Approximation Algorithms Part II

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Approximation Algorithms Part II

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Beschrijving

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About 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 roundi…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About 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.

Created by:  École normale supérieure
  • Taught by:  Claire Mathieu

Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Coursework

Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.

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École normale supérieure L’École normale supérieure (ENS) est un établissement d'enseignement supérieur pour les études prédoctorales et doctorales (graduate school) et un haut lieu de la recherche française. L'ENS offre à 300 nouveaux étudiants et 200 doctorants chaque année une formation de haut niveau, largement pluridisciplinaire, des humanités et sciences sociales aux sciences dures. Régulièrement distinguée au niveau international, l'ENS a formé 10 médailles Fields et 13 prix Nobel.

Syllabus


WEEK 1


Linear Programming Duality
This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.


9 videos, 11 readings, 8 practice quizzes expand


  1. Video: Linear programming duality - example
  2. Reading: Slides
  3. Practice Quiz: Quiz 1
  4. Reading: Comment
  5. Video: Properties of LP duality
  6. Reading: Slides
  7. Practice Quiz: Quiz 2
  8. Video: Geometry of LP duality
  9. Reading: Slides
  10. Practice Quiz: Quiz 3
  11. Reading: Slides
  12. Practice Quiz: Quiz 4
  13. Video: Proof of weak duality theorem
  14. Reading: Slides
  15. Practice Quiz: Quiz 5
  16. Video: Changing the form of the LP
  17. Reading: Slides
  18. Video: Complementary slackness
  19. Practice Quiz: Quiz 6
  20. Video: Primal-dual algorithms
  21. Reading: Slides
  22. Practice Quiz: Quiz 7
  23. Reading: Slides
  24. Practice Quiz: Quiz 8
  25. Video: Vertex cover by primal-dual
  26. Reading: Slides
  27. Video: Conclusion
  28. Reading: Slides-all
  29. Peer Review: Assignment 1


WEEK 2


Steiner Forest and Primal-Dual Approximation Algorithms
This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.


8 videos, 9 readings, 8 practice quizzes expand


  1. Reading: Slides
  2. Practice Quiz: Quiz 1
  3. Video: Problem definition
  4. Reading: Slides
  5. Practice Quiz: Quiz 2
  6. Video: A special case: Steiner tree
  7. Reading: Slides
  8. Practice Quiz: Quiz 3
  9. Video: LP relaxation for Steiner forest
  10. Reading: Slides
  11. Practice Quiz: Quiz 4
  12. Video: ... and its dual
  13. Reading: Slides
  14. Practice Quiz: Quiz 5
  15. Video: Primal-dual algorithm, Part1
  16. Reading: Slides
  17. Practice Quiz: Quiz 6
  18. Video: Primal-dual algorithm,Part 2
  19. Reading: Slides
  20. Practice Quiz: Quiz 7
  21. Video: Analysis
  22. Reading: Slides
  23. Practice Quiz: Quiz 8
  24. Video: Proof of the main lemma
  25. Reading: Slides-all
  26. Peer Review: Assignment 2


WEEK 3


Facility Location and Primal-Dual Approximation Algorithms
This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.


9 videos, 10 readings, 8 practice quizzes expand


  1. Reading: Slides
  2. Practice Quiz: Quiz 1
  3. Video: Problem definition
  4. Reading: Slides
  5. Practice Quiz: Quiz 2
  6. Video: A linear programming relaxation
  7. Reading: Slides
  8. Practice Quiz: Quiz 3
  9. Video: ...and its dual
  10. Reading: Slides
  11. Practice Quiz: Quiz 4
  12. Video: A primal-dual algorithm
  13. Reading: Slides
  14. Practice Quiz: Quiz 5
  15. Video: Analyzing the service cost
  16. Reading: Slides
  17. Practice Quiz: Quiz 6
  18. Video: Analyzing the facility opening cost
  19. Reading: Slides
  20. Practice Quiz: Quiz 7
  21. Video: A better algorithm
  22. Reading: Slides
  23. Practice Quiz: Quiz 8
  24. Video: Analysis
  25. Reading: Slides
  26. Video: Conclusion
  27. Reading: Slides-all
  28. Peer Review: Assignment 3


WEEK 4


Maximum Cut and Semi-Definite Programming
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.


11 videos, 12 readings, 9 practice quizzes expand


  1. Video: Definition
  2. Reading: Slides
  3. Practice Quiz: Quiz 1
  4. Video: A 2-approximation
  5. Reading: Slides
  6. Practice Quiz: Quiz 2
  7. Video: A linear programming relaxation...
  8. Reading: Slides
  9. Practice Quiz: Quiz 3
  10. Reading: Slides
  11. Practice Quiz: Quiz 4
  12. Video: ...with an integrality gap of almost 2
  13. Reading: Slides
  14. Practice Quiz: Quiz 5
  15. Video: Proof of Lemma
  16. Video: A quadratic programming relaxation
  17. Reading: Slides
  18. Practice Quiz: Quiz 6
  19. Reading: Slides
  20. Video: General facts about semidefinite programming
  21. Practice Quiz: Quiz 7
  22. Reading: Slides
  23. Video: A rounding algorithm
  24. Practice Quiz: Quiz 8
  25. Reading: Sldies
  26. Video: Analysis
  27. Practice Quiz: Quiz 9
  28. Video: General facts about MaxCut
  29. Reading: Slides
  30. Reading: Slides-all
  31. Peer Review: Assignment 4
  32. Video: The end!
  33. Reading: Comment

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