Database normalization

In the design of a relational database management system (RDBMS), the process of organizing data to minimize redundancy is called normalization. The goal of database normalization is to decompose relations with anomalies in order to produce smaller, well-structured relations. 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 via 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.^[1] Codd went on to define the Second Normal Form (2NF) and Third Normal Form (3NF) in 1971,^[2] and Codd and Raymond F. Boyce defined the Boyce-Codd Normal Form (BCNF) in 1974.^[3] Higher normal forms were defined by other theorists in subsequent years, the most recent being the Sixth Normal Form (6NF) introduced by Chris Date, Hugh Darwen, and Nikos Lorentzos in 2002.^[4]

Informally, a relational database table (the computerized representation of a relation) is often described as "normalized" if it is in the Third Normal Form.^[5] Most 3NF tables are free of insertion, update, and deletion anomalies, i.e. in most cases 3NF tables adhere to BCNF, 4NF, and 5NF (but typically not 6NF).

A standard piece of database design guidance is that the designer should create a fully normalized design; selective denormalization can subsequently be performed for performance reasons.^[6] However, some modeling disciplines, such as the dimensional modeling approach to data warehouse design, explicitly recommend non-normalized designs, i.e. designs that in large part do not adhere to 3NF.^[7]

Objectives of normalization

A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic.^[8] (SQL is an example of such a data sub-language, albeit one that Codd regarded as seriously flawed.)^[9]

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"^[10]

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 when he temporarily ceases to be assigned to any courses.

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

• The same information can be expressed on multiple rows; therefore updates to the table may result in logical inconsistencies. For example, each record in an "Employees' Skills" table might contain an Employee ID, Employee Address, and Skill; thus a change of address for a particular employee will potentially need to be applied to multiple records (one for each of his skills). If the update is not carried through successfully—if, that is, the employee's address is updated on some records but not others—then the table is left in an inconsistent state. Specifically, the table provides conflicting answers to the question of what this particular employee's address is. This phenomenon is known as an update anomaly.
• There are circumstances in which certain facts cannot be recorded at all. For example, each record in a "Faculty and Their Courses" table might contain a Faculty ID, Faculty Name, Faculty Hire Date, and Course Code—thus we can record the details of any faculty member who teaches at least one course, but we cannot record the details of a newly-hired faculty member who has not yet been assigned to teach any courses except by setting the Course Code to null. 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, effectively also deleting the faculty member. 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 an unnormalized data structure, such as the following non-1NF representation of customers' credit card transactions, involves more complexity than is really necessary:

Customer	Transactions
Jones	Tr. ID Date Amount 12890 14-Oct-2003 −87 12904 15-Oct-2003 −50
Wilkins	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 there corresponds a repeating group of transactions. The automated evaluation of any query relating to customers' transactions therefore would broadly involve two stages:

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

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

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

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

Now each row represents an individual credit card transaction, and the DBMS can obtain the answer of interest, simply by finding all rows with a Date falling in October, and summing their Amounts. 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.

Background to normalization: definitions

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}.

Trivial functional dependency

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

Full functional dependency

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

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

Transitive dependency

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

Multivalued dependency

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

Join dependency

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

Superkey

A superkey is 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.

Examples: Imagine a table with the fields <Name>, <Age>, <SSN> and <Phone Extension>. This table has many possible superkeys. Three of these are <SSN>, <Phone Extension, Name> and <SSN, Name>. Of those listed, 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

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

Normal forms

The normal forms (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 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.

The main normal forms are summarized below.

