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Showing posts with label The Relational Data Model and Relational Database. Show all posts
Database Management System × The Relational Data Model and Relational Database
The SELECT operation (denoted byσ
(sigma)) is used to select a subset of the tuples from a relation based on a
selection condition. The selection condition acts as a filterand keeps only
those tuples that satisfy the qualifying condition. Tuples satisfying the condition
are selected whereas the other tuples are discarded (filtered out)
Database State for COMPANY
• Examples:
– Select the EMPLOYEE tuples
whose department number is 4:
σ DNO = 4 (EMPLOYEE)
σ Select the employee tuples
whose salary is greater than $30,000:
_SALARY > 30,000 (EMPLOYEE)
– In general, the select operation
is denoted by σ <selection condition>(R) where
the symbol σ (sigma) is used to
denote the select operator
the selection condition is a
Boolean (conditional) expression specified
on the attributes of relation R
tuples that make the condition true
are selected
(appear in the result of the
operation)
tuples that make the condition false
are filtered out
(discarded from the result of the
operation)
The Boolean expression specified
in <selection condition> is made up of a number of clauses of the form:
<attribute name>
<comparison op> <constant value>
or
<attribute name>
<comparison op> <attribute name>
Where <attribute name> is
the name of an attribute of R, <comparison op> id normally
one of the operations
{=,>,>=,<,<=,!=}
Clauses can be arbitrarily
connected by the Boolean operators and, or and not
• For example, To select
the tuples for all employees who either work in
department 4 and make over $25000
per year, or work in department 5 and make
over $30000, the select operation
should be:
_ (DNO=4 AND Salary>25000 )
OR (DNO=5 AND Salary>30000 ) (EMPLOYEE)
The following
query results refer to this database
Examples of
applying SELECT and PROJECT operations
SELECT Operation
Properties
– SELECT s is commutative:
σ
<condition1>(σ <
condition2>(R)) = σ <condition2>
(σ < condition1>
(R))
– A cascade of SELECT
operations may be replaced by a
single selection with a conjunction of
all the conditions:
σ
<cond1>( σ <
cond2> (σ <cond3>(R))
= σ
<cond1> AND < cond2> AND < cond3>(R)
Database Management System × The Relational Data Model and Relational Database
Relational Algebra consists of
several groups of operations
Unary Relational
Operations
SELECT (symbol: s (sigma))
PROJECT (symbol: _ (pi))
RENAME (symbol: r (rho))
Relational
Algebra Operations From Set Theory
UNION ( U ), INTERSECTION ( _ ),
DIFFERENCE (or MINUS, – )
CARTESIAN PRODUCT ( x )
Binary
Relational Operations
JOIN (several variations of JOIN
exist)
DIVISION
Additional
Relational Operations
OUTER JOINS, OUTER UNION
Unary Relational
Operations
SELECT (symbol: s (sigma))
PROJECT (symbol: _ (pi))
RENAME (symbol: r (rho))
Database Management System × The Relational Data Model and Relational Database
Introduction
Relational Algebra is a procedural
language used for manipulating relations. The relational model gives the
structure for relations so that data can be stored in that format but
relational algebra enables us to retrieve information from relations. Some advanced
SQL queries requires explicit relational algebra operations, most commonly outer
join.
Relations are seen as sets of
tuples, which means that no duplicates are allowed. SQL behaves differently in
some cases. Remember the SQL keyword distinct. SQL is declarative, which means
that you tell the DBMS what you want.
Set operations
Relations in relational algebra
are seen as sets of tuples, so we can use basic set operations.
Review of
concepts and operations from set theory
_ Set
_ Element
_ No duplicate elements
_ No order among the elements
_ Subset
_ Proper subset (with fewer
elements)
_ Superset
_ Union
_ Intersection
_ Set Difference
_ Cartesian product
Database Management System × The Relational Data Model and Relational Database
Integrity constraints should not
be violated by the update operations. Several update operations may have to be
grouped together. Updates may propagate to cause other updates automatically.
This may be necessary to maintain integrity constraints. In case of integrity
violation, several actions can be taken:
1. Cancel the operation that
causes the violation (REJECT option)
2. Perform the operation but
inform the user of the violation
3. Trigger additional updates so
the violation is corrected (CASCADE option, SET NULL option)
4. Execute a user-specified error-correction routine
Database Management System × The Relational Data Model and Relational Database
It is based on application
semantics and cannot be expressed by the model per se
E.g., “the max. no. of hours per
employee for all projects he or she works on is 56 hrs per week”
A constraint specification
language may have to be used to express these
SQL-99 allows triggers and ASSERTIONS to allow for
some of these.
Database Management System × The Relational Data Model and Relational Database
Statement of the constraint
The value in the foreign key
column (or columns) FK of the the referencing relation R1 can be either:
(1) a value of an existing
primary key value of the corresponding primary key PK in the referenced
relation R2,, or..
(2) a null.
In case (2), the FK in R1 should not be a part of
its own primary key.
Database Management System × The Relational Data Model and Relational Database
The initial design is typically
not complete. Some aspects in the requirements will be represented as
relationships
ER model has three main concepts:
Entities (and their entity types
and entity sets)
Attributes (simple, composite,
multi valued)
Relationships (and their
relationship types and relationship sets)
Database Management System × The Relational Data Model and Relational Database
Relational Database Schema: A set
S of relation schemas that belong to the same database. S is the name of the database.
