• For Individuals
  • For Businesses
  • For Universities
  • For Governments
Coursera
Online Degrees
Careers
Log In
Join for Free
Coursera
École normale supérieure
Approximation Algorithms Part II
  • About
  • Modules
  • Recommendations
  • Testimonials
  • Reviews
  1. Browse
  2. Computer Science
  3. Algorithms

Discover new skills with $120 off courses from industry experts. Save now.

École normale supérieure

Approximation Algorithms Part II

Claire Mathieu

Instructor: Claire Mathieu

12,250 already enrolled

4 modules
Gain insight into a topic and learn the fundamentals.
4.8

(44 reviews)

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

4 modules
Gain insight into a topic and learn the fundamentals.
4.8

(44 reviews)

4 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace
  • About
  • Modules
  • Recommendations
  • Testimonials
  • Reviews

Skills you'll gain

  • Mathematical Modeling
  • Probability
  • Graph Theory
  • Combinatorics
  • Theoretical Computer Science
  • Algorithms
  • Operations Research
  • Linear Algebra

Details to know

Assessments

33 assignments¹

AI Graded see disclaimer
Taught in English

See how employees at top companies are mastering in-demand skills

Learn more about Coursera for Business
 logos of Petrobras, TATA, Danone, Capgemini, P&G and L'Oreal

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•10 minutes
  • Complementary slackness•5 minutes
  • Primal-dual algorithms•5 minutes
  • Vertex cover by primal-dual•23 minutes
  • Conclusion•3 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 72 minutes
  • Problem definition•3 minutes
  • A special case: Steiner tree•12 minutes
  • LP relaxation for Steiner forest•6 minutes
  • ... and its dual•4 minutes
  • Primal-dual algorithm, Part1•10 minutes
  • Primal-dual algorithm,Part 2•12 minutes
  • Analysis•13 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 63 minutes
  • Problem definition•5 minutes
  • A linear programming relaxation•4 minutes
  • ...and its dual•8 minutes
  • A primal-dual algorithm•7 minutes
  • Analyzing the service cost•7 minutes
  • Analyzing the facility opening cost•7 minutes
  • A better algorithm•11 minutes
  • Analysis•7 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...•11 minutes
  • ...with an integrality gap of almost 2•10 minutes
  • Proof of Lemma•7 minutes
  • A quadratic programming relaxation•4 minutes
  • General facts about semidefinite programming•7 minutes
  • A rounding algorithm•7 minutes
  • Analysis•6 minutes
  • General facts about MaxCut•6 minutes
  • The end!•3 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

Earn a career certificate

Add this credential to your LinkedIn profile, resume, or CV. Share it on social media and in your performance review.

Instructor

Claire Mathieu
Claire Mathieu
École normale supérieure
2 Courses•32,242 learners

Offered by

École normale supérieure

Offered by

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.

Explore more from Algorithms

  • Status: Free
    Free
    É

    École normale supérieure

    Approximation Algorithms Part I

    Course

  • E

    EIT Digital

    Approximation Algorithms

    Course

  • Status: Free Trial
    Free Trial
    U

    University of Colorado Boulder

    Approximation Algorithms and Linear Programming

    Course

  • Status: Free Trial
    Free Trial
    U

    University of Colorado Boulder

    Approximation Methods

    Course

Why people choose Coursera for their career

Felipe M.
Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."

Learner reviews

4.8

44 reviews

  • 5 stars

    88.63%

  • 4 stars

    6.81%

  • 3 stars

    2.27%

  • 2 stars

    2.27%

  • 1 star

    0%

Showing 3 of 44

P
PV
5

Reviewed on Feb 15, 2017

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

A
AP
5

Reviewed on Oct 27, 2016

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

R
RA
5

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.

View more reviews
Coursera Plus

Open new doors with Coursera Plus

Unlimited access to 10,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription

Learn more

Advance your career with an online degree

Earn a degree from world-class universities - 100% online

Explore degrees

Join over 3,400 global companies that choose Coursera for Business

Upskill your employees to excel in the digital economy

Learn more

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

Visit the learner help center

¹ Some assignments in this course are AI-graded. For these assignments, your data will be used in accordance with Coursera's Privacy Notice.

Coursera Footer

Technical Skills

  • ChatGPT
  • Coding
  • Computer Science
  • Cybersecurity
  • DevOps
  • Ethical Hacking
  • Generative AI
  • Java Programming
  • Python
  • Web Development

Analytical Skills

  • Artificial Intelligence
  • Big Data
  • Business Analysis
  • Data Analytics
  • Data Science
  • Financial Modeling
  • Machine Learning
  • Microsoft Excel
  • Microsoft Power BI
  • SQL

Business Skills

  • Accounting
  • Digital Marketing
  • E-commerce
  • Finance
  • Google
  • Graphic Design
  • IBM
  • Marketing
  • Project Management
  • Social Media Marketing

Career Resources

  • Essential IT Certifications
  • High-Income Skills to Learn
  • How to Get a PMP Certification
  • How to Learn Artificial Intelligence
  • Popular Cybersecurity Certifications
  • Popular Data Analytics Certifications
  • What Does a Data Analyst Do?
  • Career Development Resources
  • Career Aptitude Test
  • Share your Coursera Learning Story

Coursera

  • About
  • What We Offer
  • Leadership
  • Careers
  • Catalog
  • Coursera Plus
  • Professional Certificates
  • MasterTrack® Certificates
  • Degrees
  • For Enterprise
  • For Government
  • For Campus
  • Become a Partner
  • Social Impact
  • Free Courses
  • ECTS Credit Recommendations

Community

  • Learners
  • Partners
  • Beta Testers
  • Blog
  • The Coursera Podcast
  • Tech Blog

More

  • Press
  • Investors
  • Terms
  • Privacy
  • Help
  • Accessibility
  • Contact
  • Articles
  • Directory
  • Affiliates
  • Modern Slavery Statement
  • Do Not Sell/Share
Learn Anywhere
Download on the App Store
Get it on Google Play
Logo of Certified B Corporation
© 2025 Coursera Inc. All rights reserved.
  • Coursera Facebook
  • Coursera Linkedin
  • Coursera Twitter
  • Coursera YouTube
  • Coursera Instagram
  • Coursera TikTok
Coursera

Welcome back

​
Your password is hidden
​

or

New to Coursera?


Having trouble logging in? Learner help center

This site is protected by reCAPTCHA Enterprise and the Google Privacy Policy and Terms of Service apply.