Normal form	Defined by	Brief definition
First normal form (1NF)	Two versions: E.F. Codd (1970), C.J. Date (2003)[11]	Table faithfully represents a relation and has no repeating groups
Second normal form (2NF)	E.F. Codd (1971)[2]	No non-prime attribute in the table is functionally dependent on a proper subset of a candidate key
Third normal form (3NF)	E.F. Codd (1971);[2] see +also Carlo Zaniolo's equivalent but differently-expressed definition (1982)[12]	Every non-prime attribute is non-transitively dependent on every candidate key in the table
Elementary Key Normal Form (EKNF)	C.Zaniolo (1982);[13]	Every non-trivial functional dependency in the table is either the dependency of an elementary key attribute or a dependency on a superkey
Boyce–Codd normal form (BCNF)	Raymond F. Boyce and E.F. Codd (1974)[14]	Every non-trivial functional dependency in the table is a dependency on a superkey
Fourth normal form (4NF)	Ronald Fagin (1977)[15]	Every non-trivial multivalued dependency in the table is a dependency on a superkey
Fifth normal form (5NF)	Ronald Fagin (1979)[16]	Every non-trivial join dependency in the table is implied by the superkeys of the table
Domain/key normal form (DKNF)	Ronald Fagin (1981)[17]	Every constraint on the table is a logical consequence of the table's domain constraints and key constraints
Sixth normal form (6NF)	C.J. Date, Hugh Darwen, and Nikos Lorentzos (2002)[4]	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)

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).

See also

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

Notes and references

1. ^ 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. http://www.acm.org/classics/nov95/toc.html. 
2. ^ ^{a b c} 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.
3. ^ 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).
4. ^ ^{a b} C.J. Date, Hugh Darwen, Nikos Lorentzos. Temporal Data and the Relational Model. Morgan Kaufmann (2002), p. 176
5. ^ C.J. Date. An Introduction to Database Systems. Addison-Wesley (1999), p. 290
6. ^ Chris Date, for example, writes: "I believe firmly that anything less than a fully normalized design is strongly contraindicated ... [Y]ou should "denormalize" only as a last resort. That is, you should back off from a fully normalized design only if all other strategies for improving performance have somehow failed to meet requirements." Date, C.J. Database in Depth: Relational Theory for Practitioners. O'Reilly (2005), p. 152.
7. ^ Ralph Kimball, for example, writes: "The use of normalized modeling in the data warehouse presentation area defeats the whole purpose of data warehousing, namely, intuitive and high-performance retrieval of data." Kimball, Ralph. The Data Warehouse Toolkit, 2nd Ed.. Wiley Computer Publishing (2002), p. 11.
8. ^ "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 Ianguages (programming, command- or problem-oriented)." Codd, "A Relational Model of Data for Large Shared Data Banks", p. 381
9. ^ Codd, E.F. Chapter 23, "Serious Flaws in SQL", in The Relational Model for Database Management: Version 2. Addison-Wesley (1990), pp. 371–389
10. ^ Codd, E.F. "Further Normalization of the Data Base Relational Model", p. 34
11. ^ Date, C. J. "What First Normal Form Really Means" in Date on Database: Writings 2000–2006 (Springer-Verlag, 2006), pp. 127–128.
12. ^ Zaniolo, Carlo. "A New Normal Form for the Design of Relational Database Schemata." ACM Transactions on Database Systems 7(3), September 1982.
13. ^ Zaniolo, Carlo. "A New Normal Form for the Design of Relational Database Schemata." ACM Transactions on Database Systems 7(3), September 1982.
14. ^ 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). New York, N.Y.: North-Holland (1974).
15. ^ Fagin, Ronald (September 1977). "Multivalued Dependencies and a New Normal Form for Relational Databases". ACM Transactions on Database Systems 2 (1): 267. doi:10.1145/320557.320571. http://www.almaden.ibm.com/cs/people/fagin/tods77.pdf. 
16. ^ Ronald Fagin. "Normal Forms and Relational Database Operators". ACM SIGMOD International Conference on Management of Data, May 31-June 1, 1979, Boston, Mass. Also IBM Research Report RJ2471, Feb. 1979.
17. ^ Ronald Fagin (1981) A Normal Form for Relational Databases That Is Based on Domains and Keys, Communications of the ACM, vol. 6, pp. 387–415

• 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
• 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

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