A
relational database is a
databaseA database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
that conforms to
relational modelThe relational model for database management is a database model based on first-order predicate logic, first formulated and proposed in 1969 by Edgar F...
theory. The software used in a relational database is called a relational database management system (RDBMS). Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself. A relational database is the predominant choice in storing data, over other models like the hierarchical database model or the
network modelThe network model is a database model conceived as a flexible way of representing objects and their relationships. Its distinguishing feature is that the schema, viewed as a graph in which object types are nodes and relationship types are arcs, is not restricted to being a hierarchy or lattice.The...
.
Terminology
The term
relational database was originally defined by and is attributed to Edgar Codd at IBM Almaden Research Center in 1970.
Relational database theory uses a set of mathematical terms, which are roughly equivalent to
SQLSQL is a programming language designed for managing data in relational database management systems ....
database terminology. The table below summarizes some of the most important relational database terms and their SQL database equivalents.
| Relational term |
SQL equivalent |
| relation In relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
, base relvarIn relational databases, a relvar is a term coined by C. J. Date as an abbreviation for the concept of relation variable, which is the actual term used by the inventor of the relational model, E. F. Codd, regarding the same concept...
|
table |
| derived relvar |
view, query result, result set |
| tuple |
row |
| attribute |
column |
Relations or Tables
A
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
is defined as a set of
tupleIn mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
s that have the same
attributesIn computing, an attribute is a specification that defines a property of an object, element, or file. It may also refer to or set the specific value for a given instance of such....
. A tuple usually represents an object and information about that object. Objects are typically physical objects or concepts. A relation is usually described as a
tableIn relational databases and flat file databases, a table is a set of data elements that is organized using a model of vertical columns and horizontal rows. A table has a specified number of columns, but can have any number of rows...
, which is organized into
rowsIn the context of a relational database, a row—also called a record or tuple—represents a single, implicitly structured data item in a table. In simple terms, a database table can be thought of as consisting of rows and columns or fields...
and
columnsIn the context of a relational database table, a column is a set of data values of a particular simple type, one for each row of the table. The columns provide the structure according to which the rows are composed....
. All the data referenced by an attribute are in the same
domainIn mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined...
and conform to the same constraints.
The relational model specifies that the tuples of a relation have no specific order and that the tuples, in turn, impose no order on the attributes. Applications access data by specifying queries, which use operations such as
select to identify tuples,
project to identify attributes, and
join to combine relations. Relations can be modified using the
insert,
delete, and
update operators. New tuples can supply explicit values or be derived from a query. Similarly, queries identify tuples for updating or deleting.
It is necessary for each tuple of a relation to be uniquely identifiable by some combination (one or more) of its attribute values. This combination is referred to as the primary key.
Base and derived relations
In a relational database, all data are stored and accessed via
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
s. Relations that store data are called "base relations", and in implementations are called "tables". Other relations do not store data, but are computed by applying relational operations to other relations. These relations are sometimes called "derived relations". In implementations these are called "
viewsIn database theory, a view consists of a stored query accessible as a virtual table in a relational database or a set of documents in a document-oriented database composed of the result set of a query or map and reduce functions...
" or "queries". Derived relations are convenient in that though they may grab information from several relations, they act as a single relation. Also, derived relations can be used as an
abstraction layerAn abstraction layer is a way of hiding the implementation details of a particular set of functionality...
.
Domain
A domain describes the set of possible values for a given attribute, and can be considered a constraint on the value of the attribute. Mathematically, attaching a domain to an attribute means that any value for the attribute must be an element of the specified set.
The character data value 'ABC', for instance, is not in the integer domain. The integer value 123, satisfies the domain constraint.
Constraints
Constraints make it possible to further restrict the domain of an attribute. For instance, a constraint can restrict a given integer attribute to values between 1 and 10. Constraints provide one method of implementing business rules in the database. SQL implements constraint functionality in the form of
check constraintA check constraint is a condition that defines valid data when adding or updating an entry in a table of a relational database. A check constraint is applied to each row in the table. The constraint must be a predicate. It can refer to a single or multiple columns of the table...
s.
Constraints restrict the data that can be stored in
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
s. These are usually defined using expressions that result in a boolean value, indicating whether or not the data satisfies the constraint. Constraints can apply to single attributes, to a tuple (restricting combinations of attributes) or to an entire relation.
Since every attribute has an associated domain, there are constraints (
domain constraints). The two principal rules for the relational model are known as
entity integrity and
referential integrity.
