| Course Information | Syllabus | Lectures | Assignments | Exams |
| Lecture 23 - November 19 |
Probabilistically checkable proofs - introduction
Exponential length PCP
[notes]
|
| Lecture 22 - November 14 |
Probabilistically checkable proofs - introduction
[notes]
|
| Lecture 21 - November 12 |
Introduction to Analysis of Boolean Functions
[notes]
|
| Lecture 20 - November 7 |
Introduction to Analysis of Boolean Functions
[notes]
Linearity testing
[notes]
|
| Lecture 19 - November 5 | |
| Lecture 18 - October 31 |
Coloring 3-colorable graphs cont.
[notes]
|
| Lecture 17 - October 29 |
Coloring 3-colorable graphs
[notes]
|
| Lecture 16 - October 24 |
Goemans-Williamson algorithm for Maxcut
[notes]
|
| Lecture 15 - October 22 |
Semidefinite programming
[notes]
|
| Lecture 14 - October 17 |
Sherali-Adams LP hierarchy cont.
Integrality gaps
|
| Lecture 13 - October 15 |
LP duality
- A combinatorial algorithm for weighted vertex cover
[notes]
Sherali-Adams LP hierarchy
[notes]
|
| Lecture 12 - October 10 |
LP duality
[notes]
|
| Lecture 11 - October 8 |
LP applications: three examples
- Weighted min vertex cover
[notes]
- Weighted set cover
[notes]
- Min cost perfect matching in bipartite graphs
[notes]
|
| Lecture 10 - October 3 |
LP applications: Beck-Fiala theorem
[notes]
|
| Lecture 9 - October 1 |
Finding a min-cost perfect matching in bipartite graphs
- Isolation lemma
[notes]
Linear programming
[notes]
|
| Lecture 8 - September 26 |
Finding perfect matching in bipartite graphs
[notes]
|
| Lecture 7 - September 24 |
Polynomial identity testing
[notes]
Freivalds' algorithm revisited
|
| Lecture 6 - September 19 |
A ln(n)-approximation for Set Cover
[notes]
A n/log(n) approximation for Max Clique
|
| Lecture 5 - September 17 |
Approximate DNF counting - cont.
[notes]
An FPT algorithm for Vertex Cover
[notes]
|
| Lecture 4 - September 12 |
Discrepancy using Chernoff bound
[notes]
Approximate DNF counting
[notes]
|
| Lecture 3 - September 10 |
Linearity of expectation
Concentration inequalities
[notes]
- Markov's inequality
- Chebyshev inequality
- Chernoff inequality
7/8-approximation of 3CNF
|
| Lecture 2 - September 5 |
A sample of randomized algorithms:
- Freivalds' algorithm for cheking that AB=C for three matrices
[wiki]
- Karger's algorithm for min cut
[notes]
|
| Lecture 1 - September 3 |
Introduction
A sample of approximation algorithms:
- 2-approximation of the minimum vertex cover
[notes]
- More advanced results:
-- [Karakostas]
A sample of randomized algorithms:
- computing the area of a ball using MCMC algorithm
[notes]
|