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Approximation Algorithms Part II

Claire Mathieu

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.

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Syllabus

Linear Programming Duality

This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.

Steiner Forest and Primal-Dual Approximation Algorithms

This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.

Facility Location and Primal-Dual Approximation Algorithms

This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.

Maximum Cut and Semi-Definite Programming

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.

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Provides a practical understanding of designing approximation algorithms using linear programming duality

Covers advanced techniques like semi-definite programming, expanding learners' knowledge of optimization algorithms

Taught by Claire Mathieu, an expert in approximation algorithms and combinatorial optimization

Builds on knowledge from the first part of the course, assuming familiarity with basic approximation algorithms

Requires a strong foundation in linear algebra and optimization, which may not be suitable for all learners

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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 II with these activities:

Read Introduction to Linear Programming

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Provides a foundational overview of linear programming and will support the understanding of more advanced concepts that will be discussed during the course.

View Introduction to Probability on Amazon

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Read Chapters 1 and 2
Review the linear programming terminology
Solve practice problems

Join a Study Group for Approximation Algorithms

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Facilitates collaborative learning and enables learners to engage with peers, exchange ideas, and clarify concepts, fostering a deeper understanding of the course material.

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Find a study group for approximation algorithms
Attend study group meetings regularly

Implement a Linear Programming Solver

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Builds on the principles of linear programming and puts them into practice, facilitating a deeper understanding through hands-on application.

Browse courses on Linear Programming

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Choose a programming language and a library for linear programming
Implement the simplex algorithm
Test your solver on a variety of linear programming problems

Three other activities

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Show all six activities

Solve Linear Programming Problems on LeetCode

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Provides additional practice in solving linear programming problems, enhancing the learner's problem-solving skills and reinforcing the concepts covered during the course.

Browse courses on Linear Programming

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Register on LeetCode
Solve easy and medium difficulty linear programming problems

Follow a Tutorial on Semi-Definite Programming

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Provides structured guidance on the concepts of semi-definite programming, complementing the course material and facilitating a comprehensive understanding of this advanced topic.

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Find a tutorial on semi-definite programming
Follow the tutorial and complete the exercises

Design an Approximation Algorithm for a Steiner Forest

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Challenges learners to apply the theoretical concepts of approximation algorithms and Steiner forests to solve a practical problem, fostering critical thinking and problem-solving abilities.

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Study the Steiner forest problem
Understand the greedy algorithm for Steiner forest
Design an approximation algorithm for Steiner forest

Career center

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

Data Scientist

As a Data Scientist, you will work with a team of Data Scientists and Data Analysts to build, train, and maintain machine learning and data analytics models. You will use your knowledge of linear programming, optimization, and algorithms to design and implement mathematical models that can be used to solve complex data science problems. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Data Scientists.

See salaries and explore the career path for Data Scientist

Software Engineer

As a Software Engineer, you will design, develop, and maintain software applications. You will use your knowledge of linear programming and optimization to design algorithms that can be used to solve complex software engineering problems. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Software Engineers.

See salaries and explore the career path for Software Engineer

Operations Research Analyst

As an Operations Research Analyst, you will use mathematical and analytical techniques to solve complex problems in a variety of industries. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as supply chain management, logistics, and manufacturing. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Operations Research Analysts.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

As a Financial Analyst, you will use mathematical and analytical techniques to evaluate the financial performance of companies and make investment recommendations. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as portfolio optimization, risk management, and financial planning. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Financial Analysts.

See salaries and explore the career path for Financial Analyst

Actuary

As an Actuary, you will use mathematical and analytical techniques to assess risk and uncertainty. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as insurance, pensions, and risk management. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Actuaries.

See salaries and explore the career path for Actuary

Quantitative Analyst

As a Quantitative Analyst, you will use mathematical and analytical techniques to develop and implement trading strategies. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as portfolio optimization,リスク management, and trading. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Quantitative Analysts.

See salaries and explore the career path for Quantitative Analyst

Business Analyst

As a Business Analyst, you will use mathematical and analytical techniques to solve business problems. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as supply chain management, logistics, and manufacturing. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Business Analysts.

See salaries and explore the career path for Business Analyst

Data Analyst

As a Data Analyst, you will use mathematical and analytical techniques to analyze data and make recommendations. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as customer relationship management, fraud detection, and marketing. This course will help you build a foundation in linear programming duality, primal-dual approximation algorithms, and semi-definite programming, which are all essential techniques for Data Analysts.

See salaries and explore the career path for Data Analyst

Statistician

As a Statistician, you will use mathematical and analytical techniques to collect, analyze, and interpret data. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as clinical trials, public health, and market research. This course may be useful for gaining a deeper understanding of statistical techniques and methods.

See salaries and explore the career path for Statistician

Economist

As an Economist, you will use mathematical and analytical techniques to study the economy. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as public policy, economic forecasting, and international trade. This course may be useful for gaining a deeper understanding of economic principles and theories.

See salaries and explore the career path for Economist

Market Researcher

As a Market Researcher, you will use mathematical and analytical techniques to collect and analyze data about consumer behavior. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as product development, brand management, and advertising. This course may be useful for gaining a deeper understanding of market research techniques and methods.

See salaries and explore the career path for Market Researcher

Operations Manager

As an Operations Manager, you will use mathematical and analytical techniques to improve the efficiency of operations. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as supply chain management, logistics, and manufacturing. This course may be useful for gaining a deeper understanding of operations management techniques and methods.

See salaries and explore the career path for Operations Manager

Project Manager

As a Project Manager, you will use mathematical and analytical techniques to plan and execute projects. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as scheduling, resource allocation, and risk management. This course may be useful for gaining a deeper understanding of project management techniques and methods.

See salaries and explore the career path for Project Manager

Systems Analyst

As a Systems Analyst, you will use mathematical and analytical techniques to analyze and design information systems. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as data management, software development, and systems integration. This course may be useful for gaining a deeper understanding of systems analysis techniques and methods.

See salaries and explore the career path for Systems Analyst

Database Administrator

As a Database Administrator, you will use mathematical and analytical techniques to design and maintain databases. You will use your knowledge of linear programming and optimization to design and implement mathematical models that can be used to solve problems in areas such as data storage, data retrieval, and data security. This course may be useful for gaining a deeper understanding of database administration techniques and methods.

See salaries and explore the career path for Database Administrator

Reading list

We've selected 31 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 II.

Approximation Algorithms

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A classic textbook in the field of approximation algorithms, providing a comprehensive overview of the subject. It serves as a valuable reference for researchers and practitioners alike.

Approximation Algorithms

Hardcover

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APPROXIMATION ALGORITHMS

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