RSS
Twitter
Facebook
Showing posts with label Database Management System. 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.
Database Management System × Entity-Relationship Model
Relations can be represented as
two-dimensional data tables with rows and columns
The rows of a relation are called
tuples.
The columns of a relation are
called attributes.
The attributes draw values from a
domain (a legal pool of values).
The number of tuples in a
relation is called its cardinality while the number of attributes in a relation
is called its degree
A relation also consists of a
schema and an instance
Schema defines the structure of a
relation which consists of a fixed set of attributedomain pairs.
An instance of a relation is a
time-varying set of tuples where each tuple consists of attribute-value pairs.
Database Management System × Entity-Relationship Model
Data Integrity falls into the
following categories
Entity integrity
Entity integrity ensures that
each row can be uniquely identified by an attribute called the Primary key. The
Primary key cannot have a NULL value.
Domain integrity
Domain integrity refers to the
range of valid entries for a given column. It ensures that there are only valid
entries in the column.
Referential
integrity
Referential integrity ensures
that for every value of a Foreign key, there is a matching value of the Primary
key.
Database Management System × Entity-Relationship Model
Before beginning to draw the ER
model, read the requirements specification carefully. Document any assumptions
you need to make.
1. Identify entities - list all
potential entity types. These are the object of interest in
the system. It is better to put
too many entities in at this stage and them discard
them later if necessary.
2. Remove duplicate entities -
Ensure that they really separate entity types or just two names for the same
thing.
o Also do not include the system
as an entity type
o e.g. if modelling a library,
the entity types might be books, borrowers, etc.
o The library is the system, thus
should not be an entity type.
3. List the attributes of each
entity (all properties to describe the entity which are relevant to the
application).
o Ensure that the entity types
are really needed.
o are any of them just attributes
of another entity type?
o if so keep them as attributes
and cross them off the entity list.
o Do not have attributes of one
entity as attributes of another entity!
4. Mark the primary keys.
o Which attributes uniquely
identify instances of that entity type?
o This may not be possible for
some weak entities.
5. Define the relationships
o Examine each entity type to see
its relationship to the others.
6. Describe the cardinality and
optionality of the relationships
o Examine the constraints between
participating entities.
7. Remove redundant relationships
o Examine the ER model for
redundant relationships.
ER modelling is an iterative
process, so draw several versions, refining each one
until you are happy with it. Note
that there is no one right answer to the problem, but some solutions are better
than others!
Overview
• construct an ER model
• understand the problems
associated with ER models
• understand the modelling concepts of Enhanced ER
modelling
Database Management System × Entity-Relationship Model
Bus
(reg-no,make,size,deck,no-pass)
Route (route-no,avg-pass)
Driver
(emp-no,name,address,tel-no)
Town (name)
Stage (stage-no)
Garage (name,address)
Example: Entity and Relationship
sets for the hospital called General Hospital,
Patients,
Doctors, Beds, Examines, Bed
Assigned, Accounts, has Account.
patients, entity set with
attributes SSNo, LastName, FirstName, HomePhone, Sex,
DateofBirth, Age, Street, City,
State, Zip.
doctors, entity set with
attributes SSNo, LastName, FirstName, OfficePhone, Pager,
Specialty.
examines, relational set with
attributes Date, Time, Diagnosis, Fee.
beds, entity set with attributes
RoomNumber, BedNumber, Type, Status,
PricePerHour.
Bed_assigned, relational set with
attributes DateIn, TimeIn, DateOut, TimeOut,
Amount.
accounts, weak entity set with
attributes DateIn, DateOut, Amount.
has_account, relational set with no Attributes
Database Management System × Entity-Relationship Model
Bus - Company owns busses and
will hold information about them.
Route - Buses travel on routes
and will need described.
Town - Buses pass through towns
and need to know about them
Driver - Company employs drivers, personnel will hold
their data.
Stage - Routes are made up of
stages
Garage - Garage houses buses, and
need to know where they are.
A bus is allocated to a route and
a route may have several buses.
Bus-route (m:1) is serviced by
A route comprises of one or more
stages.
route-stage (1:m) comprises
One or more drivers are allocated
to each stage.
driver-stage (m:1) is allocated .
A stage passes through some or
all of the towns on a route.
stage-town (m:n) passes-through
A route passes through some or
all of the towns
route-town (m:n) passes-through
Some of the towns have a garage
garage-town (1:1) is situated
A garage keeps buses and each bus
has one `home' garage
garage-bus (m:1) is garaged
Database Management System × Entity-Relationship Model
A relationship can be optional or
mandatory.
If the relationship is mandatory
an entity at one end of the relationship
must be related to an entity at the other end.
The optionality can be different
at each end of the relationship
For example, a student must be on
a course. This is mandatory. To the relationship
`student studies course' is
mandatory.
But a course can exist before any
students have enrolled. Thus the relationship
`course is_studied_by student' is
optional.
To show optionality, put a circle
or `0' at the `optional end' of the relationship.
As the optional relationship is
`course is_studied_by student', and the optional part of this is the student,
then the `O' goes at the student end of the relationship connection.
It is important to know the
optionality because you must ensure that whenever you
create a new entity it has the
required mandatory links.
