Approximation Algorithms and Linear Programming from Coursera

This course continues our data structures and algorithms specialization by focussing on the use of linear and integer programming formulations for solving algorithmic problems that seek optimal solutions to problems arising from domains such as resource allocation, scheduling, task assignment, and variants of the traveling salesperson problem. Next, we will study algorithms for NP-hard problems whose solutions are guaranteed to be within some approximation factor of the best possible solutions. Such algorithms are often quite efficient and provide useful bounds on the optimal solutions. The learning will be supported by instructor provided notes, readings from textbooks and assignments. Assignments will include conceptual multiple-choice questions as well as problem solving assignments that will involve programming and testing algorithms.

This course can be taken for academic credit as part of CU Boulder’s Masters of Science in Computer Science (MS-CS) degrees offered on the Coursera platform. This fully accredited graduate degree offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more:

MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder

What's inside

Syllabus

Linear Programming

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.

Integer Linear Programming

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.

Approximation Algorithms : Scheduling, Vertex Cover and MAX-SAT

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.

Travelling Salesperson Problem (TSP) and Approximation Schemes

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Develops foundational knowledge in linear and integer programming, essential for resource allocation, scheduling, and other practical applications

Builds on basic data structures and algorithms, making it suitable for learners with some programming experience

Provides hands-on tutorials and assignments using Python, enhancing the learning experience

Offers the option to earn academic credit towards a Master's degree from CU Boulder, increasing its credibility

Requires extensive background knowledge in data structures and algorithms, which may limit accessibility for some learners

Focuses on theoretical concepts rather than practical applications, which may not align with the interests of all learners

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 and Linear Programming with these activities:

Refresh linear algebra skills

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Reviewing linear algebra skills will solidify your foundation for understanding linear programming.

Browse courses on Linear Algebra

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Review matrices and their operations.
Practice solving systems of linear equations.
Explore vector spaces and their properties.
Review eigenvalues and eigenvectors.

Organize and review course materials

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Organizing and reviewing course materials will help you reinforce your understanding of the concepts.

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Gather all course materials.
Organize the materials into a logical structure.
Review the materials regularly.

Follow tutorials on dynamic programming for the Travelling Salesperson Problem

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Following tutorials on dynamic programming for the Travelling Salesperson Problem will complement your understanding of the topic.

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Find tutorials on dynamic programming for the Travelling Salesperson Problem.
Follow the tutorials and implement the algorithms.
Test your solutions on different instances of the problem.

Five other activities

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Create a linear programming model for a real-world problem

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Applying linear programming to a real-world problem will deepen your understanding of its applications.

Browse courses on Linear Programming

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Identify a problem that can be modeled as a linear program.
Formulate the linear programming model.
Solve the linear programming model using a solver.
Analyze the results and draw insights.

Participate in a workshop on integer linear programming

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Participating in a workshop on integer linear programming will provide you with hands-on experience and expert guidance.

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Find workshops on integer linear programming.
Participate in the workshop.
Apply what you learn to solve real-world problems.

Attend a conference or meetup on optimization and algorithms

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Attending conferences or meetups will expose you to the latest research and industry trends in optimization and algorithms.

Browse courses on Optimization

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Find conferences or meetups on optimization and algorithms.
Attend the events.
Network with other attendees.

Write a blog post on the applications of integer linear programming

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Writing about integer linear programming will reinforce your understanding and help you communicate its applications.

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Research the applications of integer linear programming.
Choose a specific application to focus on.
Write a blog post explaining the application and how integer linear programming is used to solve it.

Solve approximation algorithm problems on LeetCode

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Solving approximation algorithm problems on LeetCode will enhance your problem-solving skills and solidify your understanding of these algorithms.

Browse courses on Approximation Algorithms

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Identify approximation algorithm problems on LeetCode.
Attempt to solve the problems using the appropriate approximation algorithms.
Review your solutions and identify areas for improvement.

