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Approximation Algorithms Part I

Claire Mathieu

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.

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Syllabus

Vertex cover and Linear Programming

We introduce the course topic by a typical example of a basic problem, called Vertex Cover, for which we will design and analyze a state-of-the-art approximation algorithm using two basic techniques, called Linear Programming Relaxation and Rounding. It is a simple, elementary application of powerful techniques.

Knapsack and Rounding

This module shows the power of rounding by using it to design a near-optimal solution to another basic problem: the Knapsack problem.

Bin Packing, Linear Programming and Rounding

This module shows the sophistication of rounding by using a clever variant for another basic problem: bin packing. (This is a more advanced module.)

Set Cover and Randomized Rounding

This module introduces a simple and powerful variant of rounding, based on probability: randomized rounding. Its power is applied to another basic problem, the Set Cover problem.

Multiway Cut and Randomized Rounding

This module deepens the understanding of randomized rounding by developing a sophisticated variant and applying it to another basic problem, the Multiway Cut problem. (This is a more advanced module.)

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Taught by Claire Mathieu, an expert in theoretical aspects of computer science

Develops a deep understanding of approximation algorithms

Provides a strong foundation for advanced work in combinatorial optimization

Suitable for students with a strong background in algorithms and mathematics

Assumes knowledge of a standard undergraduate Algorithms course

Homework assignments are of a theoretical nature and do not involve programming

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Reviews summary

Advanced algorithms part i

Learners say this course on approximation algorithms is excellent and entertaining. The course is well received by learners. Claire, the instructor, is enthusiastic about the material. Students are challenged and adequately prepared for what lies ahead.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Approximation Algorithms Part I with these activities:

Review Linear Algebra Fundamentals

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Review basic concepts in linear algebra to strengthen understanding of concepts in this course.

Browse courses on Linear Algebra

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Review vector spaces, subspaces, and linear independence.
Practice solving systems of linear equations.
Review concepts of matrix operations and properties.

Read 'Approximation Algorithms' by Vazirani

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Gain a deeper understanding of the theoretical foundations of approximation algorithms by reading a seminal book in the field.

View Approximation Algorithms on Amazon

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Read the assigned chapters and take notes.
Summarize key concepts and algorithms in your own words.
Identify connections between the book's content and the course material.

Participate in Weekly Study Groups

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Engage in active learning by collaborating with peers to discuss course material and solve problems collectively.

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Form a study group with classmates.
Meet regularly to review class notes and discuss concepts.
Work together to solve practice problems and prepare for assessments.

Four other activities

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Solve Approximation Algorithm Practice Problems

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Sharpen your problem-solving skills and reinforce concepts learned in class by working through practice problems.

Browse courses on Approximation Algorithms

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Attempt to solve basic approximation algorithm problems.
Check your answers and identify areas for improvement.
Seek help from online resources or classmates if needed.

Create a Visual Representation of Approximation Algorithms

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Enhance your understanding and retention by creating a visual representation of key concepts in approximation algorithms, such as a flowchart or infographic.

Browse courses on Approximation Algorithms

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Choose a specific approximation algorithm to focus on.
Identify the key steps and components of the algorithm.
Design a visual representation that clearly illustrates these elements.
Share your visual representation with others for feedback.

Contribute to an Open-Source Approximation Algorithm Library

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Gain hands-on experience implementing and testing approximation algorithms by contributing to an open-source project.

Browse courses on Approximation Algorithms

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Identify an open-source approximation algorithm library.
Choose a specific algorithm or feature to contribute to.
Implement and test your code according to the project's guidelines.
Submit a pull request with your contribution.

Build an Approximation Algorithm for a Real-World Problem

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Apply your knowledge of approximation algorithms to solve a practical problem in a field of your interest.

Browse courses on Approximation Algorithms

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Identify a real-world problem that can be addressed using an approximation algorithm.
Design an approximation algorithm to solve the problem.
Implement and test your algorithm using real-world data.
Evaluate the performance of your algorithm and compare it to other approaches.

