database normalization mihir

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Database models

Adata model is not just a way of structuring data: it alsodefines a set of operations that can be performed on the data.

The relational model, for example, defines operations such asselect,project, andjoin. Although these operations may not be

explicit in a particularquery language, they provide thefoundation on which a query language is built.

Contents

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1 Modelso 1.1 Flat model

o 1.2 Hierarchical modelo 1.3 Network model

o 1.4 Relational model

1.4.1 Relational operations

1.4.2 Normal Formso 1.5 Dimensional model

o 1.6 Object database models

2 References

3 See Also

Models

Various techniques are used to model data structure. Most database systems are built

around one particular data model, although it is increasingly common for products to offer

support for more than one model. For any onelogical model various physicalimplementations may be possible, and most products will offer the user some level of

control in tuning thephysical implementation, since the choices that are made have a

significant effect on performance. An example of this is the relational model: all seriousimplementations of the relational model allow the creation of indexes which provide fast

access to rows in a table if the values of certain columns are known.

Flat model

This may not strictly qualify as a data model, as defined above. The flat (or table) model

consists of a single, two-dimensional array ofdata elements, where all members of a givencolumn are assumed to be similar values, and all members of a row are assumed to be

related to one another. For instance, columns for name and password that might be used as

a part of a system security database. Each row would have the specific password associated

Database models

Common models

HierarchicalNetwork

RelationalObject-relational

Object

Other models

Associative

Concept-oriented

Multi-dimensional

Star schemaXML database
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with an individual user. Columns of the table often have a type associated with them,

defining them as character data, date or time information, integers, or floating point

numbers. This model is, incidentally, a basis of thespreadsheet.

Hierarchical model

Main article:Hierarchical model

In a hierarchical model, data is organized into a tree-like structure, implying a single

upward link in each record to describe the nesting, and a sort field to keep the records in a

particular order in each same-level list. Hierarchical structures were widely used in the

early mainframe database management systems, such as the Information ManagementSystem (IMS) by IBM, and now describe the structure of XML documents. This structure

allows one 1:N relationship between two types of data. This structure is very efficient to

describe many relationships in the real world; recipes, table of contents, ordering ofparagraphs/verses, any nested and sorted information. However, the hierarchical structure

is inefficient for certain database operations when a full path (as opposed to upward linkand sort field) is not also included for each record.

One limitation of the hierarchical model is its inability to efficiently represent redundancyin data.

Network model

Main article:Network model

The network model(defined by the CODASYL specification) organizes data using two

fundamental constructs, called records andsets. Records contain fields (which may beorganized hierarchically, as in the programming language COBOL). Sets (not to beconfused with mathematical sets) define one-to-many relationships between records: one

owner, many members. A record may be an owner in any number of sets, and a member in

any number of sets.

The network model is a variation on the hierchical model, to the extent that it is built on theconcept of multiple branches (lower-level structures) emanating from one or more nodes

(higher-level structures), while the model differs from the hierchical model in that branches

can be connected to multiple nodes. The network model is able to represent redundancy in

data more efficiently than is the hierarchical model.

The operations of the network model are navigational in style: a program maintains a

current position, and navigates from one record to another by following the relationships in

which the record participates. Records can also be located by supplying key values.

Although it is not an essential feature of the model, network databases generally implementthe set relationships by means ofpointers that directly address the location of a record on
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disk. This gives excellent retrieval performance, at the expense of operations such as

database loading and reorganization.

Most Object databases use the navigational concept to provide fast navigation acrossnetworks of objects, generally using Object Identifiers as "smart" pointers to related

objects. Objectivity/DB, for instance, implements named 1:1, 1:many, Many:1 andMany:Many named relationships that can cross databases. Many object databases also

support SQL, combining the strengths of both models.

Relational model

Main article:Relational model

The relational model was introduced in anacademic paperbyE. F. Codd in 1970 as a way

to make database management systems more independent of any particular application. It is

a mathematical model defined in terms ofpredicate logic andset theory.

The products that are generally referred to as relational databases in fact implement amodel that is only an approximation to the mathematical model defined by Codd. Three

key terms are used extensively in relational database models: relations, attributes, and

domains. A relation is a table with columns and rows. The named columns of the relationare called attributes, and the domain is the set of values the attributes are allowed to take.

The basic data structure of the relational model is the table, where information about a

particular entity (say, an employee) is represented in columns and rows (also called tuples).

Thus, the "relation" in "relational database" refers to the various tables in the database; arelation is a set of tuples. The columns enumerate the various attributes of the entity (the

employee's name, address or phone number, for example), and a row is an actual instanceof the entity (a specific employee) that is represented by the relation. As a result, each tupleof the employee table represents various attributes of a single employee.

All relations (and, thus, tables) in a relational database have to adhere to some basic rules

to qualify as relations. First, the ordering of columns is immaterial in a table. Second, there

can't be identical tuples or rows in a table. And third, each tuple will contain a single valuefor each of its attributes.

