Database relational algebra basics notes, it includes basic operators and their examples.

1. Relational
Algebra
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2. prepared by Visakh V,Assistant Professor,
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3. prepared by Visakh V,Assistant Professor,
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4. •Two formal language for the relational model
(a)Relational Algebra
(b)Relational calculus
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5. • Basic set of operation for the relational model.
• These operation enable a user to specify basic
retrieval requests.
• The result of a retrieval is a new relation, which
can be further manipulated using operations of
same algebra.
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6. •it is important for several reasons:
 provides formal foundation
for relational model
 used as basis for
implementing and optimizing
queries in RDMS
 Some of its concepts are
incorporated into SQL Standard
query language for RDMS
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7. No commercial RDBMS in use today
provides an interface for the relational
queries.
•Relational algebra operations can be divided into
UNION
INTERSECTION
SET DIFFERENCE
CARTESIAN PRODUCT
SELECT
PROJECT
JOIN etc.
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8. prepared by Visakh V,Assistant Professor,
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9. s
p
:Operate on a single relation
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10. s
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11. Syntax :
s <selection condition> (R)
<selection condition> is made up of number of clauses of the form
<attribute name > <comparison op> <attribute name>
OR
<attribute name > <comparison op> <constant value>
{ =,<,>,<=,>=,!= }
It select certain rows
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12. prepared by Visakh V,Assistant Professor,
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13. Ex : s(DNO=5 ) (EMPLOYEE)
Ex : s(SALARY>25000) (EMPLOYEE)
Lets try. . .
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14. Clauses can be connected by the
Boolean operators and, or ,not to from a
general selection condition.
s(DNO=4 AND SALARY>25000) OR (DNO=5 AND SALARY>30000) (EMPLOYEE)
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15. SELECT operation is commutative :
s <cond1> ( s <cond2> (R)) = s <cond2> ( s <cond1> (R))
Cascade of SELECT operation:
s<cond1> ( s <cond2> (… ( s <condn> (R)). . . ))
=
( s <cond1> AND <cond2> AND . . . AND <condn> (R)
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16. p
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17. Syntax :
p <attribute list > (R)
It select certain columns
Duplicate elimination : it removes any duplicate
tuples , and we get a valid relation .
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18. prepared by Visakh V,Assistant Professor,
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19. •pSEX, SALARY(EMPLOYEE)
•pLname,Fname,SALARY(EMPLOYEE)
Where is the
resultant table ???
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20. Duplicate
elimination
pFNAME, LNAME, SALARY(sDNO=5(EMPLOYEE))
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21. prepared by Visakh V,Assistant Professor,
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22. We can write the operations as a single algebra
expression by nesting the operation
or
we can apply one operation at a time and create
intermediate result relations.
pFNAME, LNAME, SALARY(sDNO=5(EMPLOYEE))
Can replace with
DEPCS2  sDNO=5(EMPLOYEE)
RESULT  pFNAME, LNAME, SALARY (DEPCS2)
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23. Renaming of attribute
TEMP  sDNO=5(EMPLOYEE)
R(FIRSTNAME,LASTNAME,SALARY) pFNAME, LNAME, SALARY (TEMP)
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24. A formal RENAME r(rho) operations:
• rename either relation name, attribute name or both
r (B1,B2,…Bn) (R)
r s (R)
r s(B1,B2,…Bn) (R)
S: new table name;
Bn: new attribute name
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25. prepared by Visakh V,Assistant Professor,
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26. UNION
INTERSECTION
&
SET DIFFERENCE
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27. : R  S
: Include all tuples
:Duplicates are eliminated
: R  S
: include all tuples that are in both R & S
: R - S
: include all tuples that are in R but not in S
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28. Union compatible
(corresponding pair have same number
of attribute and same domain)
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29. prepared by Visakh V,Assistant Professor,
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30. prepared by Visakh V,Assistant Professor,
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31. Example:
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32. Q. Retrieve the social security Number of
all employees who either work in
department 5 or directly supervise an
employee who works department 5.