Career center

Learners who complete Approximation Algorithms Part I will develop knowledge and skills that may be useful to these careers:

Operations Research Analyst

Operations research analysts use mathematical and statistical techniques to improve the efficiency of operations. They work in a variety of industries, including manufacturing, transportation, and healthcare. This course would be helpful for someone who wants to become an operations research analyst because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and improving the efficiency of operations.

See salaries and explore the career path for Operations Research Analyst

Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze financial data. They work in a variety of industries, including investment banking, asset management, and corporate finance. This course would be helpful for someone who wants to become a quantitative analyst because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing financial data.

See salaries and explore the career path for Quantitative Analyst

Data Scientist

Data scientists use scientific methods to extract knowledge and insights from data. They work in a variety of industries, including technology, finance, and healthcare. This course would be helpful for someone who wants to become a data scientist because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing data.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They work in a variety of industries, including healthcare, education, and government. This course would be helpful for someone who wants to become a statistician because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing data.

See salaries and explore the career path for Statistician

Financial Analyst

Financial analysts use financial data to make investment recommendations. They work in a variety of industries, including investment banking, asset management, and corporate finance. This course would be helpful for someone who wants to become a financial analyst because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing financial data.

See salaries and explore the career path for Financial Analyst

Risk Analyst

Risk analysts use mathematical and statistical techniques to analyze risk. They work in a variety of industries, including insurance, finance, and healthcare. This course would be helpful for someone who wants to become a risk analyst because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing risk.

See salaries and explore the career path for Risk Analyst

Actuary

Actuaries use mathematical and statistical skills to analyze risk and uncertainty. They work in a variety of industries, including insurance, finance, and healthcare. This course would be helpful for someone who wants to become an actuary because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding risk and uncertainty.

See salaries and explore the career path for Actuary

Investment Analyst

Investment analysts use financial data to make investment recommendations. They work in a variety of industries, including investment banking, asset management, and corporate finance. This course would be helpful for someone who wants to become an investment analyst because it provides a strong foundation in linear programming and rounding techniques, which are essential for understanding and analyzing financial data.

See salaries and explore the career path for Investment Analyst

Teacher

Teachers plan and deliver instruction to students in a variety of settings. They work in a variety of schools, including public schools, private schools, and charter schools. This course may be helpful for someone who wants to become a teacher because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in the classroom.

See salaries and explore the career path for Teacher

Financial Planner

Financial planners help people plan for their financial future. They work in a variety of settings, including banks, investment firms, and insurance companies. This course may be helpful for someone who wants to become a financial planner because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in financial planning.

See salaries and explore the career path for Financial Planner

Business Analyst

Business analysts use data to help businesses make better decisions. They work in a variety of industries, including technology, finance, and healthcare. This course may be helpful for someone who wants to become a business analyst because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in business analysis.

See salaries and explore the career path for Business Analyst

Machine Learning Engineer

Machine learning engineers design and develop machine learning models. They work in a variety of industries, including technology, finance, and healthcare. This course may be helpful for someone who wants to become a machine learning engineer because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in machine learning.

See salaries and explore the career path for Machine Learning Engineer

Software Engineer

Software engineers design, develop, and maintain software systems. They work in a variety of industries, including technology, finance, and healthcare. This course may be helpful for someone who wants to become a software engineer because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in software development..

See salaries and explore the career path for Software Engineer

Data Analyst

Data analysts use data to solve business problems. They work in a variety of industries, including technology, finance, and retail. This course may be helpful for someone who wants to become a data analyst because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in data analysis.

See salaries and explore the career path for Data Analyst

Web Developer

Web developers design, develop, and maintain websites. They work in a variety of industries, including technology, marketing, and education. This course may be helpful for someone who wants to become a web developer because it provides a strong foundation in linear programming and rounding techniques, which can be used to solve a variety of problems in web development.

See salaries and explore the career path for Web Developer

Reading list

We've selected 30 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Approximation Algorithms Part I.