CSE 594: Combinatorial and Graph Algorithms

Spring 2003
Time:
Tue,Thr 8:00am-9:20am, Place: Clemen 04.

### Course Syllabus

```Instructor:     Prof. Hung Q. Ngo
Office: 239 Bell Hall            Office Hours: Thursdays 1:00-3:00pm
Phone: 645-3180 x 160            Email: hungngo@cse.buffalo.edu
```

Course Description:

This course has twomain components: (a) linear programming and network flows, (c) NP-completeness and approximation algorithms. We shall spend roughly one half of the semester on each topic. We shall attempt to cover a broad range of commonly faced optimization problems, mostly on graphs, which can be naturally modelled and/or solved using linear programming, network flows, and approximation techniques. In addition to that, students are expected to gain substantial discrete mathematics problem solving skills essential for computer engineers and scientists.

The textbooks are meant mainly for references. We shall cover many topics not covered in the texts. Appropriate lecture notes shall be given.

This course is highly mathematical in nature. One aim is for students to be able to formulate a practical problems mathematically, and find familiar techniques to solve them if possible.

Course Objectives:

• Have fun learning!
• Grasp the essential ideas of approximation algorithm analysis and design, including but not limited to the following
• basic NP-completeness proofs
• linear programming formulation and solution
• network flows analysis and algorithms
• approximation algorithms design techniques for a variety of combinatorial and graph optimization problems: greedy-method, linear programming relaxation, divide and conquer, primal-dual methods, ...
• Gain substantial problem solving skills in designing algorithms and discrete mathematics

Prerequisites:

A solid background on basic algorithms. (A formal course like CSE531 suffices.)
Ability to read and quickly grasp new discrete mathematics concepts and results.
Ability to do rigorous formal proofs.

At the end of this course, each student should be able to:

• Have a good overall picture of NP-completeness, linear programming, network flows, approximation algorithms analysis and design techniques
• Solve simple to moderately difficult approximation algorithmic problems arising from practical programming situations
• Love designing and analyzing approximation algorithms

References:

• Required Textbooks:
• Vijay Vazirani, Approximation Algorithms, Springer-Verlag, 397 pages hardcover, ISBN: 3-540-65367-8, published 2001.
• Vašek Chvátal, Linear Programming, W. H. Freeman, 1983; Paperback, 1st ed., 478pp. ISBN: 0716715872, W. H. Freeman Company, January 1983.
• Other recommended references:
• Dorit Hochbaum (Editor), Approximation Algorithms for NP-Hard Problems, Hardcover: 624 pages ; Brooks/Cole Pub Co; ISBN: 0534949681; 1st edition (July 26, 1996)
• Alexander Schrijver, Theory of Linear and Integer Programming, Paperback, 1st ed., 484pp. ISBN: 0471982326, Wiley, John & Sons, Incorporated, June 1998.
• Michael R. Garey and David S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Paperback, 338pp. ISBN: 0716710455, W. H. Freeman Company, November 1990.
• Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin, Network Flows: Theory, Algorithms, and Applications, Hardcover, 1st ed., 846pp., ISBN: 013617549X, Prentice Hall, February 1993.
• Plus other reading material specified on the class homepage

Class homepage:

`        http://www.cse.buffalo.edu/~hungngo/classes/cse594_spring03/`

• Heavy! So, start early!!
• Approx. 50 pages of fairly dense reading per week
• 6 written homework assignments (to be done individually)
• 1 midterm exam (in class)
• 1 final exam (in class)

• 4 written assignments: 8% each
• Midterm: 28%
• Final: 40%
• Assignments due at the end of the lecture on the due date
• Each extra day late: 20% reduction
• Incomplete/make-up exams: not given, except in provably extraordinary cases

• No tolerance on plagiarism:
• 0 on the particular assignment/exam for first attempt
• Fail the course on the second
• Consult the University Code of Conduct for details on consequences of academic misconduct