A relational database contains multiple tables, each similar to the one in the "flat" database

model. One of the strengths of the relational model is that, in principle, any value occurring

in two different records (belonging to the same table or to different tables), implies arelationship among those two records. Yet, in order to enforce explicit integrity constraints,

relationships between records in tables can also be defined explicitly, by identifying or

non-identifying parent-child relationships characterized by assigning cardinality (1:1,(0)1:M, M:M). Tables can also have a designated single attribute or a set of attributes that

can act as a "key", which can be used to uniquely identify each tuple in the table.
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A key that can be used to uniquely identify a row in a table is called a primary key. Keys

are commonly used to join or combine data from two or more tables. For example, an

Employee table may contain a column namedLocation which contains a value that matchesthe key of aLocation table. Keys are also critical in the creation of indexes, which facilitate

fast retrieval of data from large tables. Any column can be a key, or multiple columns can

be grouped together into a compound key. It is not necessary to define all the keys inadvance; a column can be used as a key even if it was not originally intended to be one.

A key that has an external, real-world meaning (such as a person's name, a book's ISBN, or

a car's serial number) is sometimes called a "natural" key. If no natural key is suitable

(think of the many people namedBrown), an arbitrary or surrogate key can be assigned(such as by giving employees ID numbers). In practice, most databases have both

generated and natural keys, because generated keys can be used internally to create links

between rows that cannot break, while natural keys can be used, less reliably, for searchesand for integration with other databases. (For example, records in two independently

developed databases could be matched up bysocial security number, except when the

social security numbers are incorrect, missing, or have changed.)

Relational operations

Users (or programs) request data from a relational database by sending it a query that is

written in a special language, usually a dialect ofSQL. Although SQL was originally

intended for end-users, it is much more common for SQL queries to be embedded into

software that provides an easier user interface. Many web sites, such as Wikipedia, performSQL queries when generating pages.

In response to a query, the database returns a result set, which is just a list of rows

containing the answers. The simplest query is just to return all the rows from a table, butmore often, the rows are filtered in some way to return just the answer wanted.

Often, data from multiple tables are combined into one, by doing ajoin. Conceptually, this

is done by taking all possible combinations of rows (the Cartesian product), and then

filtering out everything except the answer. In practice, relational database managementsystems rewrite ("optimize") queries to perform faster, using a variety of techniques.

There are a number of relational operations in addition to join. These include project (the

process of eliminating some of the columns), restrict (the process of eliminating some of

the rows), union (a way of combining two tables with similar structures), difference (which

lists the rows in one table that are not found in the other), intersect (which lists the rowsfound in both tables), and product (mentioned above, which combines each row of one

table with each row of the other). Depending on which other sources you consult, there are

a number of other operators - many of which can be defined in terms of those listed above.These include semi-join, outer operators such as outer join and outer union, and various

forms of division. Then there are operators to rename columns, and summarizing or

aggregating operators, and if you permit relation values as attributes (RVA - relation-
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valued attribute), then operators such as group and ungroup. The SELECT statement in

SQL serves to handle all of these except for the group and ungroup operators.

The flexibility of relational databases allows programmers to write queries that were notanticipated by the database designers. As a result, relational databases can be used by

multiple applications in ways the original designers did not foresee, which is especiallyimportant for databases that might be used for decades. This has made the idea and

implementation of relational databases very popular with businesses.

Normal Forms

Main article:Database normalization

Relations are classified based upon the types of anomalies to which they're vulnerable. A

database that's in the first normal form is vulnerable to all types of anomalies, while adatabase that's in the domain/key normal form has no modification anomalies. Normal

forms are hierarchical in nature. That is, the lowest level is the first normal form, and the

database cannot meet the requirements for higher level normal forms without first havingmet all the requirements of the lesser normal forms.[1]

Dimensional model

The dimensional model is a specialized adaptation of the relational model used to represent

data indata warehouses in a way that data can be easily summarized usingOLAP queries.

In the dimensional model, a database consists of a single large table of facts that are

described using dimensions and measures. A dimension provides the context of a fact (suchas who participated, when and where it happened, and its type) and is used in queries to

group related facts together. Dimensions tend to be discrete and are often hierarchical; for

example, the location might include the building, state, and country. A measure is aquantity describing the fact, such as revenue. It's important that measures can be

meaningfully aggregated - for example, the revenue from different locations can be added

together.

In an OLAP query, dimensions are chosen and the facts are grouped and added together tocreate a summary.

The dimensional model is often implemented on top of the relational model using a star

schema, consisting of one table containing the facts and surrounding tables containing the

dimensions. Particularly complicated dimensions might be represented using multiple

tables, resulting in a snowflake schema.

A data warehouse can contain multiple star schemas that share dimension tables, allowing

them to be used together. Coming up with a standard set of dimensions is an important part

of dimensional modeling.

Object database models
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Main article:Object-relational model

Main article:Object model

In recent years, theobject-oriented paradigm has been applied to database technology,creating a new programming model known asobject databases. These databases attempt to

bring the database world and the application programming world closer together, inparticular by ensuring that the database uses the same type system as the application

program. This aims to avoid the overhead (sometimes referred to as the impedance

mismatch) of converting information between its representation in the database (for

example as rows in tables) and its representation in the application program (typically as

objects). At the same time, object databases attempt to introduce the key ideas of objectprogramming, such as encapsulation andpolymorphism, into the world of databases.

A variety of these ways have been tried for storing objects in a database. Some products

have approached the problem from the application programming end, by making the

objects manipulated by the programpersistent. This also typically requires the addition of

some kind of query language, since conventional programming languages do not have theability to find objects based on their information content. Others have attacked the problem

from the database end, by defining an object-oriented data model for the database, anddefining a database programming language that allows full programming capabilities as

well as traditional query facilities.

