The document discusses relational algebra and operators that can be used to query relational databases. It introduces select, project, join, and cross-product operators that allow filtering rows and columns and combining relations. Examples using a sample college admissions database illustrate how these operators can be applied to retrieve specific information like names and decisions of accepted applications or names and GPAs of rejected applicants. Theta join is also introduced as the basic join operation implemented in database management systems.

1. Jennifer Widom
Relational Databases
Relational Algebra (1)
Select, project, join

2. Jennifer Widom
Relational Algebra (1)
Query (expression) on set of relations produces
relation as a result

3. Jennifer Widom
Relational Algebra (1)
Examples: simple college admissions database
College(cName,state,enrollment)
Student(sID,sName,GPA,sizeHS)
Apply(sID,cName,major,decision)
cName state enr sID sName GPA HS sID cName major dec
College Student Apply

4. Jennifer Widom
Simplest query: relation name
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)
Use operators to filter, slice, combine

5. Jennifer Widom
Select operator: picks certain rows
Students with GPA>3.7
Students with GPA>3.7 and HS<1000
Applications to Stanford CS major
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

6. Jennifer Widom
Project operator: picks certain columns
ID and decision of all applications
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

7. Jennifer Widom
To pick both rows and columns…
ID and name of students with GPA>3.7
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

8. Jennifer Widom
Duplicates
List of application majors and decisions
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

9. Jennifer Widom
Cross-product: combine two relations
(a.k.a. Cartesian product)
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

10. Jennifer Widom
Cross-product: combine two relations
(a.k.a. Cartesian product)
Names and GPAs of students with HS>1000 who applied to CS
and were rejected
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

11. Jennifer Widom
Natural Join
 Enforce equality on all attributes with same name
 Eliminate one copy of duplicate attributes
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

12. Jennifer Widom
Natural Join
Names and GPAs of students with HS>1000 who applied to CS
and were rejected
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)
Names and GPAs of students with HS>1000 who applied to CS
at college with enr>20,000 and were rejected

13. Jennifer Widom
Natural Join
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

14. Jennifer Widom
Theta Join
 Basic operation implemented in DBMS
 Term “join” often means theta join
cName state enr sID sName GPA HS sID cName major dec
College Student Apply
Relational Algebra (1)

15. Jennifer Widom
Relational Algebra (1)
Query (expression) on set of relations produces
relation as a result
 Simplest query: relation name
 Use operators to filter, slice, combine
 Operators so far: select, project, cross-product,
natural join, theta join