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Approximation Algorithms Part II
  • Level Foundation
  • المدة 33 ساعات hours
  • الطبع بواسطة École normale supérieure
  • Offered by

عن

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.

الوحدات

Duality by example

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    • 2 Readings
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1 Assignment

  • Quiz 1

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  • Linear programming duality - example

2 Readings

  • Slides
  • Comment

Properties of LP duality

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1 Assignment

  • Quiz 2

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  • Properties of LP duality

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Geometry of LP duality

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  • Quiz 3

1 Videos

  • Geometry of LP duality

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Proof of weak duality

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  • Quiz 4

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  • Proof of weak duality theorem

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Changing the form of the LP

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  • Quiz 5

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  • Changing the form of the LP

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Complementary slackness

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  • Quiz 6

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  • Complementary slackness

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Primal-dual algorithms

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  • Quiz 7

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  • Primal-dual algorithms

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Vertex Cover by primal-dual

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  • Quiz 8

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  • Vertex cover by primal-dual

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Conclusion

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  • Conclusion

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Exercises

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1 Peer Review

  • Assignment 1

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Problem definition

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  • Quiz 1

1 Videos

  • Problem definition

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A special case: Steiner tree

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  • Quiz 2

1 Videos

  • A special case: Steiner tree

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A LP relaxation for Steiner forest...

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  • Quiz 3

1 Videos

  • LP relaxation for Steiner forest

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...and its dual

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  • Quiz 4

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  • ... and its dual

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Primal-dual algorithm, Part 1

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  • Quiz 5

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  • Primal-dual algorithm, Part1

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Primal-dual algorithm, Part 2

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  • Quiz 6

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  • Primal-dual algorithm,Part 2

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Analysis

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  • Quiz 7

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  • Analysis

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Proof of the main lemma

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  • Quiz 8

1 Videos

  • Proof of the main lemma

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Exercises

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1 Peer Review

  • Assignment 2

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Problem definition

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  • Quiz 1

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  • Problem definition

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A linear programming relaxation...

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  • Quiz 2

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  • A linear programming relaxation

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... and its dual

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  • Quiz 3

1 Videos

  • ...and its dual

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A primal-dual algorithm

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  • Quiz 4

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  • A primal-dual algorithm

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Analyzing the service cost

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  • Quiz 5

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  • Analyzing the service cost

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Analyzing the facility opening cost

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  • Quiz 6

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  • Analyzing the facility opening cost

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A better primal-dual algorithm

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  • Quiz 7

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  • A better algorithm

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Analysis

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  • Quiz 8

1 Videos

  • Analysis

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Conclusion

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  • Conclusion

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Exercises

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    • 1 PeerReview
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1 Peer Review

  • Assignment 3

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Definition

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  • Quiz 1

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  • Definition

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A 2-approximation

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  • Quiz 2

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  • A 2-approximation

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A linear programming relaxation...

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  • Quiz 3

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  • A linear programming relaxation...

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... that has an integrality gap of almost 2 (overview)

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  • Quiz 4

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  • ...with an integrality gap of almost 2

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Proof of lemma

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  • Quiz 5

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  • Proof of Lemma

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A quadratic programming relaxation

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  • Quiz 6

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  • A quadratic programming relaxation

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General facts about semidefinite programming

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  • Quiz 7

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  • General facts about semidefinite programming

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A rounding algorithm

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  • Quiz 8

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  • A rounding algorithm

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Analysis

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  • Quiz 9

1 Videos

  • Analysis

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  • Sldies

General facts about Maxcut

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  • General facts about MaxCut

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Exercises

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    • 1 PeerReview
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1 Peer Review

  • Assignment 4

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  • The end!

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Auto Summary

Dive deeper into the world of Approximation Algorithms with Part II, focusing on linear programming duality and semidefinite programming applied to Maxcut. This course, designed for data science and AI enthusiasts, is a continuation of Part I and offers a robust theoretical foundation in combinatorial optimization without programming tasks. Ideal for foundational learners, it spans 1980 minutes and is available via Coursera's Starter subscription. Join now to master advanced problem-solving techniques in theoretical computer science.

Claire Mathieu
Instructor

Claire Mathieu