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Daniel Kane
and
Alexander S. Kulikov
Step into the area of more complex problems and learn advanced algorithms to help solve them.
Read more
Step into the area of more complex problems and learn advanced algorithms to help solve them.
Read more
Step into the area of more complex problems and learn advanced algorithms to help solve them.
This course, part of the Algorithms and Data Structures MicroMasters program, discusses inherently hard problems that you will come across in the real-world that do not have a known provably efficient algorithm, known as NP-Complete problems.
You will practice solving large instances of some of these problems despite their hardness using very efficient specialized software and algorithmic techniques including:
- SAT-solvers
- Approximate algorithms
- Special cases of NP-hard problems
- Heuristic algorithms
What you'll learn
- NP-completeness and how to deal with it
- How to approximate algorithms
- How to use heuristic algorithms to solve a problem more quickly when classic methods are too slow
Register for this course and see more details by visiting:
OpenCourser.com/course/0jn2ck/np
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What's inside
Learning objectives
- Np-completeness and how to deal with it
- How to approximate algorithms
- How to use heuristic algorithms to solve a problem more quickly when classic methods are too slow
- Np-completeness and how to deal with it
- How to approximate algorithms
- How to use heuristic algorithms to solve a problem more quickly when classic methods are too slow
Syllabus
Week 1: NP-Complete Problems
Although many of the algorithms you've learned so far are applied in practice a lot, it turns out that the world is dominated by real-world problems without a known provably efficient algorithm. Many of these problems can be reduced to one of the classical problems called NP-complete problems which either cannot be solved by a polynomial algorithm or solving any one of them would win you a million dollars (see Millenium Prize Problems) and eternal worldwide fame for solving the main problem of computer science called P vs NP. It's good to know this before trying to solve a problem before the tomorrow's deadline :) Although these problems are very unlikely to be solvable efficiently in the nearest future, people always come up with various workarounds. In this module you will study the classical NP-complete problems and the reductions between them. You will also practice solving large instances of some of these problems despite their hardness using very efficient specialized software based on tons of research in the area of NP-complete problems.
Week 2: Coping with NP-completeness: special cases
After the previous module you might be sad: you've just went through 5 courses in Algorithms only to learn that they are not suitable for most real-world problems. However, don't give up yet! People are creative, and they need to solve these problems anyway, so in practice there are often ways to cope with an NP-complete problem at hand. We show that some special cases on NP-complete problems can, in fact, be solved in polynomial time.
Week 3: Coping with NP-completeness: exact and approximate algorithms
We consider exact algorithms that find a solution much faster than the brute force algorithm. We conclude with approximation algorithms that work in polynomial time and find a solution that is close to being optimal.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Core audience consists of students and professionals working in computer science and related fields, with an interest in algorithms, data structures, and problem-solving
Builds on the basic programming and algorithm knowledge taught in earlier courses in the Algorithms and Data Structures MicroMasters program
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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 NP-Complete Problems with these
activities:
Read 'Exact Exponential Algorithms' by Fomin and Kratsch
Show steps
Read this book to gain insights into exact exponential algorithms, which provide efficient solutions for certain NP-hard problems.
Show steps
-
Identify the chapters or sections relevant to the course.
-
Read and understand the selected chapters.
-
Summarize the key concepts and techniques.
-
Discuss the book with others.
Organize and Review Course Materials
Show steps
Review and organize lecture notes, assignments, and other course materials to enhance your understanding of the concepts covered.
Show steps
-
Gather and organize lecture notes.
-
Review and summarize key concepts from the notes.
-
Organize assignments and quizzes.
-
Practice solving problems from assignments.
Follow Tutorials on Advanced Techniques
Show steps
Watch video tutorials or read articles that cover advanced algorithmic techniques used in solving NP-hard problems.
Show steps
-
Find tutorials or articles on specific techniques.
-
Follow the tutorial or read the article.
-
Try implementing or applying the technique.
-
Discuss the technique with others.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Join a Study Group for Class Discussion
Show steps
Join or form a study group with peers to discuss and solve problems related to NP-complete problems and advanced algorithmic techniques.
Show steps
-
Find or form a study group.
-
Establish meeting times and schedules.
-
Prepare topics for discussion.
-
Participate in discussions and problem-solving.
Practice Algorithmic Problem Solving
Show steps
Practice solving algorithmic problems to improve your understanding of NP-hard problems and develop skills in using approximation and heuristic algorithms.
Browse courses on
NP-Hard Problems
Show steps
-
Identify an NP-hard problem to solve.
-
Choose an appropriate algorithm (SAT solver, approximation, or heuristic).
-
Implement the algorithm.
-
Test and analyze the solution.
Write a Summary Article on Advanced Algorithms
Show steps
Write a summary article that explains the concepts and techniques of advanced algorithms used in solving NP-hard problems.
