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Approximation Algorithms and Linear Programming
Sriram Sankaranarayanan
Sriram Sankaranarayanan
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.
Read more
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.
Read more
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
Register for this course and see more details by visiting:
OpenCourser.com/course/qnbwv8/approximation
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.
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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.
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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
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
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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 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.
Data Scientist
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.
Management Consultant
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.
Financial Analyst
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.
Software Engineer
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.
Actuary
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.
Business Analyst
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.
Industrial Engineer
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.
Operations Manager
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.
Supply Chain 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.
Project 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.
Transportation Analyst
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.
Quantitative 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.
Risk 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.
Systems Engineer
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.
For more career information including salaries, visit:
OpenCourser.com/course/qnbwv8/approximation
Reading list
We've selected 11 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 and Linear Programming .
Provides a comprehensive introduction to linear optimization, covering the basics of the subject as well as more advanced topics such as interior-point methods and duality theory. Particularly useful for background and prerequisite knowledge.
Provides a comprehensive treatment of integer linear programming, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
Provides a comprehensive introduction to approximation algorithms, covering the theory, algorithms, and applications of this important area of computer science. Particularly useful as a textbook or reference.
Provides a comprehensive treatment of the traveling salesman problem, covering the theory, algorithms, and applications of this important problem in optimization. Particularly useful as a textbook or reference.
Provides a comprehensive introduction to optimization by vector space methods, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
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Provides a comprehensive introduction to linear programming, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
Provides a comprehensive introduction to integer programming, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
Provides a comprehensive introduction to graph algorithms, covering the theory, algorithms, and applications of this important area of computer science. Particularly useful for background and prerequisite knowledge.
Save
Provides a comprehensive treatment of network flows, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
Provides a comprehensive introduction to combinatorial optimization, covering the theory, algorithms, and applications of this important area of computer science. Particularly useful as a textbook or reference.
Save
Provides a comprehensive introduction to integer programming, covering the theory, algorithms, and applications of this important area of optimization. Particularly useful as a textbook or reference.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/qnbwv8/approximation
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Effort
4 weeks of study, 11-14 hours/week
Level
Advanced
Via
Coursera
Institution
University of Colorado Boulder
Instructor
Sriram Sankaranarayanan
Language
English
Transcripts
magyar nyelv
اُردُو,
فارسی
বাংলা
پښتو
آذربایجان دیلی
This course belongs to a
collection
called
Foundations of Data Structures and Algorithms. It's comprised of five courses:
- Approximation Algorithms and Linear Programming (viewing)
- Trees and Graphs: Basics
- Algorithms for Searching, Sorting, and Indexing
- Dynamic Programming, Greedy Algorithms
- Advanced Data Structures, RSA and Quantum Algorithms
Good to know
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
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