| Prerequisites: |
Linear algebra. Some previous exposure to graph theory may be helpful, but is definitely not necessary. |
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| Instructor: | Victor Reiner (You can call me "Vic"). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Office: Vincent Hall 256 Telephone (with voice mail): (612) 625-6682 E-mail: reiner@math.umn.edu |
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| Classes: |
Monday, Wednesday 11:55 A.M. - 01:10 P.M. in Vincent Hall 211 |
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| Office hours: | Mon, Tue, Wed at 11:15am, also Wed at 3pm, and by appointment. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Course content: |
This is a junior-senior level undergrad course on various methods
and algorithms used in combinatorial optimization. Topics we hope to discuss include:
Industrial Engineering 5531 and 8531 (Engineering Optimization I and II). Since this course is in mathematics, don't be surprised if the focus is a little different, e.g. if we prove things more, and ask you to explain or prove things more often. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Texts: |
There are two texts we will use, and our homework will come from both:
in Maple, Mathematica, and MATLAB. |
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| Level | Title | Author(s), Publ. info | Location |
|---|---|---|---|
| Same or lower | Optimization in operations research | Ronald L. Rardin, Prentice Hall 1998 | In Walter library, call no.T57.7 .R37 1998 |
| Linear programming and its applications | J. K. Strayer, Springer-Verlag 1989 | On reserve in math library | |
| Introduction to linear optimization | D. Bertsimas and J.N. Tsitsiklis, Athena Scientific, 1997. | In Walter library, call no. T57.74 .B465 | |
| Introduction to operations research | F. Hillier and G. Lieberman, Holden-Day 1986 | On reserve in math library | |
| Linear programming: methods and applications | S. Gass, McGraw-Hill 1985 | On reserve in math library | |
| Higher | Theory of linear and integer programming | A. Schrijver, Wiley and Sons 1998 | On reserve in math library |
| Combinatorial optimization: algorithms and complexity | C. Papadimitriou and K. Steiglitz, Dover reprints | In Walter library, call no. QA402.5 .P37 |
| Topic | Title | Author(s), Publ. info | Location |
|---|---|---|---|
| Graph algorithms/theorems | Intro. to Graph theory, 2nd edition | D. West, Prentice Hall 2001 | On reserve in math library |
| Stable matching | Stable marriage and its relation to other combinatorial problems |
D.E. Knuth, Amer. Math. Society 1997 | In math library, call no. QA164 .K5913 1997 |
| Homework and exams: | There will be 6 homework assignments due generally every other week,
except for
Late homework will not be accepted. Early homework is fine, and can be left in my mailbox in the School of Math mailroom near Vincent Hall 105. Collaboration is encouraged as long as everyone collaborating understands thoroughly the solution, and you write up the solution in your own words, along with a note at the top of the homework indicating with whom you've collaborated. Homework solutions should be well-explained-- the grader will be told not to give credit for an unsupported answer. |
| Grading: |
Homework = 50% of grade Each of 2 midterms = 15% of grade Final exam 20% of grade. Complaints about the grading should be brought to me. |
| Policy on incompletes: | Incompletes will be given only in exceptional circumstances, where the student has completed almost the entire course with a passing grade, but something unexpected happens to prevent completion of the course. Incompletes will never be made up by taking the course again later. You must talk to me before the final exam if you think an incomplete may be warranted. |
| Other expectations | This is a 4-credit course, so I would guess that the average student should spend about 8 hours per week outside of class to get a decent grade. Part of this time each week would be well-spent making a first pass through the material in the book that we anticipate to cover in class that week, so that you can bring your questions/confusions to class and ask about them. |
| Assignment or Exam | Due date | Problems from the text |
|---|---|---|
| Homework 1 | Wed Feb. 1 |
All from Chvatal: 1.1, 1.2, 1.3, 1.4, 1.6, 2.1(a) (via dictionaries; show each dictionary and pivot step), 2.1(b) (via tableaux; show each tableau and pivot step), 2.2, 3.1, 3.9(a,b) |
| Homework 2 | Wed Feb. 15 |
All from Chvatal: 4.1(a,b), 17.1(a,b), 5.1(a,b), 5.4, (9.1, 9.2 removed from this HW) |
| Midterm exam 1 | Wed. Feb. 22 | Midterm exam 1 in PostScript, PDF |
| Homework 3 | Wed Mar. 8 |
All from Chvatal: 7.1(a), 9.3, 11.1, 15.1, 15.5, 15.12 |
| Homework 4 | Wed Mar. 29 |
From Schrijver: 2.24, 1.1, 1.2(i), 1.4, 1.6 (1.7 removed from this HW) Not from Schrijver: Solve the integer programming problem max{y: 8x+3y <= 12, -3x+y <= 0, x,y >=0, integers} (a) graphically (i.e. by inspection of a picture), (b) using branch-and-bound, in which each LP is solved graphically, (c) using Gomory cutting planes (with each LP solved by any means, including computer) |
| Midterm exam 2 | Wed. Apr. 5 | Midterm exam 2 in PostScript, PDF |
| Homework 5 | Wed Apr. 19 |
From Schrijver: 1.7, 1.10, 3.2, 3.3, 3.4, 3.5, 3.17, 3.18, 3.23(i) |
| Homework 6 | Wed Apr. 26 (note 1-week due date!) |
From Schrijver: 5.7(i) Not from Schrijver: Problems 2 and 3 regarding the Gale-Shapley algorithm from this extra problem sheet in PostScript, PDF |
| Final exam | Wed. May 3 | Final exam in PostScript, PDF |