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33. prepared by Visakh V,Assistant Professor,
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34. •UNION and INTERSECTION are
commutative but SET
DIFFERENCE is not.
R  S =R  S – (R-S )-(S-R)
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35. • Also known as CROSS PRODUCT or CROSS JOIN
• Denoted by X
• syntax :
• tab1 X tab2
• also binary set operations.
• if A has m tuples and B has n tuples then A X B has m * n
tuples .
• Cartesian product followed by SELECT is used to identify
and select related tuples from two relation.
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36. prepared by Visakh V,Assistant Professor,
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37. EMP_ID DESIGNATION SALARY
101 PROFESSOR 1,25000
102 ASSOCIATE PROF 90000
103 ASSISTANT PROF 40000
E_ID F_NAME M_NA
ME
L_NAME AGE
102 SURESH KUMAR S 43
103 SUMI M MOL 23
101 SHREELEKSHMI R S 40
TAB1
FIND salary ,name AND designation OF EACH EMPLOYEE?????
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38. DESIGNATIO
N
SALARY EMP_I
D
E_ID F_NAME M_NAME L_NAM
E
AGE
PROFESSOR 1,25000 101 102 SURESH KUMAR S 43
PROFESSOR 1,25000 101 103 SUMI M MOL 23
PROFESSOR 1.25000 101 101 SHREELEKSHMI R S 40
ASSOCIATE
PROF
90000 102 102 SURESH KUMAR S 43
ASSOCIATE
PROF
90000 102 103 SUMI M MOL 23
ASSOCIATE
PROF
90000 102 101 SHREELEKSHMI R S 40
ASSISTANT
PROF
40000 103 102 SURESH KUMAR S 43
ASSISTANT
PROF
40000 103 103 SUMI M MOL 23
ASSISTANT
PROF
40000 103 101 SHREELEKSHMI R S 40prepared by Visakh V,Assistant Professor,
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39. DESIGNATI
ON
SALARY EMP_ID E_ID F_NAME M_NAME L_NAME AGE
PROFESSO
R
1.25000 101 101 SHREELEK
SHMI
R S 40
ASSOCIATE
PROF
90000 102 102 ANIL S GANESH 28
ASSISTANT
PROF
40000 103 103 SUMI M MOL 23
SALARY F_NAME M_NAME L_NAME DESIGNATION
1.25000 RAMESH R VINOD PROFESSOR
90000 ANIL S GANESH ASSOCIATE PROF
40000 SUNIL A NARAYAN ASSISTANT PROFprepared by Visakh V,Assistant Professor,
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40. Write relational algebra expression
Retrieve a list of names of each
employee’s dependents.
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41. prepared by Visakh V,Assistant Professor,
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42. • Combine related tuples from two relation into single
tuples.
• denoted by
• R <JOIN CONDITION> S .
• Consider example
RESULT EMPLOYEE X DEPENDENT
FINAL  sSSN= ESSN (RESULT)
The above can be replaced with
FINAL  EMPLOYEE SSN=ESSN DEPENDENT .prepared by Visakh V,Assistant Professor,
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43. Retrieve the name of manager of
each department
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44. prepared by Visakh V,Assistant Professor,
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45. • A general join condition is of the form
<condition>AND<condition>AND. . . AND <condition>
Each condition of the form
Ai Bi
ᶱ
Comparison operator {=,!=,<,>,<=,>=}
•A JOIN operation with such a
general join condition is
called a THETA JOIN
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46. prepared by Visakh V,Assistant Professor,
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47. • The JOIN where the only comparison operator
used is ‘ = ‘
• It requires that two JOIN attributes have the same
name in both relation .
• if this is not the case then renaming operation done
first.
• This is basically an EQUIJOIN followed by removal of
unnecessary attributes
•Ex: DEPT_LOCS  DEPARTMENT * DEPT_LOCATIONS.
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48. Join attribute
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49. •A JOIN operation used to combine
data from multiple relations so that
related information can be presented
in a single table. This operations are
also known as inner joins.
