My slide relational algebra

Rushdi Shams, Dept of CSE, KUET 1

Database Database SystemsSystems

Relational AlgebraRelational Algebra

Version 1.0Version 1.0

2Rushdi Shams, Dept of CSE, KUET

What is Relational What is Relational AlgebraAlgebra

It is a collection of operations on It is a collection of operations on relationsrelations

If you apply relational algebra on If you apply relational algebra on some relations, the result will be some relations, the result will be another relationanother relation

You can say a relation- a table.You can say a relation- a table. So, operation on tables=another tableSo, operation on tables=another table

That is what relational algebra does!That is what relational algebra does!


Memory RefreshmentMemory Refreshment A relation is a set of attributes with values for A relation is a set of attributes with values for

each attribute such that: each attribute such that: Each attribute value must be a single value Each attribute value must be a single value

only (atomic). only (atomic). All values for a given attribute must be of the All values for a given attribute must be of the

same type (or domain). same type (or domain). Each attribute name must be unique. Each attribute name must be unique. The order of attributes is insignificant The order of attributes is insignificant No two rows (tuples) in a relation can be No two rows (tuples) in a relation can be

identical. identical. The order of the rows (tuples) is insignificant. The order of the rows (tuples) is insignificant.


2 types of operation2 types of operation

1.1. Set theory operations:Set theory operations:Union, Intersection, Difference and Union, Intersection, Difference and Cartesian product. Cartesian product.

2.2. Specific Relational Operations:Specific Relational Operations:Selection, Projection, Join, Division Selection, Projection, Join, Division

We will take a look into set theory We will take a look into set theory operations, and then we will dig operations, and then we will dig into specific relational operationsinto specific relational operations


Our example tablesOur example tables

There are 2 tables- There are 2 tables- R and S, we will R and S, we will play with them!! play with them!!


UnionUnion

RUS means, a union RUS means, a union operation on R and operation on R and S that will produce S that will produce another table which another table which will have all the will have all the rows of R and S rows of R and S except the except the duplicatesduplicates

There are 2 Sally in There are 2 Sally in R and S, so, just R and S, so, just take 1 from themtake 1 from them


DifferenceDifference

R-S means, a R-S means, a difference operation difference operation on R and S that will on R and S that will produce another produce another table which will table which will have all the rows have all the rows which is in R but which is in R but not in S.not in S.

As Sally is in R and As Sally is in R and in S, so, she has in S, so, she has been omitted.been omitted.


IntersectionIntersection

R∩S means, an R∩S means, an intersection intersection operation on R and operation on R and S that will produce S that will produce another table which another table which will have all the will have all the rows which are in rows which are in both R and S.both R and S.

As Sally is in R and As Sally is in R and in S, so, she has in S, so, she has been selected.been selected.


More UnionMore Union


More IntersectionMore Intersection


More DifferenceMore Difference


ConstraintsConstraints You see tables, and start performing set You see tables, and start performing set

theory operations on them- MISTAKE!! theory operations on them- MISTAKE!! You should remember the following You should remember the following constraints before you perform set theory constraints before you perform set theory operations on tables.operations on tables.

1.1. Attributes of relations need Attributes of relations need notnot be be identical to perform union, intersection identical to perform union, intersection and difference operations. and difference operations.

2.2. However, they However, they must havemust have the same the same number of attributes and the domains for number of attributes and the domains for corresponding attributes must be corresponding attributes must be identical. identical.


Other things to Other things to rememberremember

Union, Intersection and difference Union, Intersection and difference operators may only be applied to operators may only be applied to Union Compatible relations. Union Compatible relations.

Union and Intersection are Union and Intersection are commutative operationscommutative operationsRUS= SURRUS= SURR∩S = S∩R R∩S = S∩R

Difference operation is Difference operation is NOTNOT commutative.commutative.R - S not equal S - R R - S not equal S - R


Class PerformanceClass Performance

Find out RUTFind out RUT Find out R∩TFind out R∩T Find out R-TFind out R-T Find out T-RFind out T-R


Cartesian ProductCartesian Product It provides all the combinations of rows from two tables.It provides all the combinations of rows from two tables. If A and B are 2 tables and A has 3 rows and B has 4 rows, If A and B are 2 tables and A has 3 rows and B has 4 rows,

then Athen A×B is-×B is-A1-B1A1-B1A1-B2A1-B2A1-B3A1-B3A1-B4A1-B4A2-B1A2-B1A2-B2A2-B2A2-B3A2-B3A2-B4A2-B4A3-B1A3-B1A3-B2A3-B2A3-B3A3-B3A3-B4A3-B4


Cartesian Product Cartesian Product (continued)(continued)


More ProductMore Product


SelectionSelection

Selection and Projection are Selection and Projection are unaryunary operators. operators.

The selection operator is The selection operator is sigma (sigma (σσ)) The selection operation acts like a The selection operation acts like a

filter on a relation by filter on a relation by returning only returning only a certain number of rows. a certain number of rows.

