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Transcript
Theory of Algorithms
Introduction
Mechanics
Outline
 Exams, Dates, Homework, Grading
 No Programming Exercises
 Required Books
 Class Handouts
 Previous Exams
 Web Sites

Why Study Algorithms
The One Constant in A Changing Universe
 Techniques are Useful, and Required in
Most other Research Areas
 Some Exposure to Theory is Necessary at
the Graduate Level
 The Material is Interesting and Challenging
in its Own Right

What We will Study

Speed
 Time

Complexity
Memory Usage
 Space

Complexity
Usage of Communication Network
 Communication

Complexity
Sometimes: How to do stuff
Time Complexity
How “Fast” an Algorithm Runs
 An Algorithm is Not a Program
 Results Should Be Applicable to All
Machines
 Results Should Apply Regardless of Input
Size
 Are Some Algorithms Inherently Better than
Others?

How to Measure Speed
For Each Algorithm Find a Function f(n)
 The Argument n is the Size of the Input
 The Function f(n) Gives the Amount of
Time Required to Process the Input
 For Any Machine there Must be a Constant
K such that Kf(n) is Close to the Real Run
Time on Machine M.
 K Also Depends on the Algorithm

Some Observations About f(n)

Because of the Machine and Algorithm
Dependent Constant K, f(n) is the same as
Cf(n) for any Positive Constant C

For Small Values of n, Initialization
Dominates, so f(n) May Be Inaccurate

Only “Large” Values of n are “Interesting”