Object databases suffered because of a lack of standardization: although standards were

defined by ODMG, they were never implemented well enough to ensure interoperabilitybetween products. Nevertheless, object databases have been used successfully in many

applications: usually specialized applications such as engineering databases or molecular

biology databases rather than mainstream commercial data processing. However, object

database ideas were picked up by the relational vendors and influenced extensions made tothese products and indeed to the SQL language.
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Database normalization

Database normalization is a design technique for structuringrelational database tables.

Tables can be normalized to a greater or lesser degree. Database theory describes a table's

degree of normalization in terms ofnormal forms.The most common normal forms, fromleast normalized to most normalized, are as follows:

First normal form (1NF)

Second normal form (2NF)

Third normal form (3NF)

Boyce-Codd normal form (BCNF)

Fourth normal form (4NF)

Fifth normal form (5NF) Domain/key normal form (DKNF)

Sixth normal form (6NF)

Each normal form automatically includes the properties of lower normal formsfor

example, a table in 3NF is also in 1NF.

More highly normalized tables reduce data duplication and opportunities for various kindsof logical inconsistencies that could lead to loss of integrity of the database. They greatly

simplify development, maintenance, and expandability of the database. Higher degrees of

normalization typically involve more tables and create the need for a larger number of

joins, which can reduce performance. As a result, more highly normalized tables aretypically used for databases involving many isolable transactions (such as an automatic

teller system), while less normalized tables are used for read-mostly information (such asreports).

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 asrelations. Whenever information is representedrelationallythat is, roughly speaking, as values within rows beneath fixed column

headingsit makes sense to ask to what extent the representation is normalized.

Contents

[hide]

1 Problems addressed by normalization

2 Background to normalization: definitions
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3 History

4 Normal forms

o 4.1 First normal form

o 4.2 Second normal form

o 4.3 Third normal form

o 4.4 Boyce-Codd normal formo 4.5 Fourth normal form

o 4.6 Fifth normal form

o 4.7 Domain/key normal form

o 4.8 Sixth normal form

5 Example Of The Process

o 5.1 Starting Point

o 5.2 1NF

o 5.3 2NF

o 5.4 3NF and BCNF

o 5.5 4NF

o 5.6 5NF

6 Denormalization

o 6.1 Non-first normal form (NF)

7 Further reading

8 References

9 See also

10 External links

Problems addressed by normalizationA 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 anunnormalized "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 successfullyif, that is, the employee's address is

updated on some records but not othersthen the table is left in an inconsistentstate. 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. In the

above example, if it is the case that Employee Address is held only in the"Employees' Skills" table, then we cannot record the address of an employee whose

skills are not yet known. This phenomenon is known as an insertion anomaly.
http://en.wikipedia.org/wiki/Database_normalization#History%23Historyhttp://en.wikipedia.org/wiki/Database_normalization#Normal_forms%23Normal_formshttp://en.wikipedia.org/wiki/Database_normalization#First_normal_form%23First_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Second_normal_form%23Second_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Third_normal_form%23Third_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Boyce-Codd_normal_form%23Boyce-Codd_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Fourth_normal_form%23Fourth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Fifth_normal_form%23Fifth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Domain.2Fkey_normal_form%23Domain.2Fkey_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Sixth_normal_form%23Sixth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Example_Of_The_Process%23Example_Of_The_Processhttp://en.wikipedia.org/wiki/Database_normalization#Starting_Point%23Starting_Pointhttp://en.wikipedia.org/wiki/Database_normalization#1NF%231NFhttp://en.wikipedia.org/wiki/Database_normalization#2NF%232NFhttp://en.wikipedia.org/wiki/Database_normalization#3NF_and_BCNF%233NF_and_BCNFhttp://en.wikipedia.org/wiki/Database_normalization#4NF%234NFhttp://en.wikipedia.org/wiki/Database_normalization#5NF%235NFhttp://en.wikipedia.org/wiki/Database_normalization#Denormalization%23Denormalizationhttp://en.wikipedia.org/wiki/Database_normalization#Non-first_normal_form_.28NF.C2.B2.29%23Non-first_normal_form_.28NF.C2.B2.29http://en.wikipedia.org/wiki/Database_normalization#Further_reading%23Further_readinghttp://en.wikipedia.org/wiki/Database_normalization#References%23Referenceshttp://en.wikipedia.org/wiki/Database_normalization#See_also%23See_alsohttp://en.wikipedia.org/wiki/Database_normalization#External_links%23External_linkshttp://en.wikipedia.org/wiki/CRUD_(acronym)http://en.wikipedia.org/wiki/Database_normalization#History%23Historyhttp://en.wikipedia.org/wiki/Database_normalization#Normal_forms%23Normal_formshttp://en.wikipedia.org/wiki/Database_normalization#First_normal_form%23First_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Second_normal_form%23Second_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Third_normal_form%23Third_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Boyce-Codd_normal_form%23Boyce-Codd_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Fourth_normal_form%23Fourth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Fifth_normal_form%23Fifth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Domain.2Fkey_normal_form%23Domain.2Fkey_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Sixth_normal_form%23Sixth_normal_formhttp://en.wikipedia.org/wiki/Database_normalization#Example_Of_The_Process%23Example_Of_The_Processhttp://en.wikipedia.org/wiki/Database_normalization#Starting_Point%23Starting_Pointhttp://en.wikipedia.org/wiki/Database_normalization#1NF%231NFhttp://en.wikipedia.org/wiki/Database_normalization#2NF%232NFhttp://en.wikipedia.org/wiki/Database_normalization#3NF_and_BCNF%233NF_and_BCNFhttp://en.wikipedia.org/wiki/Database_normalization#4NF%234NFhttp://en.wikipedia.org/wiki/Database_normalization#5NF%235NFhttp://en.wikipedia.org/wiki/Database_normalization#Denormalization%23Denormalizationhttp://en.wikipedia.org/wiki/Database_normalization#Non-first_normal_form_.28NF.C2.B2.29%23Non-first_normal_form_.28NF.C2.B2.29http://en.wikipedia.org/wiki/Database_normalization#Further_reading%23Further_readinghttp://en.wikipedia.org/wiki/Database_normalization#References%23Referenceshttp://en.wikipedia.org/wiki/Database_normalization#See_also%23See_alsohttp://en.wikipedia.org/wiki/Database_normalization#External_links%23External_linkshttp://en.wikipedia.org/wiki/CRUD_(acronym)


