This course covers a variety of techniques for designing approximation algorithms. Two central themes are: (a) linear programming based techniques, and (b) combinatorial methods. Recent results on hardness of approximation, approximate counting, and semidefinite programming might also be touched upon if time allows. We shall spend roughly a third of the semester on each of linear programming and combinatorial methods. The other third is reserved for more specialized topics. 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 and other approximation techniques. In addition to that, students are expected to gain substantial discrete mathematics problem solving skills essential for computer engineers and scientists.

The textbook is meant mostly to be a reference. We shall cover many topics not covered in the texts. Appropriate lecture notes shall be given.

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

• Instructor
  • Prof. Hung Q. Ngo ( hungngo@cse.buffalo.edu)
  • Office Hours: Tuesday & Thursday 11-12am. 238 Bell Hall. Generally, you could stop by any time if my door is opened. If the door is closed, then either I'm not in or I do not wish to be disturbed. However, please try your best to come during office hours. For questions that other students might potentially be interested in, please use the class news group at sunyab.cse.594, it is also more efficient that way. Your classmates can also answer your questions.

Required Textbook: Vijay Vazirani, Approximation Algorithms, Springer-Verlag, 397 pages hardcover, ISBN: 3-540-65367-8, published 2001.

• Douglas West, Introduction to Graph Theory, Prentice Hall, 470pp, Aug 2000, 2nd edition, ISBN: 0130144002.
• Reinhard Diestel, Graph Theory, Springer-Verlag, 2nd edition, April 2000, 315pp, ISBN: 0387989765.
• Vašek Chvátal, Linear Programming, W. H. Freeman, 1983; Paperback, 1st ed., 478pp. ISBN: 0716715872 Publisher: W. H. Freeman Company, January 1983.
• 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.