| Date |
Notes |
Topics |
Additional References |
| Mar 29 |
See textbook Ch 1,2 |
Basic definitions; Cayley’s theorem |
|
| Mar 31 |
See textbook Ch 2 plus text supplement |
Another proof for Cayley’s theorem, finding a
Minimum Spanning Tree in weighted graphs, applications in phylogeny |
|
| Apr 5 |
Notes |
Basic Asymptotics, Introduction to NP-Hardness |
- a compendium of NP optimization problems
- a great book on approximation algorithms
|
| Apr 7 |
See textbook plus handout given in class. |
Eulerian and Hamiltonian Circuits, Euler's Theorem,
applications in bio-informatics: Sequencing by Hybridization |
|
| Apr 12 |
See textbook Ch 5 |
Hall's marriage theorem, system of distinct representatitves |
|
| Apr 14 |
Notes coming soon. |
finding perfect and maximum matchings and minimum vertex cover in bipartite and general graphs |
|
| Apr 19 |
MVV paper |
matching via matrix inversion |
|
| Apr 21 |
MVV paper |
matching via matrix inversion (cont'd) |
matrix inversion using parallel processing
|
| Apr 26 |
See handout given in class. |
stable matching |
|
| Apr 28 |
See handout given in class. |
stable matching |
Three books on stable marriage problem:
Donald Knuth, et al,
Al Roth, et al,
Dan Gusfield, et al
|
| May 3 |
|
Max Flow - Min Cut Theorem, Algorithms, Menger's Theorem |
Textbook Ch 7
|
| May 5 |
Textbook Ch 6 |
Dilworth's Theorem, Extremal Set Theory |
|
| May 10 |
Lecture Notes Coming Soon. |
Linear Programs, Duality, Applications to Network Flow |
|
| May 12 |
For definitions, see textbook Ch 3 |
Graph Coloring, Chromatic Number of a Graph, Brook's Theorem |
|
| May 17 |
|
Midterm - No lecture |
|
| May 19 |
Handout |
The Probabilistic Method |
A great book
by Alon and Spencer
|
| May 24 |
Coming Soon |
Planar Graphs and Four Coloring Theorem |
|
| May 26 |
Notes |
Random Walks and Spectral Graph Theory |
- A course on Spectral Graph Theory by Spielman
- A book on the relationship between random walks and electrical networks.
|