S = {R1, R2, ..., Rn}
Entity Integrity: The primary key
attributes PK of each relation schema R in S cannot have null values in any
tuple of r(R). This is because primary key values are used to identify the
individual tuples.
t[PK] ¹ null for any tuple t in
r(R)
Note: Other attributes of R may
be similarly constrained to disallow null values, even though they are not
members of the primary key.
Database Management System × The Relational Data Model and Relational Database
Constraints are conditions that must hold on all
valid relation instances. There are three main types of constraints:
1. Key constraints
2. Entity integrity constraints
3. Referential integrity constraints
Superkey of R: A set of
attributes SK of R such that no two tuples in any valid
relation instance r(R) will have the same value for
SK. That is, for any distinct tuples t1 and t2 in r(R), t1[SK] ¹ t2[SK].
Key of R: A "minimal" superkey; that is, a
superkey K such that removal of any attribute from K results in a set of
attributes that is not a superkey.
Example: The CAR relation schema:
CAR(State, Reg#, SerialNo, Make,
Model, Year)
has two keys Key1 = {State,
Reg#}, Key2 = {SerialNo}, which are also superkeys.
{SerialNo, Make} is a superkey but not a key.
If a relation has several candidate keys, one is
chosen arbitrarily to be the primary key. The primary key attributes are underlined.
Database Management System × The Relational Data Model and Relational Database
Ordering of tuples in a relation r(R): The tuples
are not considered to be ordered, even though they appear to be in the tabular
form.
Ordering of attributes in a relation schema R (and
of values within each tuple): We will consider the attributes in R(A1, A2, ...,
An) and the values in t=<v1 , v2, ..., vn> to be ordered .
(However, a more general alternative definition of
relation does not require this ordering).
Values in a tuple: All values are considered atomic
(indivisible). A special null value is used to represent values that are
unknown or inapplicable to certain tuples.
Notation:
We refer to component values of a tuple t by t[Ai] =
vi (the value of attribute Ai for tuple t). Similarly, t[Au, Av, ...,Aw] refers
to the subtuple of t containing the values of attributes Au, Av, ..., Aw, respectively.
Database Management System × The Relational Data Model and Relational Database
A Relation may be defined
in multiple ways. The Schema of a Relation: R (A1, A2, .....An)
Relation schema R is defined over attributes A1, A2, .....An.
For Example -
CUSTOMER (Cust-id, Cust-name,
Address, Phone#)
Here, CUSTOMER is a relation
defined over the four attributes Cust-id, Cust-name, Address, Phone#, each of
which has a domain or a set of valid values. For example, the domain of
Cust-id is 6 digit numbers.
A tuple is an ordered set of
values.Each value is derived from an appropriate domain. Each row in the
CUSTOMER table may be referred to as a tuple in the table and would consist of
four values.
<632895, "John
Smith", "101 Main St. Atlanta, GA 30332", "(404)
894-2000">
is a tuple belonging to the
CUSTOMER relation.
A relation may be regarded as a
set of tuples (rows). Columns in a table are also called attributes of the
relation.
A domain has a logical
definition: e.g.,
“USA_phone_numbers” are the set
of 10 digit phone numbers valid in the U.S. A domain may have a data-type or a
format defined for it. The USA_phone_numbers may have a format: (ddd)-ddd-dddd
where each d is a decimal digit. E.g., Dates have various formats such as
monthname, date, year or yyyy-mm-dd, or dd mm,yyyy etc.
An attribute designates the role
played by the domain. E.g., the domain Date may be used to define attributes “Invoice-date”
and “Payment-date”.
The relation is formed over the
cartesian product of the sets; each set has values from a domain; that domain
is used in a specific role which is conveyed by the attribute name.
For example, attribute Cust-name
is defined over the domain of strings of 25 characters. The role these strings
play in the CUSTOMER relation is that of the name of customers.
Formally,
Given R(A1, A2, .........., An)
r(R) Ì dom (A1) X dom (A2) X
....X dom(An)
R: schema of the relation
r of R: a specific
"value" or population of R.
R is also called the intension of a relation
r is also called the extension
Let S1 = {0,1}
Let S2 = {a,b,c}
Let R Ì S1 X S2
Then for example: r(R) =
{<0,a> , <0,b> , <1,c> }
is one possible “state” or
“population” or “extension” r of
the relatio R, defined over domains S1 and S2. It has three
tuples.
Example
Database Management System × The Relational Data Model and Relational Database
RELATION:
A Relation is table of values. A
relation may be thought of as a set of rows. A relation may alternately be
though of as a set of columns. Each row represents a fact that corresponds to a
real-world entity or relationship. Each row has a value of an item or set of
items that uniquely identifies that row in the table. Sometimes row-ids or sequential
numbers are assigned to identify the rows in the table. Each column typically
is called by its column name or column header or attribute name.
Database Management System × The Relational Data Model and Relational Database
The relational Model of Data is
based on the concept of a Relation. A Relation is a mathematical concept based
on the ideas of sets. The strength of the relational approach to data
management comes from the formal foundation provided by the theory of
relations. The model was first proposed by Dr. E.F. Codd of IBM in 1970 in the
following paper: "A Relational Model for Large Shared Data Banks," Communications
of the ACM, June 1970.