('"Referential integrity is the state in which all values of all foreign keys are valid. Referential integrity is based on entity integrity. Entity integrity requires that each entity have a unique key. For example, if every row in a table represents relationships for a unique entity, the table should have one column or a set of columns that provides a unique identifier for the rows of the table. This column (or set of columns) is called the parent key of the table. To ensure that the parent key does not contain duplicate values, a unique index must be defined on the column or columns that constitute the parent key. Defining the parent key is called entity integrity"')
Primary keys
A primary key uniquely defines a relationship within a database. In order for an attribute to be a good primary key it must not repeat. While natural attributes are sometimes good primary keys, surrogate keys are often used instead. A surrogate key is an artificial attribute assigned to an object which uniquely identifies it (for instance, in a table of information about students at a school they might all be assigned a student ID in order to differentiate them). The surrogate key has no intrinsic (inherent) meaning, but rather is useful through its ability to uniquely identify a tuple.
Another common occurrence, especially in regards to N:M cardinality is the composite key. A composite key is a key made up of two or more attributes within a table that (together) uniquely identify a record. (For example, in a database relating students, teachers, and classes. Classes
could be uniquely identified by a composite key of their room number and time slot, since no other class could have exactly the same combination of attributes. In fact, use of a composite key such as this can be a form of data verification, albeit a weak one.)
Foreign key
A foreign key is a reference to a key in another
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
, meaning that the referencing table has, as one of its attributes, the values of a key in the referenced table. Foreign keys need not have unique values in the referencing relation. Foreign keys effectively use the values of attributes in the referenced relation to restrict the domain of one or more attributes in the referencing relation.
A foreign key could be described formally as: "For all tuples in the referencing relation projected over the referencing attributes, there must exist a tuple in the referenced relation projected over those same attributes such that the values in each of the referencing attributes match the corresponding values in the referenced attributes."
Stored procedures
A stored procedure is executable code that is associated with, and generally stored in, the database. Stored procedures usually collect and customize common operations, like inserting a
tupleIn mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
into a
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
, gathering statistical information about usage patterns, or encapsulating complex business logic and calculations. Frequently they are used as an
application programming interfaceAn application programming interface is a source code based specification intended to be used as an interface by software components to communicate with each other...
(API) for security or simplicity. Implementations of stored procedures on SQL DBMSs often allow developers to take advantage of
proceduralProcedural programming can sometimes be used as a synonym for imperative programming , but can also refer to a programming paradigm, derived from structured programming, based upon the concept of the procedure call...
extensions (often vendor-specific) to the standard
declarativeIn computer science, declarative programming is a programming paradigm that expresses the logic of a computation without describing its control flow. Many languages applying this style attempt to minimize or eliminate side effects by describing what the program should accomplish, rather than...
SQL syntax.
Stored procedures are not part of the relational database model, but all commercial implementations include them.
Index
An index is one way of providing quicker access to data. Indices can be created on any combination of attributes on a
relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
. Queries that filter using those attributes can find matching tuples randomly using the index, without having to check each tuple in turn. This is analogous to using the index of a book to go directly to the page on which the information you are looking for is found i.e. you do not have to read the entire book to find what you are looking for. Relational databases typically supply multiple indexing techniques, each of which is optimal for some combination of data distribution, relation size, and typical access pattern.
B+ treeIn computer science, a B+ tree or B plus tree is a type of tree which represents sorted data in a way that allows for efficient insertion, retrieval and removal of records, each of which is identified by a key. It is a dynamic, multilevel index, with maximum and minimum bounds on the number of...
s,
R-treeR-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The R-tree was proposed by Antonin Guttman in 1984 and has found significant use in both research and real-world applications...
s, and
bitmapsA bitmap index is a special kind of database index that uses bitmaps.Bitmap indexes have traditionally been considered to work well for data such as gender, which has a small number of distinct values, for example male and female, but many occurrences of those values. This would happen if, for...
, hash index.
Indices are usually not considered part of the database, as they are considered an implementation detail, though indices are usually maintained by the same group that maintains the other parts of the database. It should be noted that use of efficient indexes on both primary and foreign keys can dramatically improve query performance. This is because B-tree indexes result in query times proportional to log(n) where N is the number of rows in a table and hash indexes result in constant time queries (no size dependency so long as the relevant part of the index fits into memory).
Relational operations
Queries made against the relational database, and the derived relvars in the database are expressed in a
relational calculusRelational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to specify database queries...
or a
relational algebraRelational algebra, an offshoot of first-order logic , deals with a set of finitary relations that is closed under certain operators. These operators operate on one or more relations to yield a relation...
. In his original relational algebra, Codd introduced eight relational operators in two groups of four operators each. The first four operators were based on the traditional mathematical
set operationsSet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
:
- The union
In set theory, the union of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets S_1, S_2, S_3, \dots , S_n\,\! gives a set S_1 \cup S_2 \cup S_3 \cup \dots \cup S_n.- Definition :...
operator combines the tuples of two relationIn relational model:A relation value, which is assigned to a certain relation variable, is time-varying. By using a Data Definition Language , it is able to define relation variables.The following is an example of a heading which consists of three attributes....
s and removes all duplicate tuples from the result. The relational union operator is equivalent to the SQL UNION operator.
- The intersection
In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B , but no other elements....
operator produces the set of tuples that two relations share in common. Intersection is implemented in SQL in the form of the INTERSECT operator.
