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Approximation Algorithms Part I
  • Level Foundation
  • المدة 36 ساعات hours
  • الطبع بواسطة École normale supérieure
  • Offered by

عن

Approximation algorithms, Part I How efficiently can you pack objects into a minimum number of boxes? How well can you cluster nodes so as to cheaply separate a network into components around a few centers? These are examples of NP-hard combinatorial optimization problems. It is most likely impossible to solve such problems efficiently, so our aim is to give an approximate solution that can be computed in polynomial time and that at the same time has provable guarantees on its cost relative to the optimum. This course assumes knowledge of a standard undergraduate Algorithms course, and particularly emphasizes algorithms that can be designed using linear programming, a favorite and amazingly successful technique in this area. By taking 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 first of a two-part course on Approximation Algorithms.

الوحدات

Introduction: a roadmap to this module and to this course

    • 1 Videos
    • 3 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 1: P vs. NP review

1 Videos

  • Lecture: Introduction

3 Readings

  • Slides
  • All slides for all chapters of Approx Algs part 1
  • Attempt to upload slides in Keynote format

What is vertex cover? Some examples

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 2

1 Videos

  • Lecture: Definition

1 Readings

  • Slides

An integer program for vertex cover

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 3

1 Videos

  • Lecture: Integer program

1 Readings

  • Slides

Integer programming and linear programming

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 4

1 Videos

  • Lecture: A linear programming relaxation

1 Readings

  • Slides

An approximation algorithm for vertex cover

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 5

1 Videos

  • Lecture: Approximation algorithm

1 Readings

  • Slides

Analysis: how good is our algorithm ?

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1 Assignment

  • Quiz 6

1 Videos

  • Lecture: Analysis

1 Readings

  • Slides

General facts

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    • 1 Readings
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1 Assignment

  • Quiz 7

1 Videos

  • Lecture: General facts

1 Readings

  • Slides

Exercises

    • 1 Videos
    • 4 Readings
    • 1 PeerReview
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1 Peer Review

  • Peer Graded Assignment 1

1 Videos

  • Half integrality (7:35 bug, fixed in pdf slides)

4 Readings

  • Practice Exercises
  • PDF version of the peer-graded assignment
  • Half-integrality slides
  • All slides together in one file

The knapsack problem: Definition

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 1

1 Videos

  • Lecture: Definition

1 Readings

  • Slides

Greedy algorithm

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    • 1 Readings
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1 Assignment

  • Quiz 2

1 Videos

  • Lecture: Greedy algorithm

1 Readings

  • Slides

Dynamic programming in special case

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    • 1 Readings
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1 Assignment

  • Quiz 3

1 Videos

  • Lecture: Special dynamic program

1 Readings

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Dynamic programming in general

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1 Assignment

  • Quiz 4

1 Videos

  • Lecture: General dynamic program

1 Readings

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Approximation algorithm

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1 Assignment

  • Quiz 5

1 Videos

  • Lecture: algorithm

1 Readings

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Analysis

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1 Assignment

  • Quiz 6

1 Videos

  • Lecture: analysis

1 Readings

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Approximation scheme

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1 Assignment

  • Quiz 7

1 Videos

  • Lecture: approximation scheme

1 Readings

  • Slides

Exercises

    • 2 Readings
    • 1 PeerReview
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1 Peer Review

  • Peer Assignment Knapsack

2 Readings

  • Practise Exercises
  • All slides together in one file

The Next-Fit algorithm

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 1

1 Videos

  • Lecture: Next Fit

1 Readings

  • Slides (with typo corrected)

A linear program for Bin-Packing

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 2

1 Videos

  • Lecture: a linear program

1 Readings

  • Slides

Small items

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1 Assignment

  • Quiz 3

1 Videos

  • Lecture: small items

1 Readings

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Large items, few sizes

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1 Assignment

  • Quiz 4

1 Videos

  • Lecture: large items, few sizes

1 Readings

  • Slides

Large items, many sizes

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1 Assignment

  • Quiz 5

1 Videos

  • Large items, many sizes

1 Readings

  • Slides

Large items, analysis

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1 Assignment

  • Quiz 6

1 Videos

  • Lecture: large items analysis

1 Readings

  • Slides

General algorithm

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1 Assignment

  • Quiz 7

1 Videos

  • Lecture: general algorithm

1 Readings

  • Slides

Bin packing: conclusion

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1 Videos

  • Lecture: conclusion

1 Readings

  • Slides

Exercises

    • 2 Readings
    • 1 PeerReview
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1 Peer Review

  • Peer Assignment: Bin-Packing

2 Readings

  • Practice Exercises
  • All slides together in one file

Set Cover Definition

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    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 1

1 Videos

  • Lecture: definition

1 Readings

  • Slides

Randomized Rounding

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1 Assignment

  • Quiz 2

1 Videos

  • Lecture: randomized rounding

1 Readings

  • Slides

Cost Analysis

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1 Assignment

  • Quiz 3

1 Videos

  • Lecture: cost analysis

1 Readings

  • Slides

Coverage Analysis

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1 Assignment

  • Quiz 4

1 Videos

  • Lecture: coverage analysis

1 Readings

  • Slides

Iterated Algorithm

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1 Assignment

  • Quiz 5

1 Videos

  • Lecture: iterated algorithm

1 Readings

  • Slides

Stopping Time Algorithm

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1 Assignment

  • Quiz 6

1 Videos

  • Lecture: stopping time algorithm

1 Readings

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Stopping Time Analysis

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1 Assignment

  • Quiz 7

1 Videos

  • Lecture: stopping time analysis

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Remarks

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    • 2 Readings
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1 Assignment

  • Quiz 8

1 Videos

  • Lecture:final remarks

2 Readings

  • Slides
  • A reference on this stopping time analysis

Exerices

    • 2 Readings
    • 1 PeerReview
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1 Peer Review

  • Peer Assig Set Cover

2 Readings

  • Practise Exercise
  • All slides together in one file

What is the Multiway Cut problem?

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    • 1 Assignment
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1 Assignment

  • Quiz 1 : Some context on cuts

1 Videos

  • Lecture: definition

1 Readings

  • Slides

A linear programming relaxation

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1 Assignment

  • Quiz 2

1 Videos

  • Lecture: linear programming relaxation

1 Readings

  • Slides

Randomized rounding

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1 Assignment

  • Quiz 3

1 Videos

  • Lecture: randomized rounding

1 Readings

  • Slides

Analysis

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    • 1 Assignment
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1 Assignment

  • Quiz 4

1 Videos

  • Lecture: analysis

1 Readings

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Conclusion

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1 Assignment

  • Quiz 5

1 Videos

  • Lecture: conclusion

1 Readings

  • Slides

Exercises

    • 3 Readings
    • 1 PeerReview
Show info about module content

1 Peer Review

  • Peer-graded assignment 5

3 Readings

  • Practice exercise
  • All Chapter Slides together in one file
  • Slides for all chapters of Approx Algs Part 1 together in one file

Auto Summary

Explore the fascinating world of Approximation Algorithms with this foundational course in Data Science & AI, led by expert instructors on Coursera. Dive into NP-hard combinatorial optimization problems, learning to craft efficient approximate solutions using linear programming and randomized rounding techniques. With a focus on theoretical computer science, this course spans 2160 minutes and requires prior knowledge of undergraduate algorithms. Ideal for learners aiming to tackle complex optimization challenges, subscription options include Starter and Professional tiers. Join now to enhance your problem-solving skills and computational theory expertise.

Claire Mathieu
Instructor

Claire Mathieu