1. Chapters 5-8 Relational Data Models, Relational Constraints, and Relational Algebra
Flat file: A two dimensional array of attributes or data items
ProductX Bellaire
ProductY Sugarland
ProductZ Houston
Computerization Stafford
Reorganization Houston
Newbenefits Stafford
Database Management Systems (DBMS): A generalized software system that is used to create, manage, and protect data bases
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2. Chapters 5-8

3. Attribute: A name characteristic or property of an entity = column header Entity: A “thing” in the real world with an independent existence physical existence: person, student, car
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4. GPA: 0<= GPA <= 4.0 Fname -- atomic Minit -- atomic
Domain - The valid set of atomic value for an attribute in a relation
e.g. SSN set of 9 digits
GPA: 0<= GPA <= 4.0
Atomic - each value in the domain is indivisible
Name (Fname, Minit, Lname) – not atomic
Fname -- atomic
Minit -- atomic
Lname atomic
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5. Relational Model Concepts
A Relation is a mathematical concept based on the ideas of sets
The model was first proposed by Dr. E.F. Codd of IBM Research in 1970 in the following paper:
"A Relational Model for Large Shared Data Banks," Communications of the ACM, June 1970
The above paper caused a major revolution in the field of database management and earned Dr. Codd the coveted ACM Turing Award
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6. Informal Definitions
Informally, a relation looks like a table of values.
A relation typically contains a set of rows.
The data elements in each row represent certain facts that correspond to a real-world entity or relationship
In the formal model, rows are called tuples
Each column has a column header that gives an indication of the meaning of the data items in that column
In the formal model, the column header is called an attribute name (or just attribute)
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7. Formal Definitions - Schema
The Schema (or description) of a Relation:
Denoted by R(A1, A2, .....An)
R is the name of the relation
The attributes of the relation are A1, A2, ..., An
Example:
CUSTOMER (Cust-id, Cust-name, Address, Phone#)
CUSTOMER is the relation name
Defined over the four attributes: Cust-id, Cust-name, Address, Phone#
Each attribute has a domain or a set of valid values.
For example, the domain of Cust-id is 6 digit numbers.
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8. Formal Definitions - Tuple
A tuple is an ordered set of values (enclosed in angled brackets ‘< … >’)
Each value is derived from an appropriate domain.
A row in the CUSTOMER relation is a 4- tuple and would consist of four values, for example:
<632895, "John Smith", "101 Main St. Atlanta, GA ", "(404) ">
This is called a 4-tuple as it has 4 values
A tuple (row) in the CUSTOMER relation.
A relation is a set of such tuples (rows)
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9. Formal Definitions - Domain
A domain has a logical definition:
Example: “USA_phone_numbers” are the set of 10 digit phone numbers valid in the U.S.
A domain also has a data-type or a format defined for it.
The USA_phone_numbers may have a format: (ddd)ddd-dddd where each d is a decimal digit.
Dates have various formats such as year, month, date formatted as yyyy-mm-dd, or as dd mm,yyyy etc.
The attribute name designates the role played by a domain in a relation:
Used to interpret the meaning of the data elements corresponding to that attribute
Example: The domain Date may be used to define two attributes named “Invoice-date” and “Payment-date” with different meanings
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10. Formal Definitions - State
The relation state is a subset of the Cartesian product of the domains of its attributes
each domain contains the set of all possible values the attribute can take.
Example: attribute Cust-name is defined over the domain of character strings of maximum length 25
dom(Cust-name) is varchar(25)
The role these strings play in the CUSTOMER relation is that of the name of a customer.
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11. Formal Definitions - Summary
Formally,
Given R(A1, A2, , An)
r(R)  dom (A1) X dom (A2) X ....X dom(An)
R(A1, A2, …, An) is the schema of the relation
R is the name of the relation
A1, A2, …, An are the attributes of the relation
r(R): a specific state (or "value" or “population”) of relation R – this is a set of tuples (rows)
r(R) = {t1, t2, …, tn} where each ti is an n-tuple
ti = <v1, v2, …, vn> where each vj element-of dom(Aj)
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12. Formal Definitions - Example
Let R(A1, A2) be a relation schema:
Let dom(A1) = {0,1}
Let dom(A2) = {a,b,c}
Then: dom(A1) X dom(A2) is all possible combinations:
{<0,a> , <0,b> , <0,c>, <1,a>, <1,b>, <1,c> }
The relation state r(R)  dom(A1) X dom(A2)
For example: r(R) could be {<0,a> , <0,b> , <1,c> }
this is one possible state (or “population” or “extension”) r of the relation R, defined over A1 and A2.
It has three 2-tuples: <0,a> , <0,b> , <1,c>
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13. Definition Summary Informal Terms Formal Terms Table Relation
Column Header
Attribute
All possible Column Values
Domain
Row
Tuple
Table Definition
Schema of a Relation
Populated Table
State of the Relation
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14. Super key: an attribute or a set of attributes that identifies an entity uniquely (may not be minimal set)  SSN SSN, NAME SSN, NAME, MAJOR
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15. Candidate key: a super key such that no proper subset of its attributes is itself a super key. So candidate keys must have a minimal identifier.   STUID SSN   Primary key: the candidate key that is chosen OR the candidate key that is used to identify tuples in a relation -- unique, must exist   Alternate key: A candidate key in a relation that is not selected e.g. if primary key is SSN then STUID is a alternate key
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16. Concatenated (composite) key: A primary key that is comprised of two or more attributes or data items G RADE_REPORT(STUID, COURSE#, GRADE) 
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17. Foreign key: A non-key attribute in one relation that appears as the primary key (or part of the key) in another relation EMPLOYEE(SSN, FNAME, MINIT, DNO) DEPARTMENT(DNUMBER, DNAME, MANAGER)
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18. Secondary key: a field that can have duplicate values, and that can be used as search path by the users
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19. Chapters 5-8

