University of Colorado Boulder
Approximation Algorithms and Linear Programming
University of Colorado Boulder

Approximation Algorithms and Linear Programming

9,584 already enrolled

Gain insight into a topic and learn the fundamentals.
4.9

(31 reviews)

Advanced level

Recommended experience

Flexible schedule
Approx. 48 hours
Learn at your own pace
Build toward a degree
Gain insight into a topic and learn the fundamentals.
4.9

(31 reviews)

Advanced level

Recommended experience

Flexible schedule
Approx. 48 hours
Learn at your own pace
Build toward a degree

What you'll learn

  • Formulate linear and integer programming problems for solving commonly encountered optimization problems.

  • Develop a basic understanding of how linear and integer programming problems are solved.

  • Understand how approximation algorithms compute solutions that are guaranteed to be within some constant factor of the optimal solution

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

18 quizzes, 1 assignment

Taught in English

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

Placeholder

Build your subject-matter expertise

This course is part of the Foundations of Data Structures and Algorithms Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
  • Learn new concepts from industry experts
  • Gain a foundational understanding of a subject or tool
  • Develop job-relevant skills with hands-on projects
  • Earn a shareable career certificate
Placeholder
Placeholder

Earn a career certificate

Add this credential to your LinkedIn profile, resume, or CV

Share it on social media and in your performance review

Placeholder

There are 4 modules in this course

This module introduces the basics of linear programs and shows how some algorithm problems (such as the network flow problem) can be posed as a linear program. We will provide hands-on tutorials on how to pose and solve a linear programming problem in Python. Finally, we will provide a brief overview of linear programming algorithms including the famous Simplex algorithm for solving linear programs. The problem set will guide you towards posing and solving some interesting problems such as a financial portfolio problem and the optimal transportation problem as linear programs.

What's included

7 videos2 readings5 quizzes1 programming assignment4 ungraded labs

This module will cover integer linear programming and its use in solving NP-hard (combinatorial optimization) problems. We will cover some examples of what integer linear programming is by formulating problems such as Knapsack, Vertex Cover and Graph Coloring. Next, we will study the concept of integrality gap and look at the special case of integrality gap for vertex cover problems. We will conclude with a tutorial on formulating and solving integer linear programs using the python library Pulp.

What's included

6 videos4 quizzes1 assignment1 programming assignment4 ungraded labs

We will introduce approximation algorithms for solving NP-hard problems. These algorithms are fast (often greedy algorithms) that may not produce an optimal solution but guarantees that its solution is not "too far away" from the best possible. We will present some of these algorithms starting from a basic introduction to the concepts involved followed by a series of approximation algorithms for scheduling problems, vertex cover problem and the maximum satisfiability problem.

What's included

5 videos4 quizzes1 programming assignment3 ungraded labs

We will present the travelling salesperson problem (TSP): a very important and widely applicable combinatorial optimization problem, its NP-hardness and the hardness of approximating a general TSP with a constant factor. We present integer linear programming formulation and a simple yet elegant dynamic programming algorithm. We will present a 3/2 factor approximation algorithm by Christofides and discuss some heuristic approaches for solving TSPs. We will conclude by presenting approximation schemes for the knapsack problem.

What's included

11 videos5 quizzes1 programming assignment3 ungraded labs

Instructor

Instructor ratings
4.8 (8 ratings)
Sriram Sankaranarayanan
University of Colorado Boulder
5 Courses63,746 learners

Offered by

Recommended if you're interested in Algorithms

Build toward a degree

This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹

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

Showing 3 of 31

4.9

31 reviews

  • 5 stars

    91.42%

  • 4 stars

    5.71%

  • 3 stars

    2.85%

  • 2 stars

    0%

  • 1 star

    0%

ND
5

Reviewed on Jan 16, 2024

New to Algorithms? Start here.

Placeholder

Open new doors with Coursera Plus

Unlimited access to 7,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription

Advance your career with an online degree

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

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

Upskill your employees to excel in the digital economy

Frequently asked questions