The The resulting relation will have the resulting relation will have the same number of attributessame number of attributes as the as the original relation. original relation.


Selection (continued)Selection (continued) The resulting relation The resulting relation maymay have fewer have fewer

rows than the original relation. rows than the original relation. The rows to be returned are dependent The rows to be returned are dependent

on a condition that is part of the selection on a condition that is part of the selection operator. operator.

σσC C (R) Returns only those rows in R that (R) Returns only those rows in R that satisfy condition satisfy condition CC

A condition C can be made up of any A condition C can be made up of any combination of comparison or logical combination of comparison or logical operators that operate on the attributes operators that operate on the attributes of R.of R.


Selection ExampleSelection Example

We have a table named EMP.We have a table named EMP. We will play with this table named EMP We will play with this table named EMP

for a while!for a while!


Selection Example Selection Example (continued)(continued)

Select only those Employees in the CS Select only those Employees in the CS department department

σσ Dept = ‘CS’Dept = ‘CS’ (EMP) (EMP)



Select only those Employees with last Select only those Employees with last name Smith who are assistant professorsname Smith who are assistant professors

σσ Name = ‘Smith’ Name = ‘Smith’ ΛΛ Rank = ‘Assistant’ Rank = ‘Assistant’ (EMP) (EMP)



Select only those Employees who are Select only those Employees who are either Assistant Professors or in the either Assistant Professors or in the Economics department Economics department

σσ Dept = ‘Econ’ V Rank = ‘Assistant’Dept = ‘Econ’ V Rank = ‘Assistant’ (EMP) (EMP)



Select only those Employees who are not Select only those Employees who are not in the CS department or Adjuncts in the CS department or Adjuncts

σσ ¬¬(Dept = ‘CS’ V Rank = ‘Adjunct’)(Dept = ‘CS’ V Rank = ‘Adjunct’) (EMP) (EMP)


More SelectionMore Selection



σσ(Rank = 'Adjunct' (Rank = 'Adjunct' ΛΛ Dept = 'CS') Dept = 'CS') (EMP) (EMP)

σσ Rank = 'Associate'Rank = 'Associate' ΛΛ Dept = 'CS' Dept = 'CS' EMP ) EMP )

σσ Dept = 'CS'Dept = 'CS' VV Rank = 'Associate'Rank = 'Associate' EMP ) EMP )

σσ Age > 26Age > 26 (R U S) (R U S)


ProjectionProjection Projection is also a Projection is also a UnaryUnary operator. operator. The Projection operator is The Projection operator is pi (pi (ππ)) Projection limits the columns that will be returned Projection limits the columns that will be returned

from the original relation. from the original relation. The general syntax is: The general syntax is: ππ attributesattributes R R

Where attributes is the list of attributes to be Where attributes is the list of attributes to be displayed and R is the relation. displayed and R is the relation.

The resulting table will have the same number of The resulting table will have the same number of rows as the original relation (unless there are rows as the original relation (unless there are duplicate rows produced). duplicate rows produced).

The number of columns of the resulting relation The number of columns of the resulting relation may be equal to or less than that of the original may be equal to or less than that of the original relation. relation.


Projection ExampleProjection Example

Project only the names and departments Project only the names and departments of the employees of the employees

ππ name, deptname, dept (EMP) (EMP)


Combining selection & Combining selection & projectionprojection

Show the names of all employees working Show the names of all employees working in the CS department in the CS department

ππ name name ( (σσ Dept = 'CS'Dept = 'CS' (EMP) ) (EMP) )


Combining selection & Combining selection & projection (continued)projection (continued)

Show the name and rank of those Employees Show the name and rank of those Employees who are not in the CS department or who are not in the CS department or Adjuncts Adjuncts

ππ name, rankname, rank ( ( σσ ¬¬(Rank = 'Adjunct' V Dept = 'CS')(Rank = 'Adjunct' V Dept = 'CS') (EMP) ) (EMP) )


More ProjectionMore Projection



ππ name, rankname, rank ( ( σσ ¬¬(Rank = 'Adjunct' (Rank = 'Adjunct' ΛΛ Dept = 'CS') Dept = 'CS') (EMP) ) (EMP) )

ππ fname, agefname, age ( (σσ Age > 22Age > 22 (R U S) ) (R U S) )

σσ office > 300office > 300 ( ( ππ name, rankname, rank (EMP)) (EMP))


Aggregate FunctionsAggregate Functions

We can also apply Aggregate functions to We can also apply Aggregate functions to columns and rowscolumns and rows

1.1. SUM SUM

2.2. MINIMUM MINIMUM

3.3. MAXIMUM MAXIMUM

4.4. AVERAGE, MEAN, MEDIAN AVERAGE, MEAN, MEDIAN

5.5. COUNT COUNT Aggregate functions are sometimes written Aggregate functions are sometimes written

using the Projection operator or the using the Projection operator or the Tau Tau character (character (ττ))