20. Referential Integrity Constraints for COMPANY database
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21. Chapters 5-8

22. 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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23. 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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24. Relational Algebra Overview
Relational Algebra consists of several groups of operations
Unary Relational Operations
SELECT (symbol:  (sigma))
PROJECT (symbol:  (pi))
Relational Algebra Operations From Set Theory
UNION (  ), INTERSECTION (  ), DIFFERENCE (or MINUS, – )
CARTESIAN PRODUCT ( x )
Binary Relational Operations
JOIN (several variations of JOIN exist)
DIVISION
Additional Relational Operations
OUTER JOINS, OUTER UNION
AGGREGATE FUNCTIONS (These compute summary of information: for example, SUM, COUNT, AVG, MIN, MAX)
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25.  SALARY > 30,000 (EMPLOYEE)
Unary Relational Operations: SELECT
The SELECT operation (denoted by  (sigma)) is used to select a subset of the tuples from a relation based on a selection condition.
The selection condition acts as a filter
Keeps only those tuples that satisfy the qualifying condition
Tuples satisfying the condition are selected whereas the other tuples are discarded (filtered out)
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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26. 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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27. Unary Relational Operations: SELECT (contd.)
SELECT Operation Properties
The SELECT operation  <selection condition>(R) produces a relation S that has the same schema (same attributes) as R
SELECT  is commutative:
 <condition1>( < condition2> (R)) =  <condition2> ( < condition1> (R))
Because of commutativity property, a cascade (sequence) of SELECT operations may be applied in any order:
<cond1>(<cond2> (<cond3> (R)) = <cond2> (<cond3> (<cond1> ( R)))
A cascade of SELECT operations may be replaced by a single selection with a conjunction of all the conditions:
<cond1>(< cond2> (<cond3>(R)) =  <cond1> AND < cond2> AND < cond3>(R)))
The number of tuples in the result of a SELECT is less than (or equal to) the number of tuples in the input relation R
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28. Select Works on single table and takes rows that meet a specified condition, copy them into a new table
(Table name)
Condition(s)
SQL (Structured Query language)
SELECT *
FROM (table name)
WHERE condition 1
AND condition 2
AND condition 3…
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29. 
Condition(s)
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Table

