Approximation Algorithms Part II
Keep adding new skills with 10,000+ programs for $239 (usually $399). Save now.
Ask Coursera
47 reviews
47 reviews
Details to know
See how employees at top companies are mastering in-demand skills
There are 4 modules in this course
Approximation algorithms, Part 2
This is the continuation of Approximation algorithms, Part 1. Here you will learn linear programming duality applied to the design of some approximation algorithms, and semidefinite programming applied to Maxcut. By taking the two parts of this course, you will be exposed to a range of problems at the foundations of theoretical computer science, and to powerful design and analysis techniques. Upon completion, you will be able to recognize, when faced with a new combinatorial optimization problem, whether it is close to one of a few known basic problems, and will be able to design linear programming relaxations and use randomized rounding to attempt to solve your own problem. The course content and in particular the homework is of a theoretical nature without any programming assignments. This is the second of a two-part course on Approximation Algorithms.
This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.
What's included
9 videos11 readings8 assignments1 peer review
9 videos•Total 87 minutes
- Linear programming duality - example•15 minutes
- Properties of LP duality•6 minutes
- Geometry of LP duality•10 minutes
- Proof of weak duality theorem•6 minutes
- Changing the form of the LP•11 minutes
- Complementary slackness•6 minutes
- Primal-dual algorithms•6 minutes
- Vertex cover by primal-dual•23 minutes
- Conclusion•4 minutes
11 readings•Total 110 minutes
- Slides•10 minutes
- Comment•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides-all•10 minutes
8 assignments•Total 240 minutes
- Quiz 1•30 minutes
- Quiz 2•30 minutes
- Quiz 3•30 minutes
- Quiz 4•30 minutes
- Quiz 5•30 minutes
- Quiz 6•30 minutes
- Quiz 7•30 minutes
- Quiz 8•30 minutes
1 peer review•Total 120 minutes
- Assignment 1•120 minutes
This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.
What's included
8 videos9 readings8 assignments1 peer review
8 videos•Total 73 minutes
- Problem definition•3 minutes
- A special case: Steiner tree•12 minutes
- LP relaxation for Steiner forest•6 minutes
- ... and its dual•5 minutes
- Primal-dual algorithm, Part1•11 minutes
- Primal-dual algorithm,Part 2•13 minutes
- Analysis•14 minutes
- Proof of the main lemma•9 minutes
9 readings•Total 90 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides-all•10 minutes
8 assignments•Total 240 minutes
- Quiz 1•30 minutes
- Quiz 2•30 minutes
- Quiz 3•30 minutes
- Quiz 4•30 minutes
- Quiz 5•30 minutes
- Quiz 6•30 minutes
- Quiz 7•30 minutes
- Quiz 8•30 minutes
1 peer review•Total 120 minutes
- Assignment 2•120 minutes
This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.
What's included
9 videos10 readings8 assignments1 peer review
9 videos•Total 64 minutes
- Problem definition•5 minutes
- A linear programming relaxation•4 minutes
- ...and its dual•8 minutes
- A primal-dual algorithm•8 minutes
- Analyzing the service cost•7 minutes
- Analyzing the facility opening cost•8 minutes
- A better algorithm•12 minutes
- Analysis•8 minutes
- Conclusion•4 minutes
10 readings•Total 100 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides-all•10 minutes
8 assignments•Total 240 minutes
- Quiz 1•30 minutes
- Quiz 2•30 minutes
- Quiz 3•30 minutes
- Quiz 4•30 minutes
- Quiz 5•30 minutes
- Quiz 6•30 minutes
- Quiz 7•30 minutes
- Quiz 8•30 minutes
1 peer review•Total 60 minutes
- Assignment 3•60 minutes
We introduce a generalization of linear programming, semi-definite programming.This module uses semi-definite programming to design an approximation algorithm for another basic problem, the maximum cut problem.
What's included
11 videos12 readings9 assignments1 peer review
11 videos•Total 76 minutes
- Definition•5 minutes
- A 2-approximation•5 minutes
- A linear programming relaxation...•12 minutes
- ...with an integrality gap of almost 2•11 minutes
- Proof of Lemma•7 minutes
- A quadratic programming relaxation•4 minutes
- General facts about semidefinite programming•8 minutes
- A rounding algorithm•7 minutes
- Analysis•6 minutes
- General facts about MaxCut•6 minutes
- The end!•4 minutes
12 readings•Total 120 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Slides•10 minutes
- Sldies•10 minutes
- Slides•10 minutes
- Slides-all•10 minutes
- Comment•10 minutes
9 assignments•Total 270 minutes
- Quiz 1•30 minutes
- Quiz 2•30 minutes
- Quiz 3•30 minutes
- Quiz 4•30 minutes
- Quiz 5•30 minutes
- Quiz 6•30 minutes
- Quiz 7•30 minutes
- Quiz 8•30 minutes
- Quiz 9•30 minutes
1 peer review•Total 120 minutes
- Assignment 4•120 minutes
Instructor
Offered by
Explore more from Algorithms
- Status: FreeÉ
École normale supérieure
Course
- 2
28DIGITAL
Course
- Status: Free TrialU
University of Colorado Boulder
Course
- Status: FreeP
Princeton University
Course
Why people choose Coursera for their career
Learner reviews
- 5 stars
87.23%
- 4 stars
6.38%
- 3 stars
4.25%
- 2 stars
2.12%
- 1 star
0%
Showing 3 of 47
Reviewed on Oct 27, 2016
Demanding course with lots of great algorithm concepts based on Linear Programming.
Reviewed on Mar 13, 2016
It is remarkable to note that Professor Claire Mathieu explains such a complex subject in such a elegant and understandable manner.
Reviewed on Feb 15, 2017
Even better than the first! Very good classes (except for the two first of week 3 ...)
Frequently asked questions
To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
More questions
Financial aid available,
¹ Some assignments in this course are AI-graded. For these assignments, your data will be used in accordance with Coursera's Privacy Notice.