9/23

There are circumstances in which the deletion of data representing certain facts

necessitates the deletion of data representing completely different facts. For

example, suppose a table has the attributes Student ID, Course ID, and Lecturer ID(a given student is enrolled in a given course, which is taught by a given lecturer).

If in the early stages of enrolment the number of students on the course temporarily

drops to zero, then the last of the records referencing that course must be deletedmeaning, as a side-effect, that the table no longer tells us which lecturer has been

assigned to teach the course. 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 relationaldatabase 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 informationas 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. For example,

Employee Address has a functional dependency on Employee ID, because a

particular Employee Address value corresponds to every Employee ID value. Anattribute 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 tothe attributes within its tables; understanding this, in turn, requires knowledge of

the problem domain.

Trivial functional dependency: A trivial functional dependency is a functional

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

{Employee Address}.

Full functional dependency: An attribute is fully functionally dependent on a setof 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 afullfunctional dependency, for it is

also dependent on {Employee ID}. Transitive dependency: A transitive dependency is an indirect functional

dependency, one in whichXZonly by virtue ofXYand YZ.

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 Tis subject to ajoin dependency ifTcan always berecreated by joining multiple tables each having a subset of the attributes ofT.
http://en.wikipedia.org/wiki/Functional_dependencyhttp://en.wikipedia.org/wiki/Multivalued_Dependencyhttp://en.wikipedia.org/w/index.php?title=Join_dependency&action=edithttp://en.wikipedia.org/wiki/Functional_dependencyhttp://en.wikipedia.org/wiki/Multivalued_Dependencyhttp://en.wikipedia.org/w/index.php?title=Join_dependency&action=edit


10/23

Superkey: Asuperkey 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 superkeyfor the "Employees' Skills" table; {Employee ID, Skill} would also be a superkey.

Candidate key: Acandidate 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: MostDBMSsrequire a table to be defined as having a single unique

key, rather than a number of possible unique keys. Aprimary 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 aheterogeneous 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 fordetermining 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; alsoby 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 innormal form n is to say that all of its tables are in normal form n.
http://en.wikipedia.org/wiki/Superkeyhttp://en.wikipedia.org/wiki/Superkeyhttp://en.wikipedia.org/wiki/Candidate_keyhttp://en.wikipedia.org/wiki/Candidate_keyhttp://en.wikipedia.org/wiki/Database_management_systemhttp://en.wikipedia.org/wiki/Database_management_systemhttp://en.wikipedia.org/wiki/Database_management_systemhttp://en.wikipedia.org/wiki/Primary_keyhttp://en.wikipedia.org/wiki/Primary_keyhttp://en.wikipedia.org/wiki/Edgar_F._Coddhttp://en.wikipedia.org/wiki/Database_normalization#_note-0%23_note-0http://en.wikipedia.org/wiki/Database_normalization#_note-1%23_note-1http://en.wikipedia.org/wiki/Abstract_data_typehttp://en.wikipedia.org/wiki/Abstract_data_typehttp://en.wikipedia.org/wiki/Image:Wiki_letter_w.svghttp://en.wikipedia.org/wiki/Superkeyhttp://en.wikipedia.org/wiki/Candidate_keyhttp://en.wikipedia.org/wiki/Database_management_systemhttp://en.wikipedia.org/wiki/Primary_keyhttp://en.wikipedia.org/wiki/Edgar_F._Coddhttp://en.wikipedia.org/wiki/Database_normalization#_note-0%23_note-0http://en.wikipedia.org/wiki/Database_normalization#_note-1%23_note-1http://en.wikipedia.org/wiki/Abstract_data_type


11/23

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 designedtable 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 thedesigner, 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 dependenton "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 considerationsrelevant to temporal databases.

First normal form

Main article:First normal form

The criteria forfirst normal form (1NF) are:

A table must be guaranteed not to have any duplicate records;

therefore it must have at least one candidate key.

Every column must be atomic, i.e. single-valued with respect to its

datatype. In other words, a column may represent exactly one member from

its domain. For example, a date column carrying two dates is a 1NFviolation. On the other hand, a datatype may be arbitrarily complex.

Therefore, a hypothetical date-range datatype might indeed carry two dates(or rather, one date range) without violating 1NF.

