Announcements

• Homework 2 reminder

– Due Thursday, Oct 4 at beginning of class

– Turn in hard copy in class, PDF through

Canvas

• Quiz 2 also on Thursday, Oct 4th

• Midterm Exam: Tuesday, Oct 9th

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CS2300: File Structures and

Introduction to Database Systems

Lecture 12: Relational Algebra

Doug McGeehan

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Brief Review

Relational Algebra

• Basic operations

– Selection (): Selects a subset of rows from relation.

– Projection (π) : Deletes unwanted columns from relation.

– Cross-product (X)

– Set-difference or Minus (-)

– Union (U)

• Additional operations– Renaming

– Intersection, Join

– Division

– Aggregation and grouping

– Generalized Projection

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Question (Challenging)

Find the id of the sailors who reserved ALL boats.

Reserve

daybidsid

1/1/9910258

10/10/9610122

8/8/9610158

11/11/9610358

yearnamebid

1Victory101

3Wind102

1Dream103

Boat

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Question (Challenging)

Find the id of the sailors who reserved ALL boats.

Step 1: create a table where everyone reserves all boats.

R1 (πsid Reserve) X (π bid Boat)

Step 2: find sailors who didn’t reserve all boats

R2 R1 – πsid, bid Reserve

Step 3: find sailors who reserve all boats

R3 (π sid Reserve) – (πsid R2)

Reserve (sid, bid, day) Boat (bid, name, year)

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Division

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Reconsider the Question

Find the id of the sailors who reserved ALL boats.

(πsid,bid Reserve) (πbid Boat)

Reserve (sid, bid, day)

Boat (bid, name, year)

Division

• Division is useful to express “for all” queries

• Examples:

– Find students who studied ALL of Dr Cohen’s

courses

– Find lecturers who have taught ALL of the

students

• We will use to denote division.

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Division

• Can perform R S if S’s schema is a

subset of R’s schema

• The result is a relation with all attributes

appearing in R but not in S

• R(X1,…,Xk,Y1,…,Ym), S(Y1,…,Ym):

– R S : What attributes are in the result?

Division

• Consider: – A(X1,…,Xk,Y1,…,Ym)

– B(Y1,…,Ym)

• Then AB =

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Find suppliers (sno) from A who

supply All parts (pno) from B

sno pno

S1

S1

S1

S1

S2

S2

S3

S4

S4

P1

P2

P3

P4

P1

P2

P2

P2

P4

A

P2

pno

B

sno =

S1

S2

S3

S4

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Find suppliers (sno) from A who

supply All parts (pno) from B

sno pno

S1

S1

S1

S1

S2

S2

S3

S4

S4

P1

P2

P3

P4

P1

P2

P2

P2

P4

A

sno

=S1

S4

P2

P4

pno

B

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Find suppliers (sno) from A who

supply All parts (pno) from B

sno pno

S1

S1

S1

S1

S2

S2

S3

S4

S4

P1

P2

P3

P4

P1

P2

P2

P2

P4

A

sno =S1P1

P2

P4

pno

B

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Example for Division

• Consider the following two relations

VetCheckup(vid, tagno, timestamp)

PetAnimal(tagno, name, type, breed)

• Find the ID of the veterinarian who

checked on all huskies

Aggregate Function and

Grouping

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Example

How many pancakes were purchased

over the past three months?

What is the average amount spent across

all customers on pancakes vs waffles?

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Aggregate Function and Grouping

• Specify mathematical aggregate functions

on collections of values from the database.

• Common functions – SUM

– AVERAGE

– MAXIMUM and MINIMUM

– COUNT (for counting tuples)

• Tuples can be grouped before applying the aggregation functions.

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Aggregate Function and Grouping

• Written as grouping_attributesℱF1,F2,…Fn(R)

• Group tuples having the same values for the

grouping attributes

(can be multiple attributes)

• Each function Fi is in the form:

– <function> <attribute>

– Example: Max salary; Count ssn

• Attributes in the result include grouping

attributes and all aggregation functions.18

Aggregate Function and Grouping

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yearsnamesid

3white240

3jones202

1adams450

SyearℱCount sid (R)

Report the total number of students for each year

Count_sidyear

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coursesidtid

os20220

calculus45010

db 20220

db24020

depttnametid

mathcohen10

cslevy20

Report the number of courses

taught by Dr. Levy.

T

R

Count_course

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ℱCount course (course(R*(tname=`levy’T))

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More Examples

• EMPLOYEE (SSN, Name, Salary, Year)

• ℱMAX Salary (EMPLOYEE)

– retrieves the maximum salary value from the EMPLOYEE

relation

• YearℱMIN Salary, AVG Salary (EMPLOYEE)

– retrieves the minimum and average Salary values from the

EMPLOYEE relation for each year.

• ℱSUM Salary (EMPLOYEE)

– retrieves the sum of the Salary from the EMPLOYEE relation

Generalized Projection

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Generalized Projection

• Consider the following relation and

report the net salary of an employee

• Employee(ssn, salary, tax, year)

• Net salary = salary – tax

salary-taxEmployee

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Generalized Projection

• Allows functions on attributes in the projection list.

F1,F2,…,Fn

(R)

• F1,F2,…Fn are functions over the attributes in R

and may involve constants.

• This is needed when developing reports where

computed values have to be produced

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