01a Introduction v2(1)

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FACULTY OF

ENGINEERING &

INFORMATION

TECHNOLOGIES

Algorithms and Complexity

COMP2007 COMP2907 COMP5211

School of Information technologies


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FACULTY OF

ENGINEERING &

INFORMATION

TECHNOLOGIES

Introduction

Algorithms and Complexity


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COMP2007

COMP2907

COMP5211

Textbook: Algorithm Design by Tardos & Kleinberg

All information on Sydney e-learning

http://elearning.sydney.edu.au/

Material for all units will be available on the elearning site titlted:

2013 Semester 2 - COMP2007 Algorithms and Complexity

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Contents

We will cover

Basic algorithms

Basic algorithm design methods

Reductions

Basic Complexity theory

Connections between problems

Differences between problems

Also

How to present algorithms

How to explain, analyze and argue about correctness


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Example

Sound similar? (computationally speaking...)

Shortest Path

Longest Path


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Example from textbook material


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Example

What about these?

Mergesort

Counting inversions in preference profiles


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Example


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Example

Sound similar? (computationally speaking...)

Shortest Path

Longest Path

What about these?

Mergesort

Counting inversions in preference profiles


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Admin


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Assessment

Quizzes 20%

Assignments 20%

Final exam 60%

5 quizzes

All quizzes will be in-class during your assigned tutorial time

5 Assignments

Each assignment will be available about one week before its due date. Final exam has a 40% barrier

If your exam mark is below 40%, you will not get a passing mark for the unit

Closed book, only two A4 pages of your own notes allowed


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Assessment Quizzes

Quizzes 20%

5 quizzes

All quizzes will be in-class during your assigned tutorial time On e-learning, mostly multiple choice questions, but may include other

questions too.

First quiz is in week 3


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Assessment Assignments

Assignments 20%

5 assignments

Same weight (4% each) Some programming will be required

You can use C, C++, Java, Python

All assignments must be submitted on e-learning in pdf format

All assignments will be submitted to the Turnitin similarity checking tool All code will be submitted to MOSS or/and other plagiarism detection

tool


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Contact

Taso Viglas

[email protected]

Tutors: See e-learning website for names, emails etc (coming soon)

For questions about the unit, please use the e-learning discussion forum

If this is not what you need, try to talk to your tutor during your tutorial time

Otherwise email your tutor
mailto:[email protected]:[email protected]:[email protected]


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Material

All lecture slides will be available on e-learning

Lectures will follow the textbook closely

A large part of the lecture slides are available from the textbook publisher,

covered by the publishers copyright Lectures are recorded and will be available on e-learning

Solutions to quiz questions will be available

Solutions to selected tutorial questions will be available, but some material will

only be available from your tutor during the tutorial times.

Solutions to the assignments will not be available on e-learning

Some solutions will be discussed in tutorials.


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Tutorials start in week 2

- For all algorithms units this semester- COMP2007

- COMP2907

- COMP5211

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Algorithms then, and now


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What's in an algorithm?

Algorithms can have huge impact

For example- A report to the White House from 2010 includes the following.

Professor Martin Grotschel

A benchmark production planning model solved using linearprogramming would have taken 82 years to solve in 1988, using the

computers and the linear programming algorithms of the day.

Fifteen years later, in 2003, this same model could be solved in

roughly 1 minute, an improvement by a factor of roughly

43 million


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In 2003 we can solve a problem 43 million times faster than in 1988

This is because of better hardware and better algorithms


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1988 ?

In 1988

Intel 386 and 386SX

About 275,000 transistors

clock speeds of 16MHz,20MHz, 25MHz, and

33MHz

MSDOS 4.0 and windows 2.0

VGA

Mobile phones are the size of

a brick

People dress funny and listen

to unbearable music

In 2003

Pentium M

About 140 million

transistors

Up to 2.2 GHz

AMD Athlon 64

Windows XP

iTunes


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22

Images from wikipedia, CC licence

Source: Rico Shen


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Report to the White House from 2010 includes the following.

Professor Martin Grotschel:

A benchmark production planning model solved using linear

programming would have taken 82 years to solve in 1988, using the

computers and the linear programming algorithms of the day.

Fifteen years later, in 2003, this same model could be solved in

roughly 1 minute, an improvement by a factor of roughly

43 million

Hardware: 1,000 times improvement

Algorithms: 43,000 times improvement
http://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-nitrd-report-2010.pdfhttp://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-nitrd-report-2010.pdf


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Efficient algorithms

Efficient algorithms produce results within available resource limits

In practice

Low polynomial time algorithms behave well

Exponential running times are infeasible except for very small instances, or carefully designedalgorithms

Performance depends on many obvious factors

Hardware

Software

Algorithm

Implementation of the algorithm

This unit: Analysis of algorithms, and

a little bit of implementation of algorithms


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Efficient algorithms do the job the way you want them to...

Dealing with huge data?

Do you need the exact solution?

Are you dealing with some special case and not with a general problem?

Is it ok if you miss the right solution sometimes?


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Complex, highly sophisticated algorithms can greatly improve

performance

apart from that...

Reasonably good algorithmic solutions that avoid simple, or lazy

mistakes, can have even greater contribution


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List of topics

Greedy algorithms

Divide and conquer

Dynamic programmingNetwork flows, maxflow

Mincut theorems

Complexity theory

P, NP, and NP-completenessIntractability

Approximation, Randomization

Optimization problems


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Preliminary List of topics

Week 1 Unit introduction, algorithms and complexity

Week 2 Introduction to graph algorithms, Intro to greedy

Week 3 Greedy algorithms

Week 4 Divide and conquer

Week 5 Dynamic programming

Week 6 Network flows, maxflow

Week 7 Mincut theorems, matching

Week 8 Other Max-flow and min-cut applications, Intro to complexity theory

Week 9 Complexity theory: Polynomial time reductions, P, NP, and NP-completeness Week 10 Intractability

Week 11 Coping with hardness: Solving special cases, approximation, randomization

Week 12 Optimization problems

Week 13 Review

Note: The following list of topics may change

01a Introduction v2(1)

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