Sometimes this second requirement is expressed like "there may not be repeatinggroups", leading to some prevalent misconceptions. The first misconception is that

1NF precludes a series of columns repeating the same domain. The second

misconception is that 1NF does not allow embedded lists. These are perhapsexamples of poor design, but not necessarily 1NF violations:

Recipe ID Ingredient 1 Ingredient 2 Ingredient 3

1 Flour Eggs Milk

2 Parsely Sage Rosemary

3 Flour Eggs Milk Recipe ID Ingredients

1 flour,eggs,milk

2 parsely,sage,rosemary

3 flour,eggs,milk

Realize that relational databases are incapable of such things,but here's a depiction

of a true 1NF violation, nonetheless:
http://en.wikipedia.org/wiki/Edgar_F._Coddhttp://en.wikipedia.org/wiki/Temporal_databasehttp://en.wikipedia.org/wiki/First_normal_formhttp://en.wikipedia.org/wiki/First_normal_formhttp://en.wikipedia.org/wiki/Candidate_keyhttp://en.wikipedia.org/wiki/Edgar_F._Coddhttp://en.wikipedia.org/wiki/Temporal_databasehttp://en.wikipedia.org/wiki/First_normal_formhttp://en.wikipedia.org/wiki/Candidate_key


12/23

Recipe ID Ingredient 1 Ingredient 2 Ingredient 3

1

3

Flour Eggs Milk

2 Parsely Sage Rosemary

Second normal form

Main article:Second normal formThe criteria forsecond 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, allfunctional dependencies of non-prime attributes on candidate keys are full

functional dependencies. For example, in an "Employees' Skills" table

whose attributes are Employee ID, Employee Address, and Skill, thecombination 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 forthird normal form (3NF) are:


Every non-prime attribute of the table must be non-transitively

dependent on every candidate key. A violation of 3NF would mean that at

least one non-prime attribute is only indirectly dependent (transitivelydependent) 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 ManagerHire Date is functionally dependent on the candidate key {Department ID},

this is only because Manager Hire Date depends on Manager ID, which inturn depends on Department ID. This transitive dependency means the tableis not in 3NF.

Boyce-Codd normal form

Main article:Boyce-Codd normal form

The criteria forBoyce-Codd normal form (BCNF) are:
http://en.wikipedia.org/wiki/Second_normal_formhttp://en.wikipedia.org/wiki/Second_normal_formhttp://en.wikipedia.org/wiki/Third_normal_formhttp://en.wikipedia.org/wiki/Third_normal_formhttp://en.wikipedia.org/wiki/Boyce-Codd_normal_formhttp://en.wikipedia.org/wiki/Boyce-Codd_normal_formhttp://en.wikipedia.org/wiki/Second_normal_formhttp://en.wikipedia.org/wiki/Third_normal_formhttp://en.wikipedia.org/wiki/Boyce-Codd_normal_form


13/23


Every non-trivial functional dependency must be a dependency on a

superkey.

Fourth normal form

Main article:Fourth normal formThe criteria forfourth normal form (4NF) are:

The table must be in BCNF.

There must be no non-trivialmultivalued dependencies on

something other than a superkey. A BCNF table is said to be in 4NFif andonly ifall of itsmultivalued dependencies are functional dependencies.

Fifth normal form

Main article:Fifth normal formThe criteria forfifth normal form (5NF and also PJ/NF) are:


There must be no non-trivial join dependencies that do not followfrom 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 (orDKNF) requires that a table not be subject to anyconstraints other than domain constraints and key constraints.

Sixth normal form

This normal form was, as of 2005, only recently proposed: the sixth normal form (6NF)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[3] for a relational temporal extension, [4],for further discussionon Temporal Aggregation in SQL, or see TSQL2for a different approach.

Example Of The Process

The following example illustrates how a database designer might employ his knowledge of

the normal forms to make progressive improvements to an initially unnormalized databasedesign. The example is somewhat contrived: in practice, few designs lend themselves to

being normalized in strict stages in which the HNF increases at each stage.
http://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/Functional_dependencyhttp://en.wikipedia.org/wiki/Fifth_normal_formhttp://en.wikipedia.org/wiki/Fifth_normal_formhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/Domain/key_normal_formhttp://en.wikipedia.org/wiki/Domain/key_normal_formhttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Dimensionhttp://en.wikipedia.org/wiki/Database_normalization#_note-DBDebunk%23_note-DBDebunkhttp://en.wikipedia.org/wiki/Database_normalization#_note-Zimyani%23_note-Zimyanihttp://en.wikipedia.org/w/index.php?title=TSQL2&action=edithttp://en.wikipedia.org/w/index.php?title=TSQL2&action=edithttp://en.wikipedia.org/wiki/Fourth_normal_formhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/Multivalued_dependencyhttp://en.wikipedia.org/wiki/Functional_dependencyhttp://en.wikipedia.org/wiki/Fifth_normal_formhttp://en.wikipedia.org/wiki/If_and_only_ifhttp://en.wikipedia.org/wiki/Domain/key_normal_formhttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Dimensionhttp://en.wikipedia.org/wiki/Database_normalization#_note-DBDebunk%23_note-DBDebunkhttp://en.wikipedia.org/wiki/Database_normalization#_note-Zimyani%23_note-Zimyanihttp://en.wikipedia.org/w/index.php?title=TSQL2&action=edit


14/23

The database in the example captures information about the suppliers with which various

companies' divisions have relationships more specifically, it captures information about

the types of parts which each division of each company sources from its suppliers.

Starting Point

Information has been presented initially in a way that does not even meet 1NF. Everyrecord is for a particular Company/Division combination: for each of these combinations,

repeating groups of part- and supplier-related information occur. 1NF does not permit

repeating groups.