30. Find employees who work for department number 5.  employee DNO = 5
SQL:
SELECT *
FROM employee
WHERE dno = 5;
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31. Chapters 5-8

32. Query tree 
DNO=5
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Employee

33. s(DNO=4 AND SALARY>25000) OR (DNO=5 AND SALARY>30000)(EMPLOYEE)
s(DNO=4 AND SALARY>25000) OR (DNO=5 AND SALARY>30000)(EMPLOYEE)
s<cond1>(s<cond2>(R)) = s<cond2>(s<cond1>(R))
s<cond1>(s<cond2>(. . .(s<condn> (R)) . . .)) = s<cond1> AND <cond2> AND AND <condn>(R)
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34. Project Operates on a single table,
produces a vertical subset of the table,
extract the values of specified columns
eliminate duplicate rows
place the value in a new table
 (table name)
column1, column2, column3, …
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35. SELECT column1, column2, column3, … FROM (table name)
SQL:
SELECT column1, column2, column3, …
FROM (table name)
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36. 
column(s)
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Table

37. E.g. Show the names of all employees  employee fname, minit, lname
SELECT fname, minit, lname
FROM employee;
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38. Chapters 5-8

39. 
fname,minit,lname
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Employee

40. Show the names of all employees who work for department number 5
Select & project
Show the names of all employees who work for department number 5
 ( employee)
fname, minit, lname dno = 5
SELECT fname, minit, lname
FROM employee
WHERE dno = 5;
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41. Chapters 5-8

42. 
fname,minit,lname 
DNO = 5
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Employee

43. Examples of applying SELECT and PROJECT operations
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44. If R1 has X rows and M columns R2 has Y rows and N columns
PRODUCT (or Cartesian product) R1 x R2
R1 X R2 is a table where width is the width of R1 plus the width of R2 and whose columns are the columns of R1 followed by the columns of R2
If R1 has X rows and M columns
R2 has Y rows and N columns
R1 X R2 = X * Y rows and M + N columns
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45. Cartesian Product
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46. Query Tree for Cartesian ProductX
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Table1
Table2

47. Example of Query Tree
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48. Theta Join
The result of performing a SELECT operation using a comparison operator theta (=,<, <=, >, <=, <>) on the product
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49. Theta Join (>)
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50. Theta Join (ID>STUID)
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51. Query Tree for Theta Join
X ID > STUID
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Student
Credit_Hours

52. Equijoin Product with “theta” is equality
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53. Chapters 5-8
Equijoin

54. Equijoin
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55. Query Tree for Equijoin
X ID = STUID
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Student
Credit_Hours

56. Natural Join |X| Is an equijoin which the repeated column is eliminated Usually join performs over column with the same names
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57. Equi-join
Remove
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58. Remove this column
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59. Chapters 5-8

