CMPT 409/CMPT 815/MATH 796 - Approximation/Randomized Algorithms - Fall 2019

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
Property testing
- Testing sortedness [notes]
- Linearity testing [notes] [notes]
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:
A sample of randomized algorithms:
- computing the area of a ball using MCMC algorithm [notes]