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CSE 326: Data Structures
Lecture #22
Databases and Sorting
Alon Halevy
Spring Quarter 2001
Agenda
• Reminisce about Project 3.
• A bit on graphs.
• Get excited about Project 4 (short course on
databases)
• Start talking about sorting.
Database Systems
• Enable you to manage large (huge) amounts of
data:
– Store the data efficiently
– Pose complex queries on the data in a high-level
language (e.g., SQL)
– Enable concurrent access to the data by many users.
– Embed database queries into application programs.
• The market: mostly relational databases.
Terminology
Attribute names
tuples
Name
Price
Category
Manufacturer
gizmo
$19.99
gadgets
GizmoWorks
Power gizmo $29.99
gadgets
GizmoWorks
SingleTouch $149.99
photography
Canon
MultiTouch
household
Hitachi
$203.99
More Terminology
Every attribute has an atomic type.
Relation Schema: relation name + attribute names + attribute types
Relation instance: a set of tuples. Only one copy of any tuple!
Database Schema: a set of relation schemas.
Database instance: a relation instance for every relation in the schema.
Querying a Database
• The query language enables performing relational
operators:
– Selection (select a subset of the tuples from a table)
– Projection (select a subset of the columns)
– Join (match up two tables on certain attributes)
– Union, negation, aggregation, etc., etc.
• Operations take table(s) as input and produce a table.
• SQL manual is a very effective doorstop.
Selection
• Produce a subset of the tuples in a relation which
satisfy a given condition
• Unary operation… returns set with same
attributes, but ‘selects’ rows
• Use and, or, not, >, <… to build condition
• Find all employees with salary more than $40,000:
Selection Example
Employee
SSN
999999999
777777777
888888888
Name
John
Tony
Alice
DepartmentID
1
1
2
Salary
30,000
32,000
45,000
Find all employees with salary more than $40,000.
SSN
Name
888888888 Alice
DepartmentID
2
Salary
45,000
Projection
• Unary operation, selects columns
• Eliminates duplicate tuples
• Example: project social-security number and
names.
Projection Example
Employee
SSN
999999999
777777777
888888888
Name
John
Tony
Alice
SSN
999999999
777777777
888888888
Name
John
Tony
Alice
DepartmentID
1
1
2
Salary
30,000
32,000
45,000
Join (Natural)
• Most important, expensive and exciting.
• Combines two relations, selecting only related
tuples
• Resulting schema has all attributes of the two
relations, but one copy of join condition attributes
Join Example
Employee
Name
John
Tony
SSN
999999999
777777777
Dependents
EmployeeSSN
999999999
777777777
Dname
Emily
Joe
Employee_Dependents
Dname
SSN
Name
999999999 Emily
John
777777777 Joe
Tony
Step 1
• Read the schema (format given).
• Create the data structure to store tables.
• Read the data (each table is in a separate file, tuple
per line).
Step 2
• Read the query. The form is:
•
•
•
•
Select attributes
From Tables
Where selection conditions, join conditions.
Order By: attribute
• Note: no Cartesian products, may join two tables
on more than one attribute.
• Dirty hack for self joins.
Step 3
• Execute the query.
• Perform all joins (each join creates and
intermediate table).
• Perform selections
• Perform projections
• Order the output (if necessary)
Notes on Mechanics
• Groups of 3-4 students. Send email to Maya, Nic
and Alon by Monday, the 21st .
• Hash join (explained in section yesterday).
• Grading: demos (15 minutes per group) + 2-page
writeup.
• Dates?
• You have a lot of freedom in this project. You’ll
have to make a lot of choices on your own.
• Data (about you)
• Help: all of us + Peter Mork (pmork@cs)
• Homework 5 turn-in.
Sorting
• Given a set of N numbers, put them in order.
• We’ll see several algorithms for comparison sort:
–
–
–
–
Insertion sort
Merge sort
Quicksort
Heap sort.
• How well can we expect to do?? What is the
minimum # of comparisons that any algorithm
could do.
Decision tree to sort list A,B,C
B<A
A<B
B<A
A<B
B,A,C.
A
A,C,B.
C,A,B.
facts
Legend A,B,C
C<A
C
B<
B,C,A.
B<A
C<A
C<B
C<
C
A<
A<B
C<B
A
B
A,B,C.
C<
C
A<
C<
C
B<
C,B,A
Internal node, with facts known so far
Leaf node, with ordering of A,B,C
Edge, with result of one comparison
Max depth of the decision tree
• How many permutations are there of N numbers?
• How many leaves does the tree have?
• What’s the shallowest tree with a given number of leaves?
• What is therefore the worst running time (number of
comparisons) by the best possible sorting algorithm?
Stirling’s approximation
n
n!  2n  
e
n
n

n 
log(n !)  log  2 n   


e




  n n 
 log( 2 n )  log      (n log n)
 e  