Career center

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

Operations Research Analyst

Operations Research (OR) Analysts are experts in using advanced analytical techniques to solve complex problems in various industries. This course in Approximation Algorithms and Linear Programming provides a solid foundation in linear and integer programming, essential tools for OR Analysts. By mastering these techniques, you'll be well-equipped to formulate and solve complex optimization problems commonly encountered in areas such as resource allocation, scheduling, and logistics.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

Data Scientists leverage their knowledge in mathematics, statistics, and computer science to extract insights from data. This course in Approximation Algorithms and Linear Programming equips you with the skills to formulate data-driven optimization problems as linear programs and solve them efficiently. The course also covers techniques for handling large-scale datasets, a key challenge in data science.

See salaries and explore the career path for Data Scientist

Management Consultant

Management Consultants provide advice and guidance to businesses on various strategic and operational issues. This course in Approximation Algorithms and Linear Programming equips you with the analytical tools to identify and solve complex problems in areas such as resource allocation, scheduling, and logistics. The course also enhances your problem-solving and decision-making skills, essential for success in management consulting.

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Financial Analyst

Financial Analysts use quantitative techniques to evaluate and make recommendations on investments. This course in Approximation Algorithms and Linear Programming provides a strong foundation in linear and integer programming techniques, which are essential for solving complex optimization problems in portfolio optimization, risk management, and capital budgeting.

See salaries and explore the career path for Financial Analyst

Software Engineer

Software Engineers design, develop, and maintain software systems. This course in Approximation Algorithms and Linear Programming equips you with the skills to formulate and solve complex optimization problems that arise in software design, such as resource allocation, task scheduling, and network optimization. The course also covers techniques for designing efficient algorithms, a key requirement for software engineering.

See salaries and explore the career path for Software Engineer

Actuary

Actuaries use mathematical and statistical techniques to assess and manage risk. This course in Approximation Algorithms and Linear Programming provides a solid foundation in optimization techniques, which are essential for modeling and solving complex risk management problems in insurance and finance.

See salaries and explore the career path for Actuary

Business Analyst

Business Analysts identify and solve business problems by analyzing data and developing solutions. This course in Approximation Algorithms and Linear Programming equips you with the skills to formulate and solve complex optimization problems commonly encountered in business analysis, such as resource allocation, scheduling, and supply chain management.

See salaries and explore the career path for Business Analyst

Industrial Engineer

Industrial Engineers design and improve processes and systems in various industries. This course in Approximation Algorithms and Linear Programming provides a strong foundation in optimization techniques, which are essential for solving complex problems in areas such as manufacturing, logistics, and healthcare.

See salaries and explore the career path for Industrial Engineer

Operations Manager

Operations Managers plan and oversee the day-to-day operations of businesses. This course in Approximation Algorithms and Linear Programming equips you with the skills to optimize resource allocation, scheduling, and logistics, which are critical functions in operations management.

See salaries and explore the career path for Operations Manager

Supply Chain Manager

Supply Chain Managers oversee the flow of goods and services from suppliers to customers. This course in Approximation Algorithms and Linear Programming provides a strong foundation in optimization techniques, which are essential for solving complex problems in supply chain management, such as inventory management, transportation, and distribution.

See salaries and explore the career path for Supply Chain Manager

Project Manager

Project Managers plan, execute, and close projects. This course in Approximation Algorithms and Linear Programming equips you with the skills to optimize resource allocation, scheduling, and risk management, which are essential functions in project management.

See salaries and explore the career path for Project Manager

Transportation Analyst

Transportation Analysts study and analyze transportation systems to improve efficiency and safety. This course in Approximation Algorithms and Linear Programming equips you with the skills to optimize routing, scheduling, and resource allocation in transportation networks.

See salaries and explore the career path for Transportation Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze and make investment decisions. This course in Approximation Algorithms and Linear Programming provides a strong foundation in optimization techniques, which are essential for solving complex problems in portfolio optimization, risk management, and asset pricing.

See salaries and explore the career path for Quantitative Analyst

Risk Analyst

Risk Analysts assess and manage risks in various industries. This course in Approximation Algorithms and Linear Programming provides a solid foundation in optimization techniques, which are essential for solving complex problems in risk management, such as portfolio optimization, credit risk analysis, and operational risk assessment.

See salaries and explore the career path for Risk Analyst

Systems Engineer

Systems Engineers design and manage complex systems, such as software systems, telecommunication networks, and transportation systems. This course in Approximation Algorithms and Linear Programming equips you with the skills to optimize system design, performance, and reliability.

See salaries and explore the career path for Systems Engineer