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50. • Used when we want to keep all the tuples in R
• three main variation are
• LEFT OUTER JOIN
• RIGHT OUTER JOIN
• FULL OUTER JOIN
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51. • Relation instructor1
• Relation teaches1
ID course_id
10101
12121
76766
CS-101
APL-101
BIO-101
Comp. Sci.
Applied
PED
ID dept_name
10101
12121
15151
name
Sreejith
Suresh
Sreeja
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52. • Join
instructor teaches
ID dept_name
10101
12121
Comp. Sci.
Applied
course_id
CS-101
APL-201
name
Sreejith
Suresh
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53.  Left Outer Join
instructor teaches
ID dept_name
10101
12121
15151
Comp. Sci.
Applied
PED
course_id
CS-101
APL-201
null
name
Sreejith
Suresh
Sreeja
ID course_id
10101
12121
76766
CS-101
APL-101
BIO-101
Comp. Sci.
Applied
PED
ID dept_name
10101
12121
15151
name
Sreejith
Suresh
Sreeja
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54.  Right Outer Join
instructor teaches
ID dept_name
10101
12121
76766
Comp. Sci.
Applied
null
course_id
CS-101
APL-201
BIO-101
name
Sreejith
Suresh
null
ID course_id
10101
12121
76766
CS-101
APL-101
BIO-101
Comp. Sci.
Applied
PED
ID dept_name
10101
12121
15151
name
Sreejith
Suresh
Sreeja
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55.  Full Outer Join
instructor teaches
ID dept_name
10101
12121
15151
76766
Comp. Sci.
Applied
PED
null
course_id
CS-101
APL-201
null
BIO-101
name
Sreejith
Suresh
Sreeja
null
ID course_id
10101
12121
76766
CS-101
APL-101
BIO-101
Comp. Sci.
Applied
PED
ID dept_name
10101
12121
15151
name
Sreejith
Suresh
Sreeja
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56. Additional
• semi join
• left semi join.
• Right semi join:
Rno Name AGE
1 A 40
2 B 42
3 C 38
R_no Phone
1 9865321245
3 9764316598
5 9598946532
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57. •left semi join.
• Right semi join:
Rno Name AGE
1 Mahati 40
3 Meenu 38
R_no Phone
1 9865321245
3 9764316598
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58. •Denoted by 
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59. R S
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60. YEAR TOUR_PART_EM_ID
2003 1001
2004 1001
2013 1001
2008 1003
2009 1003
2008 1004
2004 1004
2011 1004
2003 1004
2003 1002
2004 1002
2011 1002
2013 1002
2012 1002
EMP_id NAME ADDRESS
1001 SURESH AAAA
1002 LALAN BBBB
1003 JC CCCC
1004 ANVAR DDDD
Retrieve the name &
address of employees who
participated in all tour that
‘Suresh ‘sir attended .
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61. Retrieve the names of employees who work on all
the project that ‘John Smith’ works on
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62. prepared by Visakh V,Assistant Professor,
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63. prepared by Visakh V,Assistant Professor,
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64. • allowing functions of attributes to be
included in the projection
•EX:
•pSALARY-DEDUCTION, SALARY * 0.25(sDNO=5(EMPLOYEE))
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65. • SUM
•AVERAGE
•MAXIMUM
•MINIMUM
•COUNT
•Aggregate function operation using the symbol
<grouping attribute> <function list>(R)
Calligraphic G
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66. a. r R(DNO,NO_OF_EMPLOYEES,AVERAGE_SAL) (Dno COUNT ssn, AVERAGE salary(EMPLOYEE))
b. Dno COUNT ssn, AVERAGE salary(EMPLOYEE)
c. COUNT ssn, AVERAGE salary(EMPLOYEE)
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67. Precedence of relational operators:
1.[SELECT, PROJECT, RENAME]
(highest).
2.[PRODUCT, JOIN].
3.INTERSECTION.
4.[UNION, --]
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