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Approximation Algorithms Part I

Approx. 36 hours to complete

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Course Summary

Learn about approximation algorithms and how they are used to solve NP-hard problems in this course. Discover new ways to approach algorithmic problem-solving and gain valuable skills for a career in computer science.

Key Learning Points

Understand the basics of approximation algorithms and their applications
Learn how to analyze the performance of approximation algorithms
Discover new approaches to algorithmic problem-solving

Job Positions & Salaries of people who have taken this course might have

- USA: $85,000
- India: ₹1,200,000
- Spain: €35,000
- USA: $85,000
- India: ₹1,200,000
- Spain: €35,000
- USA: $110,000
- India: ₹1,800,000
- Spain: €40,000
- USA: $85,000
- India: ₹1,200,000
- Spain: €35,000
- USA: $110,000
- India: ₹1,800,000
- Spain: €40,000
- USA: $120,000
- India: ₹2,000,000
- Spain: €45,000

Learning Outcomes

Understand the fundamentals of approximation algorithms and their applications
Gain new insights into algorithmic problem-solving
Develop skills in performance analysis and combinatorial optimization

Prerequisites or good to have knowledge before taking this course

Basic knowledge of algorithms and data structures
Familiarity with complexity theory

Course Difficulty Level

Intermediate

Course Format

Online
Self-Paced
Video Lectures
Quizzes

Similar Courses

Algorithms, Part I
Algorithms, Part II

Related Education Paths

Notable People in This Field

Donald Knuth
Richard Stallman

Related Books

Description

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.

Outline

Vertex cover and Linear Programming
Lecture: Introduction
Lecture: Definition
Lecture: Integer program
Lecture: A linear programming relaxation
Lecture: Approximation algorithm
Lecture: Analysis
Lecture: General facts
Half integrality (7:35 bug, fixed in pdf slides)
Slides
All slides for all chapters of Approx Algs part 1
Attempt to upload slides in Keynote format
Slides
Slides
Slides
Slides
Slides
Slides
Practice Exercises
PDF version of the peer-graded assignment
Half-integrality slides
All slides together in one file
Quiz 1: P vs. NP review
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7

Knapsack and Rounding
Lecture: Definition
Lecture: Greedy algorithm
Lecture: Special dynamic program
Lecture: General dynamic program
Lecture: algorithm
Lecture: analysis
Lecture: approximation scheme
Slides
Slides
Slides
Slides
Slides
Slides
Slides
Practise Exercises
All slides together in one file
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7

Bin Packing, Linear Programming and Rounding
Lecture: Next Fit
Lecture: a linear program
Lecture: small items
Lecture: large items, few sizes
Large items, many sizes
Lecture: large items analysis
Lecture: general algorithm
Lecture: conclusion
Slides (with typo corrected)
Slides
Slides
Slides
Slides
Slides
Slides
Slides
Practice Exercises
All slides together in one file
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7

Set Cover and Randomized Rounding
Lecture: definition
Lecture: randomized rounding
Lecture: cost analysis
Lecture: coverage analysis
Lecture: iterated algorithm
Lecture: stopping time algorithm
Lecture: stopping time analysis
Lecture:final remarks
Slides
Slides
Slides
Slides
Slides
Slides
Slides
Slides
A reference on this stopping time analysis
Practise Exercise
All slides together in one file
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7
Quiz 8

Multiway Cut and Randomized Rounding
Lecture: definition
Lecture: linear programming relaxation
Lecture: randomized rounding
Lecture: analysis
Lecture: conclusion
Slides
Slides
Slides
Slides
Slides
Practice exercise
All Chapter Slides together in one file
Slides for all chapters of Approx Algs Part 1 together in one file
Quiz 1 : Some context on cuts
Quiz 2
Quiz 3
Quiz 4
Quiz 5

Summary of User Reviews

Learn about approximation algorithms in this Coursera course. Students rave about the engaging lectures and useful assignments. Overall, this course receives high praise from its users.

Key Aspect Users Liked About This Course

Many users appreciated the clear and engaging lectures provided by the instructor.

Pros from User Reviews

The course breaks down complex topics into manageable pieces for beginners.
Instructors are knowledgeable and responsive to questions.
The assignments are valuable and provide hands-on experience.
The course is well-structured and easy to follow.
The course provides a solid foundation for further study in the field.

Cons from User Reviews

Some users wished for more challenging assignments.
The course may be too slow-paced for advanced students.
The course material can be dry or repetitive at times.
Some users found the course to be too theoretical without enough practical applications.
The course may require a significant time commitment for some students.

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