1

The Relational ModelBy

Elena CirianiCS157A

February 19, 2004

Professor Lee

2

INTRODUCTIONThe 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.

3

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.

4

Structure of Relational Database (Section 3.1)

• 3.1.1 Basic Structure

• 3.1.2 Database Schema

• 3.1.3 Keys

• 3.1.4 Schema Diagram

• 3.1.5 Query Languages

5

Basic Structure

account-number branch-name balance

A-101 Downtown 500

A-102 Perryridge 400

A-201 Brighton 900

A-215 Mianus 700

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.

6

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

7

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, branch-name, balance) This means that account is a relation on Account-schema by account(Account-schema)

8

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.

9

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

10

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

11

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

12

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

13

account-number

branch-name

balance

Schema Diagram

branch-name

branch-cityassets

customer-nameloan-number

customer-name

customer-streetcustomer-city

customer-nameaccount-number

loan-number

branch-nameamount

account depositor customer

branch loanborrowerdependency

relation shade indicates primary key

A database schema with primary and foreign key dependencies

primary

14

Query LanguagesUsers 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

15

The Relational AlgebraTopics(section 3.2)

• 3.2.1 Fundamental Operations– 3.2.1.1 The Select Operation– 3.2.1.2 The Project Operation– 3.2.1.3 Composition of Relational Operations– 3.2.1.4 The Union Operation– 3.2.1.5 The Set Difference Operation– 3.2.1.6 The Cartesian-Product Operation– 3.2.1.7 The Rename Operation

16

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

17

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))

18

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)

19

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))

20

The Relational Algebra(continued)

(Section 3.2.3)

• 3.2.3 Additional OperationsThe following operations make a relational algebra query easier when the basic expression may become lengthy

– 3.2.3.1 The Set-Intersection Operation– 3.2.3.2 The Natural-Join Operation– 3.2.3.3 The Division Operation– 3.2.3.4 The Assignment Operation

21

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))

22

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 loan)– Πcustomer-name, loan-number, amount

(borrower.loan-number = loan.loan-number (borrower x loan))

23

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))

24

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)