Princeton COS 423 Analysis of Algorithms Lectures

COS 423 Analysis of Algorithms Lectures, Spring 2001

The following table contains links to whatever electronic slides or demos were used in class. Note that not all of this material was actually covered in Spring 2001.

Here is a link to a more recent version of some of these lecture slides that supplement the textbook by Jon Kleinberg and Éva Tardos.

Topic	Slides	In-class Demos	Reading

Introduction

Stable matching	pdf	Gale-Shapley

Greedy algorithms

Greed	pdf	Activity selection Greed is good	CLR, Chapter 17
Shortest path	pdf		CLR, Chapter 25
Minimum spanning tree	pdf	Red rule, blue rule	CLR, Chapter 24

Divide-and-conquer paradigm

Divide and conquer	pdf	Counting inversions	CLR, Chapter 4, 8 31.2, 35.4
Linear time selection	pdf		CLR 10.3
Fast Fourier transform	pdf		CLR, Chapter 32

Dynamic programming

Dynamic programming	pdf		CLR, Chapter 16
Negative cycle	pdf		CLR, Chapter 26

Reductions

Linear time reductions	pdf		CLR, Chapter 31.5
Maximum flow	pdf	Augmenting path Breadth-first search	CLR, Chapter 27.1, 27.2
Reductions to max flow	pdf		CLR, Chapter 27.3
Polynomial time reductions	pdf		CLR, Chapter 36

Intractability and coping with intractability

NP completeness	pdf	Longest path song by Daniel Barrett	CLR, Chapter 36
Approximation algorithms	pdf	List scheduling	CLR, Chapter 37 survey paper (optional)
Linear programming	pdf		Scientific American handout

Beyond worst case complexity

Average case analysis	pdf		CLR, Chapter 8
Amortized analysis	pdf	Dynamic table Splay trees	CLR, Chapter 13-15, 18 Splay handout from Duke
Competitive analysis	pdf	Paging

Conclusions

Wrapup	pdf		Top 10 algorithms
Acknowledgments	pdf

Data Structures

Binary and binomial heaps	ppt pdf		Binomial heap applet
Fibonacci heaps	ppt pdf		CLR Chapter 20

How to read and print the files

Acrobat: to view Acrobat (.pdf) files, you can use Acrobat Reader.
Java: to run Java applets, use a browser that supports Java 1.2 or download the latest Java plug-in.
Powerpoint: to view PowerPoint files (.ppt), use a browser that supports viewing them, or download a free PowerPoint viewer. If the equations don't view properly, be sure you have the Symbol and MT Extra fonts. Installing the Microsoft Equation Editor (from Windows setup) will accomplish this.
To print the PowerPoint files, we recommend printing 4 or 6 to the page. To get the best results, don't use the PowerPoint "Print -> Handout" option. Instead, use "Print -> Properties -> Advanced -> Pages Per Sheet -> 6 Landscape." Also, we recommend selecting "Print -> Properties -> Page Setup -> Color" and deselecting "Print -> Grayscale", even if you have a black and white printer.
The style file used to print the slides is cs423-handouts.pot; the style file used to to display the slides in lecture is cs423-cos104.pot.

Acknowledgments

These lecture notes were heavily influenced by the unpublished manuscript Introduction to Algorithms, written by Jon Kleinberg and Éva Tardos. The lecture notes also adapt material from the following sources.

A. Aho, J. Hopcroft, J. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.
R. K. Ahuja, T. L. Magnanti, J. B. Orlin. Network Flows. Prentice-Hall, 1993.
G. Brassard, P. Bratley. Fundamentals of Algorithmics. Prentice-Hall, 1996.
T. Cormen, C. Leiserson, R. Rivest. Introduction to Algorithms. McGraw-Hill, 2001.
M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
D. Gusfield and R. Irving. The Stable Marriage Problem. MIT Press, 1989.
U. Manber. Introduction to Algorithms -- A Creative Approach. Addison Wessley, 1989.
D. Kozen. The Design and Analysis of Algorithms. Springer-Verlag, 1992.
R. E. Tarjan. Data Structures and Network Algorithms. SIAM, 1983.

Instructors: if you use these slides in class, please provide a link back to this page.

Errata

These lecture notes are being used for the first time this semester. If you discover any typos or errors, I would be grateful if you let me know via email.

Kevin Wayne