Suppliers and Parts By Company Division

CompanyCompany

Founder

Company

LogoDivision Part Type Supplier

Supplier

Country

Allied

Clock andWatch

Horace

Washington Sundial Clocks

Spring

Pendulum

SpringToothed Wheel

Tensile Globodynamics

Tensile Globodynamics

Pieza de AceroPieza de Acero

USA

USA

MexicoMexico

N

N

NN

AlliedClock and

Watch

HoraceWashington

Sundial WatchesQuartz CrystalTuning Fork

Battery

MicrofluxMicroflux

Dakota Electrics

BelgiumBelgium

USA

EE

N

GlobalRobot

NilsNeumann

GearboxIndustrialRobots

Flywheel

AxleAxle

Mechanical Arm

Wheels 4 Less

Wheels 4 LessTransEuropa

TransEuropa

USA

USAItaly

Italy

N

NE

E

Global

Robot

Nils

Neumann Gearbox

Domestic

Robots

Artificial BrainArtificial Brain

Metal HousingBackplate

Prometheus LabsFrankenstein Labs

Pieza de AceroPieza de Acero

LuxembourgGermany

MexicoMexico

EE

NN

1NF

We eliminate the repeating groups by ensuring that each group appears on its own record.

The unique identifier for a record is now {Company, Division, Part Type, Supplier}.


CompanyCompany

Founder

Company

Logo

Division Part Type SupplierSupplier

Country

Supplier

ContinentAlliedClock and

Watch

Horace

WashingtonSundial Clocks Spring

Tensile

GlobodynamicsUSA N. Amer.

AlliedClock and

Watch

HoraceWashington

Sundial Clocks PendulumTensileGlobodynamics

USA N. Amer.

Allied Horace Sundial Clocks Spring Pieza de Acero Mexico N. Amer.


15/23

Clock and

WatchWashington

AlliedClock and

Watch

Horace

WashingtonSundial Clocks

Toothed

WheelPieza de Acero Mexico N. Amer.

AlliedClock and

Watch

HoraceWashington

Sundial WatchesQuartzCrystal

Microflux Belgium Europe

Allied

Clock andWatch

HoraceWashington

Sundial WatchesTuningFork


Allied

Clock andWatch

HoraceWashington

Sundial Watches BatteryDakotaElectrics

USA N. Amer.

Global

Robot

Nils

NeumannGearbox

Industrial

RobotsFlywheel Wheels 4 Less USA N. Amer.

GlobalRobot

NilsNeumann

GearboxIndustrialRobots

Axle Wheels 4 Less USA N. Amer.

Global

Robot

Nils

NeumannGearbox

Industrial

RobotsAxle TransEuropa Italy Europe

Global

Robot

Nils

NeumannGearbox

Industrial

Robots

Mechanical

ArmTransEuropa Italy Europe

Global

Robot

Nils

NeumannGearbox

Domestic

Robots

Artificial

Brain

Prometheus

LabsLuxembourg Europe

Global

Robot

Nils

NeumannGearbox

Domestic

Robots

Artificial

Brain

Frankenstein

LabsGermany Europe

GlobalRobot

NilsNeumann

Gearbox DomesticRobots

MetalHousing

Pieza de Acero Mexico N. Amer.

Global

Robot

Nils

NeumannGearbox

Domestic

RobotsBackplate Pieza de Acero Mexico N. Amer.

2NF

One problem with the design at this stage is that Company Founder and Company Logodetails for a given company may appear redundantly on more than one record; so may the

Supplier Countries and Continents for a given supplier. These phenomena arise from the

part-key dependencies of a) the Company Founder and Company Logo attributes onCompany, and b) the Supplier Country and Supplier Continent attributes on Supplier. 2NF

does not permit part-key dependencies. We correct the problem by splitting out the

Company Founder and Company Logo details into their own table, called Companies, as


16/23

well as splitting out the Supplier Country and Supplier Continent details into their own

table, called Suppliers.


Company Division Part Type Supplier

Allied Clock and Watch Clocks Spring Tensile GlobodynamicsAllied Clock and Watch Clocks Pendulum Tensile Globodynamics

Allied Clock and Watch Clocks Spring Pieza de Acero

Allied Clock and Watch Clocks Toothed Wheel Pieza de Acero

Allied Clock and Watch Watches Quartz Crystal Microflux

Allied Clock and Watch Watches Tuning Fork Microflux

Allied Clock and Watch Watches Battery Dakota Electrics

Global Robot Industrial Robots Flywheel Wheels 4 Less

Global Robot Industrial Robots Axle Wheels 4 Less

Global Robot Industrial Robots Axle TransEuropa

Global Robot Industrial Robots Mechanical Arm TransEuropaGlobal Robot Domestic Robots Artificial Brain Prometheus Labs

Global Robot Domestic Robots Artificial Brain Frankenstein Labs

Global Robot Domestic Robots Metal Housing Pieza de Acero

Global Robot Domestic Robots Backplate Pieza de Acero

Companies

Company Company Founder Company Logo

Allied Clock and Watch Horace Washington Sundial

Global Robot Nils Neumann Gearbox

Suppliers

Supplier Supplier Country Supplier ContinentTensile Globodynamics USA N. Amer.

Pieza de Acero Mexico N. Amer.


Dakota Electrics USA N. Amer.

Wheels 4 Less USA N. Amer.

