CMPT 409/CMPT 815 - Approximation/Randomized Algorithms - Fall 2020

Course Information Syllabus Lectures Assignments Exams


Lecture 18 - Novemeber 30
Hardness of Approximating CSPs [notes]
Hardness of approximating clique, FGLSS reduction [notes]
Lecture 17 - Novemeber 25
Hardness of Approximation
Probabilistically Checkable Proofs [notes]
Lecture 16 - Novemeber 23
Introduction to Analysis of Boolean Functions [notes]
Linearity testing [notes]
Lecture 15 - Novemeber 18
Sublinear time algorithms
- Approximating diameter [notes]
- Testing sortedness [notes]
Lecture 14 - Novemeber 16
Coloring 3-colorable graphs using SDP [notes]
Lecture 13 - Novemeber 9
Semidefinite Programming [notes]
0.878-approximation for Max-Cut [notes]
Coloring 3-colorable graphs with O(n^0.5) colors [notes]
Midterm solutions - Novemeber 4

Midterm - Novemeber 2
No lecture notes

Review before midterm - October 28

Lecture 12 - October 26
LP duality
- A combinatorial algorithm for weighted vertex cover [notes]
Sherali-Adams LP hierarchy [notes]

Lecture 11 - October 21
Linear Programming Duality [notes]

Lecture 10 - October 19
Linear Programming - more applications
Intergality gaps [notes]
Min cost perfect matching in bipartite graphs [notes]
Beck-Fiala theorem [notes]

Lecture 9 - October 14
Linear Programming - applications [notes]
Weighted min vertex cover
Weighted min set cover

Lecture 8 - October 7
Linear Programming [notes]
Weighted min vertex cover [notes]

Lecture 7 - September 30
Isolation Lemma
Perfect Matchings in Bipartite Graphs [notes]

Lecture 6 - September 28
Polynomial Identity Testing [notes]
Freivalds' algorithm revisited
Perfect Matchings in Bipartite Graphs

Lecture 5 - September 23
A ln(n)-approximation for Set Cover [notes]
log(n)/n-approximation for Max Clique

Lecture 4 - September 21
7/8-approximation for 3CNF - deterministic algorithm
Discrepancy using Chernoff bound [notes]
Approximate DNF counting [notes]

Lecture 3 - September 16
Linearity of expectation
Concentration inequalities [notes]
- Markov's inequality
- Chebyshev inequality
- Chernoff inequality
7/8-approximation of 3CNF

Lecture 2 - September 14
A sample of randomized algorithms:
- computing the area of a ball using MCMC algorithm [notes]
- Freivalds' algorithm for verifying matrix multiplication [wiki]
- Karger's algorithm for min cut [notes]

Lecture 1 - September 9
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]