Show steps
-
Research and understand the advanced algorithms.
-
Organize and outline the content of the article.
-
Write the first draft.
-
Review and edit the article.
Volunteer as an Algorithm Tutor
Show steps
Volunteer as a tutor to help others understand advanced algorithmic concepts and problem-solving techniques.
Show steps
-
Find opportunities to volunteer as a tutor.
-
Prepare lesson plans.
-
Meet with students and provide guidance.
-
Evaluate student progress.
Participate in Algorithm Competitions
Show steps
Participate in algorithm competitions to test your skills and learn from others in solving complex algorithmic problems.
Show steps
-
Find and register for algorithm competitions.
-
Prepare for the competitions.
-
Participate in the competitions.
-
Review and learn from the results.
Read 'Exact Exponential Algorithms' by Fomin and Kratsch
Show steps
Read this book to gain insights into exact exponential algorithms, which provide efficient solutions for certain NP-hard problems.
Show steps
Show steps
Show steps
- Identify the chapters or sections relevant to the course.
- Read and understand the selected chapters.
- Summarize the key concepts and techniques.
- Discuss the book with others.
Organize and Review Course Materials
Show steps
Review and organize lecture notes, assignments, and other course materials to enhance your understanding of the concepts covered.
Show steps
Show steps
Show steps
- Gather and organize lecture notes.
- Review and summarize key concepts from the notes.
- Organize assignments and quizzes.
- Practice solving problems from assignments.
Follow Tutorials on Advanced Techniques
Show steps
Watch video tutorials or read articles that cover advanced algorithmic techniques used in solving NP-hard problems.
Show steps
Show steps
Show steps
- Find tutorials or articles on specific techniques.
- Follow the tutorial or read the article.
- Try implementing or applying the technique.
- Discuss the technique with others.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Join a Study Group for Class Discussion
Show steps
Join or form a study group with peers to discuss and solve problems related to NP-complete problems and advanced algorithmic techniques.
Show steps
Show steps
Show steps
- Find or form a study group.
- Establish meeting times and schedules.
- Prepare topics for discussion.
- Participate in discussions and problem-solving.
Practice Algorithmic Problem Solving
Show steps
Practice solving algorithmic problems to improve your understanding of NP-hard problems and develop skills in using approximation and heuristic algorithms.
Browse courses on
NP-Hard Problems
Show steps
Show steps
Show steps
- Identify an NP-hard problem to solve.
- Choose an appropriate algorithm (SAT solver, approximation, or heuristic).
- Implement the algorithm.
- Test and analyze the solution.
Write a Summary Article on Advanced Algorithms
Show steps
Write a summary article that explains the concepts and techniques of advanced algorithms used in solving NP-hard problems.
Show steps
Show steps
Show steps
- Research and understand the advanced algorithms.
- Organize and outline the content of the article.
- Write the first draft.
- Review and edit the article.
Volunteer as an Algorithm Tutor
Show steps
Volunteer as a tutor to help others understand advanced algorithmic concepts and problem-solving techniques.
Show steps
Show steps
Show steps
- Find opportunities to volunteer as a tutor.
- Prepare lesson plans.
- Meet with students and provide guidance.
- Evaluate student progress.
Participate in Algorithm Competitions
Show steps
Participate in algorithm competitions to test your skills and learn from others in solving complex algorithmic problems.
Show steps
Show steps
Show steps
- Find and register for algorithm competitions.
- Prepare for the competitions.
- Participate in the competitions.
- Review and learn from the results.
Career center
Learners who complete NP-Complete Problems will develop knowledge and skills
that may be useful to these careers:
Algorithms Engineer
Algorithms Engineer
Algorithms Engineers design new algorithms or refine existing ones to improve efficiency, speed, and accuracy of computer programs. With the increase in data complexity in our world today, it has become imperative that Algorithms Engineers produce efficient algorithms to process these large amounts of data. This course can help an Algorithms Engineer by teaching them how to cope with hard problems that do not have known efficient algorithms, known as NP-Complete problems. Students will learn about SAT solvers, approximate algorithms, special cases of NP-hard problems, and heuristic algorithms, equipping them with valuable techniques for solving real-world challenges.
Data Scientist
Data Scientist
Data Scientists use their knowledge of data analysis techniques and programming languages to extract insights from data. This course can help a Data Scientist by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of real-world problems, such as fraud detection, customer segmentation, and forecasting.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. This course can help a Software Engineer by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of software development tasks, such as designing efficient algorithms, optimizing performance, and finding bugs.
