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Approximation Algorithms Part II

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Approximation Algorithms Part II

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Gain insight into a topic and learn the fundamentals.
4.8

47 reviews

4 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

Gain insight into a topic and learn the fundamentals.
4.8

47 reviews

4 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

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 videosTotal 87 minutes
  • Linear programming duality - example15 minutes
  • Properties of LP duality6 minutes
  • Geometry of LP duality10 minutes
  • Proof of weak duality theorem6 minutes
  • Changing the form of the LP11 minutes
  • Complementary slackness6 minutes
  • Primal-dual algorithms6 minutes
  • Vertex cover by primal-dual23 minutes
  • Conclusion4 minutes
11 readingsTotal 110 minutes
  • Slides10 minutes
  • Comment10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides-all10 minutes
8 assignmentsTotal 240 minutes
  • Quiz 130 minutes
  • Quiz 230 minutes
  • Quiz 330 minutes
  • Quiz 430 minutes
  • Quiz 530 minutes
  • Quiz 630 minutes
  • Quiz 730 minutes
  • Quiz 830 minutes
1 peer reviewTotal 120 minutes
  • Assignment 1120 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 videosTotal 73 minutes
  • Problem definition3 minutes
  • A special case: Steiner tree12 minutes
  • LP relaxation for Steiner forest6 minutes
  • ... and its dual5 minutes
  • Primal-dual algorithm, Part111 minutes
  • Primal-dual algorithm,Part 213 minutes
  • Analysis14 minutes
  • Proof of the main lemma9 minutes
9 readingsTotal 90 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides-all10 minutes
8 assignmentsTotal 240 minutes
  • Quiz 130 minutes
  • Quiz 230 minutes
  • Quiz 330 minutes
  • Quiz 430 minutes
  • Quiz 530 minutes
  • Quiz 630 minutes
  • Quiz 730 minutes
  • Quiz 830 minutes
1 peer reviewTotal 120 minutes
  • Assignment 2120 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 videosTotal 64 minutes
  • Problem definition5 minutes
  • A linear programming relaxation4 minutes
  • ...and its dual8 minutes
  • A primal-dual algorithm8 minutes
  • Analyzing the service cost7 minutes
  • Analyzing the facility opening cost8 minutes
  • A better algorithm12 minutes
  • Analysis8 minutes
  • Conclusion4 minutes
10 readingsTotal 100 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides-all10 minutes
8 assignmentsTotal 240 minutes
  • Quiz 130 minutes
  • Quiz 230 minutes
  • Quiz 330 minutes
  • Quiz 430 minutes
  • Quiz 530 minutes
  • Quiz 630 minutes
  • Quiz 730 minutes
  • Quiz 830 minutes
1 peer reviewTotal 60 minutes
  • Assignment 360 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 videosTotal 76 minutes
  • Definition5 minutes
  • A 2-approximation5 minutes
  • A linear programming relaxation...12 minutes
  • ...with an integrality gap of almost 211 minutes
  • Proof of Lemma7 minutes
  • A quadratic programming relaxation4 minutes
  • General facts about semidefinite programming8 minutes
  • A rounding algorithm7 minutes
  • Analysis6 minutes
  • General facts about MaxCut6 minutes
  • The end!4 minutes
12 readingsTotal 120 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Slides10 minutes
  • Sldies10 minutes
  • Slides10 minutes
  • Slides-all10 minutes
  • Comment10 minutes
9 assignmentsTotal 270 minutes
  • Quiz 130 minutes
  • Quiz 230 minutes
  • Quiz 330 minutes
  • Quiz 430 minutes
  • Quiz 530 minutes
  • Quiz 630 minutes
  • Quiz 730 minutes
  • Quiz 830 minutes
  • Quiz 930 minutes
1 peer reviewTotal 120 minutes
  • Assignment 4120 minutes

Instructor

École normale supérieure
2 Courses32,642 learners

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AP
·

Reviewed on Oct 27, 2016

Demanding course with lots of great algorithm concepts based on Linear Programming.

RA
·

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.

PV
·

Reviewed on Feb 15, 2017

Even better than the first! Very good classes (except for the two first of week 3 ...)

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