- The difference
In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...
operator acts on two relations and produces the set of tuples from the first relation that do not exist in the second relation. Difference is implemented in SQL in the form of the EXCEPT or MINUS operator.
- The cartesian product
In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets...
of two relations is a join that is not restricted by any criteria, resulting in every tuple of the first relation being matched with every tuple of the second relation. The cartesian product is implemented in SQL as the CROSS JOIN join operator.
The remaining operators proposed by Codd involve special operations specific to relational databases:
- The selection, or restriction, operation retrieves tuples from a relation, limiting the results to only those that meet a specific criteria, i.e. a subset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
in terms of set theory. The SQL equivalent of selection is the SELECT query statement with a WHERE clause.
- The projection operation extracts only the specified attributes from a tuple or set of tuples.
- The join operation defined for relational databases is often referred to as a natural join. In this type of join, two relations are connected by their common attributes. SQL's approximation of a natural join is the INNER JOIN join operator.
- The relational division operation is a slightly more complex operation, which involves essentially using the tuples of one relation (the dividend) to partition a second relation (the divisor). The relational division operator is effectively the opposite of the cartesian product operator (hence the name).
Other operators have been introduced or proposed since Codd's introduction of the original eight including relational comparison operators and extensions that offer support for nesting and hierarchical data, among others.
Normalization
Normalization was first proposed by Codd as an integral part of the relational model. It encompasses a set of procedures designed to eliminate nonsimple domains (non-atomic values) and the redundancy (duplication) of data, which in turn prevents data manipulation anomalies and loss of data integrity. The most common forms of normalization applied to databases are called the normal forms. Normalization trades reducing redundancy for increased
information entropyIn information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...
. Normalization is criticised because it increases complexity and processing overhead required to join multiple tables representing what are conceptually a single item .
Relational database management systems
Relational databases, as implemented in relational database management systems, have become a predominant choice for the storage of information in new databases used for financial records, manufacturing and logistical information, personnel data and much more. Relational databases have often replaced legacy hierarchical databases and network databases because they are easier to understand and use, even though they are much less efficient. As computer power has increased, the inefficiencies of relational databases, which made them impractical in earlier times, have been outweighed by their ease of use. However, relational databases have been challenged by
Object DatabaseAn object database is a database management system in which information is represented in the form of objects as used in object-oriented programming...
s, which were introduced in an attempt to address the
object-relational impedance mismatchThe object-relational impedance mismatch is a set of conceptual and technical difficulties that are often encountered when a relational database management system is being used by a program written in an object-oriented programming language or style; particularly when objects or class definitions...
in relational database, and
XML databaseAn XML database is a data persistence software system that allows data to be stored in XML format. This data can then be queried, exported and serialized into the desired format.Two major classes of XML database exist:...
s.
The three leading commercial relational database vendors are
OracleOracle Corporation is an American multinational computer technology corporation that specializes in developing and marketing hardware systems and enterprise software products – particularly database management systems...
,
MicrosoftMicrosoft Corporation is an American public multinational corporation headquartered in Redmond, Washington, USA that develops, manufactures, licenses, and supports a wide range of products and services predominantly related to computing through its various product divisions...
, and
IBMInternational Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...
. The three leading
open sourceThe term open source describes practices in production and development that promote access to the end product's source materials. Some consider open source a philosophy, others consider it a pragmatic methodology...
implementations are
MySQLMySQL officially, but also commonly "My Sequel") is a relational database management system that runs as a server providing multi-user access to a number of databases. It is named after developer Michael Widenius' daughter, My...
,
PostgreSQLPostgreSQL, often simply Postgres, is an object-relational database management system available for many platforms including Linux, FreeBSD, Solaris, MS Windows and Mac OS X. It is released under the PostgreSQL License, which is an MIT-style license, and is thus free and open source software...
, and
SQLiteSQLite is an ACID-compliant embedded relational database management system contained in a relatively small C programming library. The source code for SQLite is in the public domain and implements most of the SQL standard...
.
Amazon Relational Database ServiceAmazon Relational Database Service or Amazon RDS is a distributed relational database service by Amazon.com. It is a web service running "in the cloud" and provides users a relational database for use in their applications. Amazon RDS makes it easy to set up, operate, and scale a relational database...
is a database as a service offering MySQL and Oracle database engines.
Watermarking for Relational Databases
Digital watermarkingDigital watermarking is the process of embedding information into a digital signal which may be used to verify its authenticity or the identity of its owners, in the same manner as paper bearing a watermark for visible identification. In digital watermarking, the signal may be audio, pictures, or...
for relational databases emerged as a candidate solution to provide copyright protection, tamper detection, traitor tracing, maintaining integrity of relational data. Many watermarking techniques have been proposed in the literature to address these purposes. A survey of the current state-of-the-art and a classification of the different techniques according to their intent, the way they express the watermark, the cover type, the granularity level, and their verifiability, can be found in.