TransEuropa Italy Europe

Prometheus Labs Luxembourg Europe

Frankenstein Labs Germany Europe

3NF and BCNF

There is still, however, redundancy in the design. The Supplier Continent for a given

Supplier Country may appear redundantly on more than one record. This phenomenon

arises from the dependency of non-key attribute Supplier Continent on non-key attributeSupplier Country, and means that the design does not conform to 3NF. To achieve 3NF

(and, while we are at it, BCNF), we create a separate Countries table which tells us which

continent a country belongs to.


17/23



Allied Clock and Watch Clocks Spring Tensile Globodynamics

Allied Clock and Watch Clocks Pendulum Tensile Globodynamics









Global Robot Industrial Robots Mechanical Arm TransEuropa

Global Robot Domestic Robots Artificial Brain Prometheus Labs




Suppliers

Supplier Supplier Country

Tensile Globodynamics USA

Pieza de Acero Mexico

Microflux Belgium

Dakota Electrics USA

Wheels 4 Less USA

TransEuropa Italy

Prometheus Labs Luxembourg

Frankenstein Labs Germany

Companies




Countries

Country Continent

USA N. Amer.

Mexico N. Amer.

Belgium Europe

Italy Europe

Luxembourg Europe

4NF


18/23

What happens if a company has more than one founder or more than one logo? (Let us

assume for the sake of the example that both of these things may happen.) One way of

handling the situation would be to alter the primary key of our Companies table to{Company, Company Founder, Company Logo}. Representing multiple founders and

multiple logos then becomes possible, but at the price of redundancy:

Companies




International Broom Gareth Patterson Whirlwind

International Broom Sandra Patterson Whirlwind

International Broom Gareth Patterson Sweeper

International Broom Sandra Patterson Sweeper

This type of redundancy reflects the fact that the design does not conform to 4NF. We

correct the design by separating facts about founders from facts about logos.



Allied Clock and Watch Clocks Spring Tensile Globodynamics

Allied Clock and Watch Clocks Pendulum Tensile Globodynamics









Global Robot Industrial Robots Mechanical Arm TransEuropa

Global Robot Domestic Robots Artificial Brain Prometheus Labs




Companies

Company

Allied Clock and Watch

Global Robot

International Broom

Company Logos

Company Company Logo

Allied Clock and Watch Sundial


19/23

Global Robot Gearbox

International Broom Whirlwind

International Broom Sweeper

Company Founders

Company Company Founder

Allied Clock and Watch Horace Washington

Global Robot Nils Neumann

International Broom Gareth Patterson

International Broom Sandra Patterson

Suppliers




Microflux Belgium


Wheels 4 Less USA

TransEuropa Italy



Countries

Country Continent

USA N. Amer.

Mexico N. Amer.

Belgium Europe

Italy Europe

Luxembourg Europe

5NF

We know that the Clocks division of Allied Clock and Watch relies upon its suppliers to

provide springs, pendulums, and toothed wheels. We also know that the Clocks divisiondeals with suppliers Tensile Globodynamics and Pieza de Acero. Let us suppose for the

sake of the example that the following rule applies: if a supplier that a division deals with

offers a part that the division needs, the division will always purchase it. If, for example,Tensile Globodynamics start producing Toothed Wheels, then Allied Clock and Watch will

start purchasing them. This rule leads to redundancy in our design as it stands, causing it to

fall short of 5NF. We correct the design by recording part-types-by-company-division

separately from suppliers-by-company-division, and adding a further table that providesinformation as to which suppliers offer which parts.

Part Types By Company Division

Company Division Part Type

Allied Clock and Watch Clocks Spring


20/23

Allied Clock and Watch Clocks Pendulum

Allied Clock and Watch Clocks Toothed Wheel

Allied Clock and Watch Watches Quartz Crystal

Allied Clock and Watch Watches Tuning Fork

Allied Clock and Watch Watches Battery

Global Robot Industrial Robots Flywheel

Global Robot Industrial Robots Axle

Global Robot Industrial Robots Mechanical Arm

Global Robot Domestic Robots Artificial Brain

Global Robot Domestic Robots Metal Housing

Global Robot Domestic Robots Backplate

Suppliers By Company Division

Company Division Supplier

Allied Clock and Watch Clocks Tensile Globodynamics

Allied Clock and Watch Clocks Pieza de Acero

Allied Clock and Watch Watches Microflux

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Denormalization

Main article:Denormalization

Databases intended forOnline Transaction Processing (OLTP)are typically more

normalized than databases intended forOn Line Analytical Processing (OLAP). OLTPApplications 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 OLAPoperations 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 Intelligenceapplications.Specifically, dimensional tables in a star schemaoften 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 thisdenormalization itself provides any increase in performance, or if the concurrent removal
http://en.wikipedia.org/wiki/Denormalizationhttp://en.wikipedia.org/wiki/Denormalizationhttp://en.wikipedia.org/wiki/Online_transaction_processinghttp://en.wikipedia.org/wiki/Online_transaction_processinghttp://en.wikipedia.org/wiki/OLAPhttp://en.wikipedia.org/wiki/OLAPhttp://en.wikipedia.org/wiki/Business_Intelligencehttp://en.wikipedia.org/wiki/Business_Intelligencehttp://en.wikipedia.org/wiki/Dimension_tablehttp://en.wikipedia.org/wiki/Star_schemahttp://en.wikipedia.org/wiki/Star_schemahttp://en.wikipedia.org/wiki/Extract%2C_transform%2C_loadhttp://en.wikipedia.org/wiki/Snowflake_schemahttp://en.wikipedia.org/wiki/Denormalizationhttp://en.wikipedia.org/wiki/Online_transaction_processinghttp://en.wikipedia.org/wiki/OLAPhttp://en.wikipedia.org/wiki/Business_Intelligencehttp://en.wikipedia.org/wiki/Dimension_tablehttp://en.wikipedia.org/wiki/Star_schemahttp://en.wikipedia.org/wiki/Extract%2C_transform%2C_loadhttp://en.wikipedia.org/wiki/Snowflake_schema


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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 incomputerized 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 aplatform (such as Palm), or no changes are to be made to the data and a swift response is

crucial.

