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 3colorable graphs cont.
[notes]

Lecture 17  October 29 
Coloring 3colorable graphs
[notes]

Lecture 16  October 24 
GoemansWilliamson algorithm for Maxcut
[notes]

Lecture 15  October 22 
Semidefinite programming
[notes]

Lecture 14  October 17 
SheraliAdams LP hierarchy cont.
Integrality gaps

Lecture 13  October 15 
LP duality
 A combinatorial algorithm for weighted vertex cover
[notes]
SheraliAdams 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: BeckFiala theorem
[notes]

Lecture 9  October 1 
Finding a mincost 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
7/8approximation 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:
 2approximation 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]
