Download The Relational Model

The Relational
Model
By
Elena Ciriani
CS157A
February 19, 2004
Professor Lee
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INTRODUCTION
The relational model is the most used data model for
commercial data-processing because it is simple to
use and to maintain.
A relational data model is based on a collection of
tables. The user of the database system may query
these tables, insert new tuples, and update (modify)
tuples. There are several languages for expressing
these operations.
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TOPICS
• Structure of Relational database
– A row in a table represents a relationship
among a set of values where the columns are
the representation of the attributions
• The Relational Algebra
– It defines a set of algebraic operations that
operate on tables, and output tables as their
results. These operations can be combined to
get expressions that express desired queries.
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Structure of Relational Database
(Section 3.1)
•
•
•
•
•
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
Basic Structure
Database Schema
Keys
Schema Diagram
Query Languages
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Basic Structure
The account table below represents a relation in the
relational model. The three columns titles are the
attributes and their domains.
Each row is called a tuple.
An account is a subset of the set of all possible tuples.
account-number
branch-name balance
A-101
Downtown
500
A-102
Perryridge
400
A-201
Brighton
900
A-215
Mianus
700
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Database Schema
• Database Schema is the logical design of
the database
• Database instance is a snapshot of the data
in the DB at a given instance in time
• Relation instance is the programming
language notion of a value of a variable
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Database Schema
Relation schema consists of a list of
attributes and their corresponding domain.
As a convention, uppercase letter are used so
Account-schema=(account-number, branchname, balance) This means that account is a
relation on Account-schema by
account(Account-schema)
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Database Schema
Relation instance is the set of values of a
relation at a specific moment in time. This
values may change in time causing a change in
the relation as it is updated.
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Keys
• Superkey is a set of one or more attributes that
allow us to identify uniquely an entity in the entity
set.
• Candidate Key are minimal superkey in an entity,
one of those keys is selected to be the primary key
• Primary Key is a candidate key that is chosen to
identify entities within an entity set
• Foreign Key is a primary key of another relation
schema
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Keys
If K of R is a superkey for R, then the
relation r(R) does not have two tuples
with the same value. So if t1 and t2 are in r
t1 = t2
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How to determine keys
• Strong entity set: the entity primary key
becomes the relation primary key
• Weak entity set: the primary key of the
relation is the union of the strong entity set
primary key and the discriminator
• Relation set: the union of the primary keys
of the related entity sets becomes a
superkey of the relation
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How to determine keys
• Combined tables: in a many-to-one, the
primary key of the many becomes the
relation primary key. In a one-to-one either
primary key can be used
• Multivalued attributes: the entity primary
key becomes the primary key
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Schema Diagram
A database schema with primary and foreign key
dependencies
relation
primary
account
account-number
branch-name
balance
branch
shade indicates primary key
depositor
customer
customer-name
account-number
customer-name
dependency
loan
branch-name
loan-number
branch-city
assets
branch-name
amount
customer-street
customer-city
borrower
customer-name
loan-number
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Query Languages
Users use query languages to request information
from the database SQL is the most spread.
Database uses two types of query languages:
Procedural language: the user instructs the
system to perform a sequence of operations on the
database
Nonprocedural language: the user describes the
desired information without giving a specific
procedure for obtain the information
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The Relational Algebra
Topics(section 3.2)
• 3.2.1 Fundamental Operations
–
–
–
–
–
–
–
3.2.1.1
3.2.1.2
3.2.1.3
3.2.1.4
3.2.1.5
3.2.1.6
3.2.1.7
The Select Operation
The Project Operation
Composition of Relational Operations
The Union Operation
The Set Difference Operation
The Cartesian-Product Operation
The Rename Operation
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Relational Algebra
The relational algebra is a pure procedural query
language. It consists of a set of operations that
take one or two relations as input in an expression
and produced a new relation as their result.
A constant relation is written inside {}
A general expression is construct in
subexpressions
If they works on one relation are called unary
operation otherwise are said to be binary
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Unary Operations
• Select operation: choose the tuples that satisfy a
given predicament.
–σ branch-name = “Perryridge”(loan)
• Project operation: allows the user to select
particular attributes of a relationship
– Πloan-number, amount (loan)
• Rename operation: give a name to the results of
relational algebra expressions
– ρbig-loans(σamount > 1200 (loan))
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Binary Operation
• Union operation: allows the user to unify two
different relations and display the result
– Πcustomer-name (borrower) U Πcustomer-name (depositor)
• Difference operation: finds the tuples that are
in one relation but not in another
– Πcustomer-name (borrower) - Πcustomer-name (depositor)
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Binary Operation
• Cartesian-product: combines information from
any two relations
– σ branch-name = “Perryridge”(borrower x loan)
• Composition of operation: means that to find
information we can associate more operation into
an expression
– Πcustomer-name (σ customer-city = “Harrison”(customer))
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The Relational Algebra(continued)
(Section 3.2.3)
• 3.2.3 Additional Operations
The following operations make a relational
algebra query easier when the basic
expression may become lengthy
–
–
–
–
3.2.3.1
3.2.3.2
3.2.3.3
3.2.3.4
The Set-Intersection Operation
The Natural-Join Operation
The Division Operation
The Assignment Operation
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Additional Operation
• Set-Intersection Operation: find all the attributes
that appear in both relations
– Πcustomer-name (borrower) ∩ Π customer-name (depositor)
– Πcustomer-name (borrower) – (Πcustomer-name (borrower) –
Πcustomer-name (depositor))
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Additional Operation
• Natural-Join Operation: forms a Cartesian
product of its two arguments, performs a selection
forcing equality on those attributes that appears in
both relations and removes any duplicates
– Πcustomer-name, loan-number, amount (borrower
– Πcustomer-name, loan-number, amount
loan)
(borrower.loan-number = loan.loan-number (borrower x loan))
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Additional Operation
• Division operation: is suited to queries that
include the phrase “for all”
– Πcustomer-name, branch-name (depositor account)
Πbranch-name (σ branch-city = “Brooklyn”(branch))
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Additional Operation
• Assignment operation: write part of a
relational expression to a temporary relation
variable. This variable is used later in
expression of a query
– temp1 ← Πcustomer-name (borrower)
– temp2 ← Πcustomer-name (depositor)
– Result = temp1 – (temp1 – temp2)
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