] Given that database tables embody a relation-like form, the defining characteristic of one in first normal form is that it does not allow nulls or duplicate rows. Simply put, a table with a unique key and without any nullable columns is in 1NF.

A misconception looms from the common assertion that a 1NF table may not have repeating groups^[4]. While that statement itself is axiomatic, experts disagree about what qualifies as a "repeating group", thus the precise definition of 1NF is the subject of some controversy. Notwithstanding, this theoretical uncertainty applies to relations, not tables. Table manifestations are intrinsically free of variable repeating groups because they are structurally constrained to the same number of columns in all rows.

See the first normal form article for a fuller discussion of the nuances of 1NF.

Second normal form

Main article: Second normal form

The criteria for second normal form (2NF) are:

• The table must be in 1NF.
• None of the non-prime attributes of the table are functionally dependent on a part (proper subset) of a candidate key; in other words, all functional dependencies of non-prime attributes on candidate keys are full functional dependencies.^[5] For example, in an "Employees' Skills" table whose attributes are Employee ID, Employee Address, and Skill, the combination of Employee ID and Skill uniquely identifies records within the table. Given that Employee Address depends on only one of those attributes – namely, Employee ID – the table is not in 2NF.
• Note that if none of a 1NF table's candidate keys are composite – i.e. every candidate key consists of just one attribute – then we can say immediately that the table is in 2NF.

Third normal form

Main article: Third normal form

The criteria for third normal form (3NF) are:

• The table must be in 2NF.
• Every non-prime attribute of the table must be non-transitively dependent on every candidate key.^[5] A violation of 3NF would mean that at least one non-prime attribute is only indirectly dependent (transitively dependent) on a candidate key. For example, consider a "Departments" table whose attributes are Department ID, Department Name, Manager ID, and Manager Hire Date; and suppose that each manager can manage one or more departments. {Department ID} is a candidate key. Although Manager Hire Date is functionally dependent on the candidate key {Department ID}, this is only because Manager Hire Date depends on Manager ID, which in turn depends on Department ID. This transitive dependency means the table is not in 3NF.

Boyce-Codd normal form

Main article: Boyce-Codd normal form

A table is in Boyce-Codd normal form (BCNF) if and only if, for every one of its non-trivial functional dependencies X → Y, X is a superkey—that is, X is either a candidate key or a superset thereof.^[6]

Fourth normal form

Main article: Fourth normal form

A table is in fourth normal form (4NF) if and only if, for every one of its non-trivial multivalued dependencies X →→ Y, X is a superkey—that is, X is either a candidate key or a superset thereof.^[7]

Fifth normal form

Main article: Fifth normal form

The criteria for fifth normal form (5NF and also PJ/NF) are:

• The table must be in 4NF.
• There must be no non-trivial join dependencies that do not follow from the key constraints. A 4NF table is said to be in the 5NF if and only if every join dependency in it is implied by the candidate keys.

Domain/key normal form

Main article: Domain/key normal form

Domain/key normal form (or DKNF) requires that a table not be subject to any constraints other than domain constraints and key constraints.

Sixth normal form

A table is in sixth normal form (6NF) if and only if it satisfies no non-trivial join dependencies at all.^[8] This obviously means that the fifth normal form is also satisfied. The sixth normal form was only defined when extending the relational model to take into account the temporal dimension. Unfortunately, most current SQL technologies as of 2005 do not take into account this work, and most temporal extensions to SQL are not relational. See work by Date, Darwen and Lorentzos^[9] for a relational temporal extension, Zimyani^[10] for further discussion on Temporal Aggregation in SQL, or TSQL2 for a non-relational approach.

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 super market 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 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. It has never been proven that this denormalization itself provides any increase in performance, or if the concurrent removal of data constraints is what increases the performance. The need for denormalization has waned as computers and RDBMS software have become more powerful.

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)

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 the first normal form, by allowing "sets and sets of sets to be attribute domains" (Schek 1982). This extension is a (non-optimal) way of implementing hierarchies in relations. Some theoreticians have dubbed this practitioner developed method, "First Ab-normal Form", Codd defined a relational database as using relations, so any table not in 1NF could not be considered to be relational.

Consider the following table:

Assume a person has several favorite colors. Obviously, favorite colors consist of a set of colors modeled by the given table.

To transform this NF² table into a 1NF an "unnest" operator is required which extends the relational algebra of the higher normal forms. The reverse operator is called "nest" which is not always the mathematical inverse of "unnest", although "unnest" is the mathematical inverse to "nest". Another constraint required is for the operators to be bijective, which is covered by the Partitioned Normal Form (PNF).

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
• Date, C.J., & Darwen, H., & Pascal, F. Database Debunkings
• H.-J. Schek, P.Pistor Data Structures for an Integrated Data Base Management and Information Retrieval System

Notes and References

1. ^ His term eliminate is misleading, as nothing is "lost" in normalization. He probably described eliminate in a mathematical sense to mean elimination of complexity.
2. ^ Codd, E.F. (June 1970). "A Relational Model of Data for Large Shared Data Banks". Communications of the ACM 13 (6): 377-387. 
3. ^ "[T]he overriding requirement, to the effect that the table must directly and faithfully represent a relation, follows from the fact that 1NF was originally defined as a property of relations, not tables." Date, C.J. "What First Normal Form Really Means" in Date on Database: Writings 2000-2006 (Springer-Verlag, 2006), p. 128.
4. ^ "First normal form excludes variable repeating fields and groups" Kent, William. "A Simple Guide to Five Normal Forms in Relational Database Theory", Communications of the ACM 26 (2), Feb. 1983, pp. 120-125.
5. ^ ^{a b} 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 24th-25th, 1971.) IBM Research Report RJ909 (August 31st, 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 23rd, 1974). Republished in Proc. 1974 Congress (Stockholm, Sweden, 1974). New York, N.Y.: North-Holland (1974).
7. ^ "A relation schema R* is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency X →→ Y holds for R*, then so does the functional dependency X → A for every column name A of R*. Intuitively all dependencies are the result of keys." Fagin, Ronald (September 1977). "Multivalued Dependencies and a New Normal Form for Relational Databases". ACM Transactions on Database Systems 2 (1): 267. 
8. ^ Date, Chris J.; Hugh Darwen, Nikos A. Lorentzos [January 2003]. "Chapter 10: Database Design", Temporal Data and the Relational Model: A Detailed Investigation into the Application of Interval and Relation Theory to the Problem of Temporal Database Management. Oxford: Elsevier LTD, p. 176. ISBN 1558608559. 
9. ^ Date, C. J., & Lorentzos, N., & Darwen, H. (2002). Temporal Data & the Relational Model (1st ed.). Morgan Kaufmann. ISBN 1-55860-855-9.
10. ^ Zimyani, E. (June 2006). Temporal Aggregates and Temporal Universal Quantification in Standard SQL. ACM SIGMOD Record 35 (2).

See also

• Aspect (computer science)
• Cross-cutting concern
• Refactoring
• Business rules

External links

• Database Normalization Basics by Mike Chapple (About.com)
• Database Normalization Intro, Part 2
• An Introduction to Database Normalization by Mike Hillyer.
• Normalization by ITS, University of Texas.
• Rules of Data Normalization by Data Model.org
• A tutorial on the first 3 normal forms by Fred Coulson
• Free PDF poster available by Marc Rettig
• Description of the database normalization basics by Microsoft

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