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
18.997 Topics in Combinatorial Optimization
9 March 2004
Matroids
Lecturer: Michel X. Goemans
Scribe: Bridget Eileen Tenner
For reference, see Chapter 39 of Schrijvers book.
Denition 1 A matroid M = (
18.997 Topics in Combinatorial Optimization
April 6th, 2004
Lecture 15
Lecturer: Michel X. Goemans
1
Scribe: Supratim Deb
Matroid Matching
The Matroid matching Problem: Given a matroid M = (S, I ), le
April 8, 2004
18.997 Topics in Combinatorial Optimization
Lecture 16
Lecturer: Michel X. Goemans
Scribe: Jonathan Kelner
This lecture is about jump systems. While they are briey discussed in chapter 4
April 27, 2004
18.997 Topics in Combinatorial Optimization
Lecture 20
Lecturer: Michel X. Goemans
1
Scribe: Jan Vondrk
a
k -arc-connected orientations
We continue the discussion of how a 2k -edge-conn
April 22th, 2004
18.997 Topics in Combinatorial Optimization
Lecture 19
Lecturer: Michel X. Goemans
1
Scribe: Ben Recht
Special cases of submodular ows
We saw last time that orientation of a 2k -edge
March 4, 2004
18.997 Topics in Combinatorial Optimization
Lecture 8
Lecturer: Michel X. Goemans
Scribe: Constantine Caramanis
This lecture covers the proof of the Bessy-Thomass Theorem, formerly known
18.997 Topics in Combinatorial Optimization
March 2, 2004
Lecture 7
Lecturer: Michel X. Goemans
1
Scribe: Jan Vondrk
a
Gallais Conjecture
In this lecture, we will be concerned with graph coverings by
18.997 Topics in Combinatorial Optimization
February 10th, 2004
Lecture 3
Lecturer: Michel X. Goemans
Scribe: Dan Stratila
In this lecture we will cover:
1. Topics related to Edmonds-Gallai decomposit
18.997 Topics in Combinatorial Optimization
February 5, 2004
Lecture 2
Lecturer: Michel X. Goemans
Scribe: Robert Kleinberg
In this lecture, we will:
Present Edmonds algorithm for computing a maximum
February 12, 2004
18.997 Topics in Combinatorial Optimization
Lecture 4
Lecturer: Michel X. Goemans
Scribe: Constantine Caramanis
This lecture covers: the Matching polytope, total dual integrality, an
18.997 Topics in Combinatorial Optimization
February 24th, 2004
Lecture 7
Lecturer: Michel X. Goemans
Scribe: Ben Recht
In this lecture, we investigate the relationship between total dual integrality
18.997 Topics in Combinatorial Optimization
February 26th, 2004
Lecture 6
Lecturer: Michel X. Goemans
Scribe: Joungkeun Lim
Last time, we saw that the matching polytope was dened by:
x( (v ) 1 v V
x(E
18 March 2004
18.997 Topics in Combinatorial Optimization
Lecture 12
Lecturer: Michel X. Goemans
Scribe: Vahab S. Mirrokni
Last time, we stated the following theorem by Edmonds and Lawler about the ma
18.997 Topics in Combinatorial Optimization
March 4, 2004
Lecture 8
Lecturer: Michel X. Goemans
Scribe: Constantine Caramanis
This lecture covers the proof of the Bessy-Thomass Theorem, formerly known
18.997 Topics in Combinatorial Optimization
April 1st, 2004
Lecture 14
Lecturer: Michel X. Goemans
Scribe: Mohamed Mostagir
In this lecture, we continue with more results on matroid union, as well as
18.997 Topics in Combinatorial Optimization
February 5, 2004
Lecture 2
Lecturer: Michel X. Goemans
Scribe: Robert Kleinberg
In this lecture, we will:
Present Edmonds algorithm for computing a maximu
18.997 Topics in Combinatorial Optimization
February 10th, 2004
Lecture 3
Lecturer: Michel X. Goemans
Scribe: Dan Stratila
In this lecture we will cover:
1. Topics related to Edmonds-Gallai decomposit
18.997 Topics in Combinatorial Optimization
February 12, 2004
Lecture 4
Lecturer: Michel X. Goemans
Scribe: Constantine Caramanis
This lecture covers: the Matching polytope, total dual integrality, an
18.997 Topics in Combinatorial Optimization
February 24th, 2004
Lecture 5
Lecturer: Michel X. Goemans
Scribe: Ben Recht
In this lecture, we investigate the relationship between total dual integrality
18.997 Topics in Combinatorial Optimization
February 26th, 2004
Lecture 6
Lecturer: Michel X. Goemans Last time, we saw that the matching polytope was dened by: x( (v ) 1 v V x(E (S ) |S | , for |S |
18.997 Topics in Combinatorial Optimization
18 March 2004
Lecture 12
Lecturer: Michel X. Goemans
Scribe: Vahab S. Mirrokni
Last time, we stated the following theorem by Edmonds and Lawler about the ma
18.997 Topics in Combinatorial Optimization
March 30, 2004
Lecture 13
Lecturer: Michel X. Goemans
Scribe: Constantine Caramanis
Last lecture we covered matroid intersection, and dened matroid union. I
18.997 Topics in Combinatorial Optimization
March 2, 2004
Lecture 7
Lecturer: Michel X. Goemans
1
Scribe: Jan Vondrk
a
Gallais Conjecture
In this lecture, we will be concerned with graph coverings by
18.997 Topics in Combinatorial Optimization
16 March 2004
Lecture 11
Lecturer: Michel X. Goemans
Scribe: Fumei Lam
Let M1 = (S, I1 ), M2 = (S, I2 ) be two matroids on common ground set S with rank fun
18.997 Topics in Combinatorial Optimization
9 March 2004
Matroids
Lecturer: Michel X. Goemans
Scribe: Bridget Eileen Tenner
For reference, see Chapter 39 of Schrijvers book.
Denition 1 A matroid M = (
18.997 Topics in Combinatorial Optimization
March 11, 2004
Lecture 10
Lecturer: Michel X. Goemans
Scribe: Nicole Immorlica
Matroid theory was rst formalized in 1935 by Whitney [5] who introduced the n
18.997 Topics in Combinatorial Optimization
April 6th, 2004
Lecture 15
Lecturer: Michel X. Goemans
1
Scribe: Supratim Deb
Matroid Matching
The Matroid matching Problem: Given a matroid M = (S, I ), le
February 3rd, 2004
18.997 Topics in Combinatorial Optimization
Lecture 1
Lecturer: Michel X. Goemans
1
Scribe: Nick Harvey
Nonbipartite Matching
Our rst topic of study is matchings in graphs which are