Math/AMath 514, Networks and Combinatorial Optimization, Autumn 2019
Instructor : Rekha R. Thomas
 Office : Padelford C438
 Office hours : Monday 35 pm
Teaching Assistant : Daiwei He
 Office : Padelford C8B
 Office hours : Tuesday 13 pm
Course Information
 Description : This is a graduate class on the
fundamentals of network optimization (aka combinatorial optimization).
The majority of these problems involve finding the "best" candidate
among a set of objects associated with a network/directed graph. Many
of these problems come from realworld applications and as such it is
important to solve large instances of these problems in
practice. Therefore, along with understanding the mathematical
structure of the problems, we will also be interested in algorithms
for solving them and the complexity/difficulty of these algorithms
from a computer science point of view. This is a rigorous mathematical
introduction to network optimization with proofs. Students are expected
to solve both theoretical and practical problems in homework, and write
mathematical proofs.
 Lecture : CMU 326, MW 9:0010:15
 Textbook : There is no official textbook for the class.
The lectures will follow notes written by Lex Schrijver that you can find
here. You are encouraged to
read additional materials to help your understanding. Here are some of
the popular books on combinatorial optimization that you can consult
as needed:
 Additional References :
 J. Lee, A First Course in Combinatorial Optimization, Cambridge University Press, 2004.
 W. Cook, W. Cunningham, W. Pulleyblank and A. Schrijver, Combinatorial Optimization.
 C. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, PrenticeHall, 19
82.
 B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms, Algorithms and Combinatorics 21 S
pringer, Berlin Heidelberg New York, 2006.
 3volume book by A. Schrijver, Combinatorial Optimization: Polyhedra and Efficiency , SpringerVerlag, 2003.
 Required Work:
 There will be daily reading assignments from the book. I will
cover essentials but many of the details and discussions will be left
as reading assignments.
 Your grade will be based on class participation and homework
assignments. It is crucial that homeworks are
done by yourself. Homeworks are due weekly on (most) Wednesdays in
class. Some announcements are only
made in class and so please do not rely on just the information on
this website to keep up with the class.
 NO EXAMS
ASSIGNMENTS

To read before the quarter starts : Chapter 6 in Schrijver's
notes on "Problems, Algorithms and Running Times". Chapter 6 is
essential for the whole course and can be read independently of all
other chapters.

Homework 1 (due in class on Wednesday Oct 2)
Exercises from Chapter 1 of Schrijver's notes: 1.7, 1.8, 1.9, 1.11
9/25: Reading: Section 1.4 in Schrijver's notes
9/30: Reading: Section 10.1
10/2: Reading: Section 2.1
Homework 2 (due in class on Wednesday Oct 9)
Exercises 10.1, 2.2, 2.4, 2.5
10/7: Reading: Section 2.1,2.2
10/9: Reading: Section 2.2,2.3
Homework 2 (due in class on Wednesday Oct 16)
Exercises 2.6(ii), 2.8, 2.16, 2.21
10/14: Reading: Section 2.3, 2.4
10/16: Reading: Section 2.4
Homework 4 (due in class on Wednesday Oct 23)
Exercises 2.23, 2.26, 2.27, 2.28
for the last problem you can find the definition of C^* in problem 2.13
10/21: Reading: Section 3.1, 3.2
10/23: Reading: Section 3.3, 3.4
Homework 5 (due in class on Wednesday Oct 30)
Exercises 3.3, 3.11, 3.17, 3.19
10/28: Reading: Section 3.6, 8.1, 8.2
10/30: Reading: Section 8.2, 8.3
Homework 6 (due in class on Wednesday Nov 13)
Exercises 3.25, 8.4, 8.7, 8.14, 8.16
11/13: Reading: Section 4.2, 8.4
11/18: Reading: Section 4.3
Homework 7 (due in class on Wednesday Nov 20)
Problems 1.1, 1.2 (ii), 1.4, 1.5
Explain why the model in used in problem 1.1 works
11/20: Reading: Section 4.3, 4.5, 4.6
Homework 8 (due in class on Wednesday !!! Dec 4 !!!)
Exercises 4.7(ii), 4.9, 4.10, 4.11, 4.15,
Explain why the model in Application 4.4 on pp 73 works.
11/25: Reading:
Applications of max flow (from Cook, Cunningham, Pulleyblank and Schrijver)