Approximation Algorithms I: Solving NP-Hard Problems
Learn to design efficient algorithms for NP-hard optimization problems with provable performance guarantees in this theoretical computer science course.
Learn to design efficient algorithms for NP-hard optimization problems with provable performance guarantees in this theoretical computer science course.
Dive into the world of approximation algorithms for NP-hard combinatorial optimization problems. This course, taught by Claire Mathieu, focuses on designing efficient algorithms that provide approximate solutions with provable guarantees. You'll explore key techniques like linear programming relaxation, rounding, and randomized rounding applied to fundamental problems such as Vertex Cover, Knapsack, Bin Packing, Set Cover, and Multiway Cut. Through theoretical assignments and peer-graded projects, you'll develop skills in algorithm design and analysis, preparing you to tackle complex optimization challenges in computer science and operations research.
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What you'll learn
Design approximation algorithms for NP-hard combinatorial optimization problems
Apply linear programming relaxation and rounding techniques to solve complex problems
Analyze the performance guarantees of approximation algorithms
Implement randomized rounding for problems like Set Cover and Multiway Cut
Understand the theoretical foundations of approximation algorithms in computer science
Develop skills in mathematical proofs and algorithm analysis
Skills you'll gain
This course includes:
5.13 Hours PreRecorded video
34 assignments
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There are 5 modules in this course
This course, led by Claire Mathieu, introduces students to the design and analysis of approximation algorithms for NP-hard combinatorial optimization problems. The curriculum covers fundamental techniques such as linear programming relaxation, rounding, and randomized rounding. Students will apply these methods to solve classic problems including Vertex Cover, Knapsack, Bin Packing, Set Cover, and Multiway Cut. The course emphasizes theoretical understanding and mathematical proofs, teaching students how to design algorithms with provable performance guarantees. Through a series of lectures, quizzes, and peer-graded assignments, participants will develop skills in algorithm design, analysis, and problem-solving that are crucial in theoretical computer science and practical applications in operations research.
Vertex cover and Linear Programming
Module 1 · 6 Hours to complete
Knapsack and Rounding
Module 2 · 6 Hours to complete
Bin Packing, Linear Programming and Rounding
Module 3 · 6 Hours to complete
Set Cover and Randomized Rounding
Module 4 · 7 Hours to complete
Multiway Cut and Randomized Rounding
Module 5 · 6 Hours to complete
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Instructor
1st class research director in Computer Science at Centre National de la Recherche Scientifique (CNRS)
Claire Mathieu is a French computer scientist and mathematician, known for her research on approximation algorithms, online algorithms, and auction theory. She works as a director of research at the Centre national de la recherche scientifique.
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