CSE 594: Combinatorial and Graph Algorithms
Time: Tue,Thr 8:00am-9:20am, Place: Capen 260.
Instructor: Prof. Hung Q. Ngo
Office: 239 Bell Hall
Office Hours: Tuesdays & Thursdays 10-11am
Phone: 645-3180 x 160
Teaching Assistant: Mr. Jaikanth Krishnaswamy
Office Hours: TBA
This course has two main components: (a) topics in graph theory, (b)
linear programming, network flows in the context of 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 modeled 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 textbook is meant mostly 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.
- Grasp the essential ideas of graph theory, linear programming, approximation
algorithm analysis and design, including but not limited to the following
- matching theory
- graph coloring
- linear programming formulation and solution
- the primal-dual method
- connectivity and Menger's theorem
- structures in dense and sparse graphs
- Gain substantial problem solving skills in designing algorithms and discrete
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 the topics mentioned in the course objective
- Solve simple to moderately difficult approximation algorithmic problems
arising from practical programming situations
- Love designing and analyzing approximation algorithms, and solving graph
- Required Textbooks:
Diestel, Graph Theory, Springer-Verlag, 2nd edition, April
2000, 315pp, ISBN: 0387989765.
- Other recommended references:
- Douglas West,
Introduction to Graph Theory, Prentice Hall, 470pp, Aug 2000, 2nd
edition, ISBN: 0130144002.
Vazirani, Approximation Algorithms,
Springer-Verlag, 397 pages hardcover, ISBN: 3-540-65367-8, published 2001.
Chvátal, Linear Programming,
W. H. Freeman, 1983; Paperback, 1st ed., 478pp. ISBN: 0716715872, W. H.
Freeman Company, January 1983.
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.
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,
- Ravindra K. Ahuja,
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
- Heavy! So, start early!!
- Approx. 50 pages of very dense reading per week
- 4 written homework assignments (to be done individually)
- 1 midterm exam (take home)
- 1 final exam (take home)
- 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
- 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
- See also Prof. Shapiro's page on Academic Integrity of the CSE department:
- Group study/discussion is encouraged, but the submission must be your own
- I will take cheating VERY VERY seriously. Don't waste your time
- Students are encouraged to discuss homework problems with classmates, but
the version submitted must be written on your own, in your own words.
- The midterm and final exams have to be done individually, no discussion
- Absolutely no lame excuses please, such as "I have to
go home early, allow me to take the test on Dec 1", or "I had a
fight with my girlfriend, which effects my performance", blah blah blah.
Even when they are true, they are still lame.
- No extra work in the next semester given to improve your grade.