Non-first normal form (NF)

In recognition that denormalization can be deliberate and (dubiously) 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. Sometheoreticians 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:

Non-First Normal Form

Person Favorite Colors

Bob blue, red

Jane green, yellow, red

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

To transform this NF 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 mathematicalinverse to "nest". Another constraint required is for the operators to bebijective, which is

covered by the Partitioned Normal Form (PNF).

Further reading

Litt's Tips: Normalization
http://en.wikipedia.org/wiki/Bijectionhttp://en.wikipedia.org/w/index.php?title=Partitioned_Normal_Form&action=edithttp://en.wikipedia.org/w/index.php?title=PNF&action=edithttp://www.troubleshooters.com/littstip/ltnorm.htmlhttp://en.wikipedia.org/wiki/Bijectionhttp://en.wikipedia.org/w/index.php?title=Partitioned_Normal_Form&action=edithttp://en.wikipedia.org/w/index.php?title=PNF&action=edithttp://www.troubleshooters.com/littstip/ltnorm.html


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Date, C. J., & Lorentzos, N., & Darwen, H. (2002).Temporal Data & the

Relational Model(1st ed.). Morgan Kaufmann. ISBN 1-55860-855-9.

Zimyani, E (2006), Temporal Aggregates and Temporal Universal Quantificationin Standard SQL ACM SIGMOD Record, Vol 35, Number 2, June 2006.

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

References

1. ^ His term eliminate is misleading, as nothing is "lost" in normalization. Heprobably described eliminate in a mathematical sense to mean elimination of

complexity.2. ^ Codd, Edgar F. (June 1970). "A Relational Model of Data for Large Shared Data

Banks". Communications of the ACM13 (6): 377-387.3. ^ DBDebunk

4. ^ Zimyani
http://www.elsevier.com/wps/product/cws_home/680662http://www.elsevier.com/wps/product/cws_home/680662http://www.elsevier.com/wps/product/cws_home/680662http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=1558608559http://www.sigmod.org/sigmod/record/issues/0606/p16-article-zimanyi.pdfhttp://www.sigmod.org/sigmod/record/issues/0606/p16-article-zimanyi.pdfhttp://www.aw-bc.com/catalog/academic/product/0,1144,0321197844,00.htmlhttp://www.aw-bc.com/catalog/academic/product/0,1144,0321197844,00.htmlhttp://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0321197844http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0321197844http://www.bkent.net/Doc/simple5.htmhttp://www.bkent.net/Doc/simple5.htmhttp://www.bkent.net/Doc/simple5.htmhttp://www.dbdebunk.com/http://en.wikipedia.org/wiki/Database_normalization#_ref-0%23_ref-0http://en.wikipedia.org/wiki/Database_normalization#_ref-1%23_ref-1http://en.wikipedia.org/wiki/Edgar_F._Coddhttp://www.acm.org/classics/nov95/toc.htmlhttp://www.acm.org/classics/nov95/toc.htmlhttp://en.wikipedia.org/wiki/Communications_of_the_ACMhttp://en.wikipedia.org/wiki/Database_normalization#_ref-DBDebunk_0%23_ref-DBDebunk_0http://www.dbdebunk.com/page/page/621935.htmhttp://en.wikipedia.org/wiki/Database_normalization#_ref-Zimyani_0%23_ref-Zimyani_0http://www.elsevier.com/wps/product/cws_home/680662http://www.elsevier.com/wps/product/cws_home/680662http://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=1558608559http://www.sigmod.org/sigmod/record/issues/0606/p16-article-zimanyi.pdfhttp://www.sigmod.org/sigmod/record/issues/0606/p16-article-zimanyi.pdfhttp://www.aw-bc.com/catalog/academic/product/0,1144,0321197844,00.htmlhttp://en.wikipedia.org/w/index.php?title=Special:Booksources&isbn=0321197844http://www.bkent.net/Doc/simple5.htmhttp://www.bkent.net/Doc/simple5.htmhttp://www.dbdebunk.com/http://en.wikipedia.org/wiki/Database_normalization#_ref-0%23_ref-0http://en.wikipedia.org/wiki/Database_normalization#_ref-1%23_ref-1http://en.wikipedia.org/wiki/Edgar_F._Coddhttp://www.acm.org/classics/nov95/toc.htmlhttp://www.acm.org/classics/nov95/toc.htmlhttp://en.wikipedia.org/wiki/Communications_of_the_ACMhttp://en.wikipedia.org/wiki/Database_normalization#_ref-DBDebunk_0%23_ref-DBDebunk_0http://www.dbdebunk.com/page/page/621935.htmhttp://en.wikipedia.org/wiki/Database_normalization#_ref-Zimyani_0%23_ref-Zimyani_0

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