Computer Scientist
Computer Scientist
Computer Scientists research and develop new computing technologies and applications. This course can help a Computer Scientist by teaching them about the theoretical foundations of computer science. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. This knowledge can be applied to a variety of research and development projects, such as designing new algorithms, developing new programming languages, and creating new software applications.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to solve complex problems in a variety of industries. This course can help an Operations Research Analyst by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of operations research problems, such as scheduling, routing, and inventory management.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data. This course can help a Quantitative Analyst by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of financial analysis tasks, such as portfolio optimization, risk management, and forecasting.
Business Analyst
Business Analyst
Business Analysts use data analysis techniques to help businesses make better decisions. This course can help a Business Analyst by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of business analysis tasks, such as market research, customer segmentation, and forecasting.
Systems Analyst
Systems Analyst
Systems Analysts design and implement computer systems. This course can help a Systems Analyst by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of systems analysis tasks, such as designing new systems, optimizing existing systems, and troubleshooting problems.
IT Consultant
IT Consultant
IT Consultants help businesses improve their use of information technology. This course can help an IT Consultant by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of IT consulting tasks, such as designing new IT systems, optimizing existing IT systems, and troubleshooting problems.
Technical Writer
Technical Writer
Technical Writers create documentation for software and other technical products. This course can help a Technical Writer by teaching them how to understand and explain complex technical concepts. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. This knowledge can help them to write clear and concise documentation that is easy for users to understand.
Product Manager
Product Manager
Product Managers are responsible for the development and launch of new products. This course can help a Product Manager by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of product management tasks, such as designing new products, planning product launches, and managing product teams.
Project Manager
Project Manager
Project Managers are responsible for planning and executing projects. This course can help a Project Manager by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of project management tasks, such as planning projects, scheduling tasks, and managing resources.
Business Development Manager
Business Development Manager
Business Development Managers are responsible for generating new business for their companies. This course can help a Business Development Manager by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of business development tasks, such as identifying new sales leads, developing new sales strategies, and closing deals.
Sales Manager
Sales Manager
Sales Managers are responsible for leading and managing sales teams. This course can help a Sales Manager by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of sales management tasks, such as setting sales targets, developing sales strategies, and managing sales teams.
Marketing Manager
Marketing Manager
Marketing Managers are responsible for developing and executing marketing campaigns. This course can help a Marketing Manager by teaching them how to solve complex problems that cannot be solved using traditional methods. They will learn about NP-Complete problems and how to deal with them, as well as approximation algorithms and heuristic algorithms. These techniques can be applied to a variety of marketing management tasks, such as developing new marketing campaigns, planning marketing budgets, and managing marketing teams.
For more career information including salaries, visit:
OpenCourser.com/course/0jn2ck/np
Reading list
We've selected 12 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
NP-Complete Problems.
Classic textbook on algorithms and provides a comprehensive overview of the field. It valuable reference for anyone interested in learning more about algorithms.
Provides a comprehensive overview of algorithms and data structures. It valuable reference for anyone interested in learning more about these topics.
Provides a rigorous introduction to the design and analysis of algorithms. It valuable reference for anyone interested in learning more about these topics.
Save
Provides a comprehensive overview of algorithm design. It valuable reference for anyone interested in learning more about this topic.
Save
Provides a comprehensive overview of algorithms. It valuable reference for anyone interested in learning more about this topic.
Provides a non-mathematical introduction to NP-completeness. It valuable resource for anyone interested in learning more about this topic.
Provides a comprehensive overview of approximation algorithms. It valuable reference for anyone interested in learning more about this topic.
Provides a comprehensive overview of heuristics. It valuable reference for anyone interested in learning more about this topic.
Provides a comprehensive overview of algorithms for hard problems. It valuable reference for anyone interested in learning more about this topic.
Provides a comprehensive overview of parameterized complexity. It valuable reference for anyone interested in learning more about this topic.
Provides a comprehensive overview of logic for computer scientists. It valuable reference for anyone interested in learning more about this topic.
Provides a comprehensive overview of proofs and types. It valuable reference for anyone interested in learning more about these topics.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/0jn2ck/np
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Effort
8 to 10 hours per week for 3 weeks
Level
Intermediate
Via
edX
Institution
The University of California, San Diego
Instructors
Daniel Kane
Alexander S. Kulikov
Language
English
Transcript
English
This course belongs to a
collection
called
Algorithms and Data Structures. It's comprised of nine courses:
- Algorithmic Design and Techniques
- Data Structures Fundamentals
- Graph Algorithms
- NP-Complete Problems (viewing)
- String Processing and Pattern Matching Algorithms
- Dynamic Programming: Applications In Machine Learning and Genomics
- Graph Algorithms in Genome Sequencing
- Algorithms and Data Structures Capstone
- Introduction to Algorithms
Good to know
Core audience consists of students and professionals working in computer science and related fields, with an interest in algorithms, data structures, and problem-solving
Builds on the basic programming and algorithm knowledge taught in earlier courses in the Algorithms and Data Structures MicroMasters program
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