Advanced Relational Algebra & SQL (Part1 ) 1 Advanced Database System.

Advanced Database System

1

Chapter 1

Advanced Relational Algebra & SQL (Part1 )

Department of Computer Science, Umm Al-Qura University University year: 1435/1436

2

Outline

Relational Algebra Unary Relational Operations Relational Algebra Operations From Set Theory Binary Relational Operations Additional Relational Operations Examples of Queries in Relational Algebra

Relational Calculus Tuple Relational Calculus Domain Relational Calculus



3

Relational Algebra Overview

Relational algebra is the basic set of operations for the relational model

These operations enable a user to specify basic retrieval requests (or queries)

The result of an operation is a new relation, which may have been formed from one or more input relationsThis property makes the algebra “closed” (all objects in relational algebra are relations)


4

Relational Algebra Overview (continued)

The algebra operations thus produce new relations These can be further manipulated using

operations of the same algebra A sequence of relational algebra

operations forms a relational algebra expression The result of a relational algebra expression

is also a relation that represents the result of a database query (or retrieval request)


5

Operators

Basic operations: Selection ( (sigma)) Selects a subset of rows from relation. Projection ( (pi)) Deletes unwanted columns from relation. Cross-product ( (Cartesian product)) Allows us to combine

two relations. Set-difference ( (minus)) Tuples in relation.1, but not in

relation.2 Union ( ) Tuples in relation.1 and in relation. 2.

Additional operations: Intersection ( ) Join ( ) division, renaming

Since each operation returns a relation, operations can be composed.


6

Unary Relational Operations: SELECT

In general, the select operation is

denoted by <selection condition>(R) where the symbol (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


7

Unary Relational Operations: SELECT

The SELECT operation (denoted by ) is used to select a subset of the tuples from a relation based on a selection condition.

Examples: Select the EMPLOYEE tuples whose department

number is 4: DNO = 4 (EMPLOYEE)

Select the employee tuples whose salary is greater than $30,000:

SALARY > 30,000 (EMPLOYEE)


8

Unary Relational Operations: PROJECT

The general form of the project operation is:

<attribute list>(R) (pi) is the symbol used to represent the

project operation <attribute list> is the desired list of

attributes from relation R. The project operation removes any

duplicate tuples This is because the result of the project

operation must be a set of tuples Mathematical sets do not allow duplicate

elements.


9

Unary Relational Operations: PROJECT (cont)

PROJECT Operation is denoted by (pi) This operation keeps certain columns

(attributes) from a relation and discards the other columns. PROJECT creates a vertical partitioning

The list of specified columns (attributes) is kept in each tuple

The other attributes in each tuple are discarded Example: To list each employee’s first and

last name and salary, the following is used:LNAME, FNAME,SALARY(EMPLOYEE


10

Examples of applying SELECT and PROJECT operations


11

Binary Relational Operations: JOIN

JOIN Operation (denoted by ) The sequence of CARTESIAN PRODECT followed by

SELECT is used quite commonly to identify and select related tuples from two relations

A special operation, called JOIN combines this sequence into a single operation

This operation is very important for any relational database with more than a single relation, because it allows us combine related tuples from various relations

The general form of a join operation on two relations R(A1, A2, . . ., An) and S(B1, B2, . . ., Bm) is:

R <join condition>S where R and S can be any relations that result from

general relational algebra expressions.


12

Binary Relational Operations: JOIN (cont.)

Example: Suppose that we want to retrieve the name of the manager of each department. To get the manager’s name, we need to combine

each DEPARTMENT tuple with the EMPLOYEE tuple whose SSN value matches the MGRSSN value in the department tuple.

We do this by using the join operation.

DEPT_MGR DEPARTMENT MGRSSN=SSN EMPLOYEE MGRSSN=SSN is the join condition

Combines each department record with the employee who manages the department

The join condition can also be specified as DEPARTMENT.MGRSSN= EMPLOYEE.SSN


13

Example of applying the JOIN operation


14

Natural Join Operator

Natural join is a dyadic operator that is written as R S where R and S are relations.

The result of the natural join is the set of all combinations of tuples in R and S that are equal on their common attribute names.


15

Natural Join Example

For an example, consider the tables Employee and Dept and their natural join:

16

Renaming

In relational algebra, a rename is a unary operation written as ρ a / b (R) where: a and b are attribute names R is a relation

Examples:1) ρemployee(Emp): Changes the name of Emp table to

employee.2) Renaming and Union



17

Cartesian Product

In mathematics, it is a set of all pairs of elements (x, y) such that x belongs to X and y to Y.

It defines a relation that is the concatenation of every tuple of relation R with every tuple of relation S.

Example:


18

Theta (θ) join

Theta joins combines tuples from different relations provided they satisfy the theta condition.

A Cartesian product with a condition applied: R1 ⋈θ R2 Example:


19

Semi join Operator

The semi join is joining similar to the natural join and written as R S where R and S are relations.

The result of the semi join is only the set of all tuples in R for which there is a tuple in S that is equal on their common attribute names.

Example: consider the tables Employee and Dept and their semi join:


20

Outer join Operator

Left outer joinR <R.primary_key = S.foreign_key> S

All rows from R are retained and unmatched rows of S are padded with NULL

Right outer joinR <R.primary_key = S.foreign_key> S All rows from S are retained and unmatched rows of R are padded with NULL


21

Right Outerjoin Example

For an example consider the tables Students and Courses and their right outer join:


22

Left Outer join Example

For an example consider the tables Students and Courses and their left outer join:


23

Union

Takes the set of rows in each table and combines them, eliminating duplicates

Participating relations must be compatible, ie have the same number of columns, and the same column names, domains, and data types


24

Set Operations-Union

Takes the set of rows in each table and combines them, eliminating duplicates

Participating relations must be compatible, ie have the same number of columns, and the same column names, domains, and data types

A B

a1 b1

a2 b2

A B

a2 b2

a3 b3

A B

a1 b1

a2 b2

a3 b3

R SR ᴜ S


25

Intersection

Takes the set of rows that are common to each relation

Participating relations must be compatible

A B

a1 b1

a2 b2

R

A B

a2 b2

a3 b3

S

A B

a2 b2

R ∩ S


26

Difference

Takes the set of rows in the first relation but not the second

Participating relations must be compatible

A B

a1 b1

a2 b2

R

A B

a2 b2

a3 b3

S

A B

a1 b1

R - S


27

Set vs Bag semantic

A bag (or multiset ) is like a set, but an element may appear more than once.

Example1: {1,2,1,3} is a bag. Example2: {1,2,3} is also a bag that happens to

be a set. The multi-set {1, 2, 1, 3} is different to multi-set

{1, 2, 3}.


28

The relational algebra on multi-sets: examples

Advanced Relational Algebra & SQL (Part1 ) 1 Advanced Database System.

Documents

Transcript of Advanced Relational Algebra & SQL (Part1 ) 1 Advanced Database System.