60. Query Tree for Natural Join
|X|
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Student
Credit_Hours

61. Semi-join: If R1 and R2 are tables
Semijoin of R1 and R2 is natural join of R1 and R2 and then projecting the result into the attributes of A
Semijoin is not cumulative
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62. insert into student1 values(‘101’,’Jim’,’Smith’);
Create tables
create table student1
(id char(3) primary key,
fname char(10),
lname char(10));
insert into student1 values(‘101’,’Jim’,’Smith’);
insert into student1 values(‘102’,’Tim’,’Brown’);
insert into student1 values(‘103’,’Babara’,’Houston’);  
create table credit_hours
(stuid char(3) primary key,
hours number(3));
insert into credit_hours values(101,60);
insert into credit_hours values(102,85);
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63. Left Semi-Join
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64. Right Semi-Join
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65. Outer Join:
Is an extension of a THETA JOIN, an EQUIJOIN, or a NATURAL JOIN
An outer join consists of all rows that appear in the usual theta join, plus an additional row for each of the tuples from the original tables that do not participate in the theta join.
In those rows that are unmatched original tuples, extend it by assigning null values to the other attributes.
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66. Left outer join unmatched rows from the first (left) table appear in the resulting table
Right outer join unmatched rows from the second (right) table appear in the resulting table
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67. Left Outer Join
Right Outer Join
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68. from student, credit_hours where id = stuid(+);
Outer Join -- Oracle
Left-outer join
select *
from student, credit_hours
where id = stuid(+);
SELECT E.FNAME, E.LNAME, dependent_name
FROM EMPLOYEE E, DEPENDENT D
WHERE E.SSN = D.ESSN(+);
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69. Right-outer join
select * from student, credit_hours where id(+) = stuid;
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70. Sample SQL create view: Chapters 5-8
create view v_emp_dno as select fname, lname, dno from employee; select * from v_emp_dno; create view v_department as select dnumber, dname from department; select * from v_department; Cartesian product: select * from v_emp_dno, v_department; Natural join: select * from v_emp_dno, v_department where dno = dnumber; Left Outer join select fname, lname, ssn, essn, dependent_name from employee, dependent where ssn = essn (+); Right Outer join select essn, dependent_name, fname, lname, ssn from employee, dependent where essn (+) = ssn;
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71. Set operations: Union, Difference, Intersection, Division
Union (U) tables must be compatible - they must have same basic structure, both relations must have the same domains.
The union of two relations is the set of tuples in either or both relations
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72. Example to illustrate the result of UNION, INTERSECT, and DIFFERENCE
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73. SQL--Union Select ssn from employee where dno = 5 Union select distinct(essn) from dependent;
5 rows selected
SSN
4 rows selected
ESSN
3 rows selected
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74. Difference (-) The difference between two relations is the set of tuples that belong to the first relation but not in the second relation.
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75. SQL--Minus Select ssn from employee minus select unique essn from dependent;
5 rows selected =
SSN
8 rows selected
ESSN
3 rows selected
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76. Intersection () The intersection of two relations is the set of tuples that belong to both relations simultaneously.
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77. 
Intersection
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78. Division () A binary operation that can be defined on two relations where the entire structure of one (the divisor) is a portion of the structure of the other (the dividen)
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79. Division
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80. Example of DIVISION
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81. Aggregate Functions and Grouping
Script F: (group attributes)  <function, attribute> (R) Functions = sum, average, maximum, minimum, count
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82. All Employees (No Group By)
SELECT sum(salary), Max (salary), min(salary), avg(salary)
FROM employee;
SUM(SALARY) MAX(SALARY) MIN(SALARY) AVG(SALARY)
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83. Example: Retrieve the department number, number of employees, and average salary in the department – Group By DNO
RESULT(DNO, NUMBER_OF_EMPLOYEES, AVG_SAL)  count SSN, Average SALARY EMPLOYEE SELECT dno, count(ssn), avg(salary) FROM employee GROUP BY dno order by dno; DNO COUNT(SSN) AVG(SALARY)
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84. SELECT dno, sum(salary), Max (salary), min(salary), avg(salary)
Group By
SELECT dno, sum(salary), Max (salary), min(salary), avg(salary)
FROM employee
GROUP BY dno;
DNO SUM(SALARY) MAX(SALARY) MIN(SALARY) AVG(SALARY)
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85. DNO  count SSN, Average SALARY (EMPLOYEE)
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86. If grouping attributes are not specified
 count SSN, Average SALARY (EMPLOYEE)
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87. SELECT sum(salary), Max (salary), min(salary), avg(salary)
FROM employee, department
WHERE dno = dnumber
AND dname = 'Research';
SUM(SALARY) MAX(SALARY) MIN(SALARY) AVG(SALARY)
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88. (select fname, lname, dno from employee where dno = 5) --------------
View
Create View V_Dno5 as
(select fname, lname, dno
from employee
where dno = 5)
view V_DNO5 created.
Select * from V_DNO5;
FNAME LNAME DNO
John Smith
Franklin Wong
Ramesh Narayan
Joyce English
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