1. Advanced Relational Algebra & SQL (Part1 )
Chapter 1
Advanced Relational Algebra & SQL (Part1 )
Department of Computer Science, Umm Al-Qura University University year: 1435/1436
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2. Outline Relational Algebra Relational Calculus
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
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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 relations
This property makes the algebra “closed” (all objects in relational algebra are relations)
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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)
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5. Operators Basic operations: Additional 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.
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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
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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)
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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.
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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
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10. Examples of applying SELECT and PROJECT operations
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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.
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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
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13. Example of applying the JOIN operation
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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.
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15. Natural Join Example
For an example, consider the tables Employee and Dept and their natural join:
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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
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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:
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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:
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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:
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20. Outer join Operator Left outer join
R <R.primary_key = S.foreign_key> S
All rows from R are retained and unmatched rows of S are padded with NULL
Right outer join
R <R.primary_key = S.foreign_key> S
All rows from S are retained and unmatched rows of R are padded with NULL
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21. Right Outerjoin Example
For an example consider the tables Students and Courses and their right outer join:
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22. Left Outer join Example
For an example consider the tables Students and Courses and their left outer join:
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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
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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
R ᴜ S R S A B a1 b1 a2 b2 a3 b3 A B a1 b1 a2 b2 A B a2 b2 a3 b3
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25. Intersection Takes the set of rows that are common to each relation
Participating relations must be compatible S R
R ∩ S A B a1 b1 a2 b2 A B a2 b2 a3 b3 A B a2 b2
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26. Difference
Takes the set of rows in the first relation but not the second
Participating relations must be compatible R S
R - S A B a1 b1 a2 b2 A B a2 b2 a3 b3 A B a1 b1
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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}.
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28. The relational algebra on multi-sets: examples
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