Aggregate Functions Aggregate Functions (continued)(continued)

Find the minimum SalaryFind the minimum Salary

ττ MIN (salary)MIN (salary) (EMP) (EMP) Find the average SalaryFind the average Salary

ττ AVG (salaryAVG (salary) (EMP) ) (EMP) Count the number of employees in the CS departmentCount the number of employees in the CS department

ττ COUNT (name)COUNT (name) ( ( σσ Dept = 'CS'Dept = 'CS' (EMP) ) (EMP) ) Find the total payroll for the Economics departmentFind the total payroll for the Economics department

ττ SUM (salary)SUM (salary) ( (σσ Dept = 'Econ'Dept = 'Econ' (EMP) ) (EMP) )


JoinJoin Join operations bring together two tables and Join operations bring together two tables and

combine their rows and columns in a specific combine their rows and columns in a specific fashion. fashion.

The generic join operator called the The generic join operator called the Theta JoinTheta Join is is It takes as arguments the columns from the two It takes as arguments the columns from the two

tables that are to be joined. tables that are to be joined. The join condition can be The join condition can be When the join condition operator is When the join condition operator is = = then we then we

call this an Equijoincall this an Equijoin Note that the columns in common are repeated. Note that the columns in common are repeated.


Join (continued)Join (continued)

Now, we have two tables Emp and depart.Now, we have two tables Emp and depart. We will play with these 2 tables for a We will play with these 2 tables for a

while!while!



Find all information on every employee Find all information on every employee including their department infoincluding their department info

EMP EMP emp.Dept = depart.Deptemp.Dept = depart.Dept DEPART DEPART



Take a look, one table has 5 rows, the Take a look, one table has 5 rows, the other has 4 rows, the resultant has 5 other has 4 rows, the resultant has 5 rows!rows!



Find all information on every employee including Find all information on every employee including department info where the employee works in an department info where the employee works in an office numbered less than the department main officeoffice numbered less than the department main office

EMP EMP (emp.office < depart.mainoffice) (emp.office < depart.mainoffice) ΛΛ (emp.dept = depart.dept) (emp.dept = depart.dept) DEPART DEPART


Natural JoinNatural Join

Notice in the generic (Theta) join Notice in the generic (Theta) join operation, any attributes in common operation, any attributes in common (such as dept above) are repeated. (such as dept above) are repeated.

The Natural Join operation removes The Natural Join operation removes these duplicate attributes. these duplicate attributes.

The natural join operator is: The natural join operator is: ** We can also assume using We can also assume using ** that the that the

join condition will be join condition will be == on the two on the two attributes in common. attributes in common.


Natural Join (continued)Natural Join (continued)

Emp * departEmp * depart There are 2 Dept columns, one is omitted!There are 2 Dept columns, one is omitted!


Outer JoinOuter Join In the Join operations so far, only those tuples In the Join operations so far, only those tuples

from both relations that satisfy the join from both relations that satisfy the join condition are included in the output relation. condition are included in the output relation.

The Outer join includes other rows as well The Outer join includes other rows as well according to a few rules. according to a few rules.

Three types of outer joins: Three types of outer joins: 1.1. Left Outer Join includes all rows in the left Left Outer Join includes all rows in the left

hand relation and includes only those matching hand relation and includes only those matching rows from the right hand relation. rows from the right hand relation.

2.2. Right Outer Join includes all rows in the right Right Outer Join includes all rows in the right hand relation and includes only those matching hand relation and includes only those matching rows from the left hand relation. rows from the left hand relation.

3.3. Full Outer Join includes all rows in the left Full Outer Join includes all rows in the left hand relation and from the right hand relation. hand relation and from the right hand relation.


Outer Join (continued)Outer Join (continued)

Now we have another 2 tables.Now we have another 2 tables. We will play with them for next few slides!We will play with them for next few slides!


Left Outer JoinLeft Outer Join

PEOPLE PEOPLE people.food = menu.foodpeople.food = menu.food MENU MENU


Right Outer JoinRight Outer Join



Full Outer JoinFull Outer Join



Outer UnionOuter Union

In this case, just go from row of table 1 to row of table 2.In this case, just go from row of table 1 to row of table 2. Take common columns just once.Take common columns just once. if matching criteria don’t match, then put NULL, else if matching criteria don’t match, then put NULL, else

include in the tableinclude in the table Repeat the same but this time go from row of table 2 to Repeat the same but this time go from row of table 2 to

row of table 1row of table 1


ReferencesReferences

Database Management Systems Database Management Systems by Prof. Holowczak, Zicklin by Prof. Holowczak, Zicklin School of Business, Baruch School of Business, Baruch College, City University of New College, City University of New YorkYork

Database Systems: Design, Database Systems: Design, Implementation & Management Implementation & Management by Rob & Coronel, 6by Rob & Coronel, 6thth Edition Edition

My slide relational algebra

Technology

Transcript of My slide relational algebra