18.438 Advanced Combinatorial Optimization
September 29, 2009
Lecture 6
Lecturer: Michel X. Goemans
Scribe: Debmalya Panigrahi
In this lecture, we will focus on Total Dual Integrality (TDI) and its application to the matching
polytope. We will also introd
18.438 Advanced Combinatorial Optimization
October 15, 2009
Lecture 9
Lecturer: Michel X. Goemans
Scribes: Shashi Mittal*
(*This scribe borrows material from scribe notes by Nicole Immorlica in the previous oering of
this course.)
1
Circuits
Denition 1 Le
18.438 Advanced Combinatorial Optimization
October 20, 2009
Lecture 10
Lecturer: Michel X. Goemans
Scribe: Anthony Kim
These notes are based on notes by Nicole Immorlica, Fumei Lam, and Vahab Mirrokni from 2004.
1
Matroid Optimization
We consider the prob
18.438 Advanced Combinatorial Optimization
October 22, 2009
Lecture 11: Matroid Intersection
Lecturer: Michel X. Goemans
1
Scribe: Jacob Steinhardt
Overview
The main goal of this lecture is to prove the min-max relation from last time regarding the
maximu
18.438 Advanced Combinatorial Optimization
November 12, 2009
Lecture 19
Lecturer: Michel X. Goemans
Scribe: Juliane Dunkel
(These notes are based on notes by Jan Vondrk and Mohammed Mahdian.)
a
In the last lecture, we showed that every 2k-edge-connected g
18.438 Advanced Combinatorial Optimization
Updated April 29, 2012
Lecture 16
Lecturer: Michel X. Goemans
Scribe: Jos Soto (2009)
e
The lecture started with some additional discussion of matroid matching and this was
included in the previous scribe notes.
18.438 Advanced Combinatorial Optimization
Updated April 29, 2012
Lecture 20
Lecturer: Michel X. Goemans
Scribe: Claudio Telha (Nov 17, 2009)
Given a nite set V with n elements, a function f : 2V Z is submodular if for all X, Y V ,
f (X Y ) + f (X Y ) f (
18.438 Advanced Combinatorial Optimization
8 October 2009
Lecture 8: Matroids
Lecturer: Michel X. Goemans
Scribe: Elette Boyle*
(*Based on notes from Bridget Eileen Tenner and Nicole Immorlica.)
1
Matroids
1.1
Denitions and Examples
Denition 1 A matroid M
18.438 Advanced Combinatorial Optimization
September 15, 2009
Lecture 2
Lecturer: Michel X. Goemans
Scribes: Robert Kleinberg (2004), Alex Levin (2009)
In this lecture, we will present Edmondss algorithm for computing a maximum matching in a
(not necessar
18.997 Topics in Combinatorial Optimization
February 3rd, 2004
Lecture 1
Lecturer: Michel X. Goemans
1
Scribe: Nick Harvey
Nonbipartite Matching
Our rst topic of study is matchings in graphs which are not necessarily bipartite. We begin with
some relevant
18.438 Advanced Combinatorial Optimization
September 17, 2009
Lecture 3
Scribe: Aleksander Madry
Lecturer: Michel X. Goemans
( Based on notes by Robert Kleinberg and Dan Stratila.)
In this lecture, we will:
Present the Edmonds-Gallai decomposition of a g
18.438 Advanced Combinatorial Optimization
Updated February 18, 2012
Lecture 4
Lecturer: Michel X. Goemans
Scribe: Yufei Zhao (2009)
In this lecture, we discuss some results on edge coloring and also introduce the notion
of nowhere-zero ows.
1
Petersens T
Massachusetts Institute of Technology
18.433: Combinatorial Optimization
Michel X. Goemans
Handout 5
February 13th, 2011
2. Lecture notes on non-bipartite matching
Given a graph G = (V, E ), we are interested in nding and charaterizing the size of a
maxim
18.438 Advanced Combinatorial Optimization
Updated February 18, 2012.
Lecture 5
Lecturer: Michel X. Goemans
Scribe: Yehua Wei (2009)
In this lecture, we establish the connection between nowhere-zero k -ows and nowhere-zero
Zk -ows. Then, we present severa