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Advanced Algorithms and Complexity

Alexander S. Kulikov, Michael Levin, Daniel M Kane, and Neil Rhodes

In previous courses of our online specialization you've learned the basic algorithms, and now you are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset.

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What's inside

Syllabus

Flows in Networks
Network flows show up in many real world situations in which a good needs to be transported across a network with limited capacity. You can see it when shipping goods across highways and routing packets across the internet. In this unit, we will discuss the mathematical underpinnings of network flows and some important flow algorithms. We will also give some surprising examples on seemingly unrelated problems that can be solved with our knowledge of network flows.
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Traffic lights

Read about what's good
what should give you pause
and possible dealbreakers
Provides a thorough foundation for intermediate learners in the field of algorithms
Delves into advanced algorithms, which are essential for solving complex problems
Taught by reputable instructors with expertise in advanced algorithms
Covers topics such as network flows and linear programming, which are highly relevant in industry
Introduces streaming algorithms commonly used in data analysis

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Reviews summary

Challenging advanced algorithms

According to learners, Advanced Algorithms and Complexity is a highly challenging course that delves deeply into core areas like Network Flows and Linear Programming, often seen as essential topics for those serious about the field. Students praise the strong theoretical foundation provided and note that the assignments are often challenging but rewarding for solidifying understanding. However, a significant portion of reviewers highlight the course's high difficulty level and mention that it seems to assume significant prior knowledge beyond the stated prerequisites, making the pace feel very fast. Some reviewers also expected more practical coding exercises, noting that the assignments are primarily proof-heavy. Overall, it is considered a valuable course for those with a very strong mathematical and algorithmic background already in place.
Covers complex core algorithms deeply.
"Absolutely brilliant course! The topics on Network Flows and Linear Programming were explained with incredible clarity."
"This course is a must for anyone serious about algorithms. The depth provided on Network Flows and Linear Programming is exceptional."
"Solid course covering essential advanced topics. NP-completeness section was eye-opening."
"Excellent course. Builds perfectly on the previous specialization courses. Topics are explained clearly, even complex ones like Network Flows."
Assignments focus on proofs, less on coding.
"But the practical application or coding exercises felt lacking. Assignments were purely theoretical proofs or problem-solving..."
"Expected more coding."
"The assignments are very proof-heavy, which wasn't my expectation."
"Assignments are hard but fair if you put in the work."
Very challenging, requires significant background.
"Found this course extremely difficult. The pace is very fast."
"The lectures assume significant prior knowledge beyond what was covered in the 'basic' courses."
"Not recommended for those without a very strong mathematical/algorithmic background."
"I struggled with the assignments and felt the support was minimal."
"The material is relevant, but the presentation can be dense. Difficulty level is quite high."

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 Advanced Algorithms and Complexity with these activities:
Read 'Introduction to Algorithms' by Thomas H. Cormen et al.
Gain a comprehensive understanding of the fundamental algorithms and data structures.
View Introduction to Algorithms, fourth edition on Amazon
Show steps
  • Purchase or borrow the book
  • Read and study the chapters relevant to the course
  • Complete the exercises and practice problems
Review linear algebra and calculus
Understand the mathematical foundations of the course.
Browse courses on Linear Algebra
Show steps
  • Review a university textbook
  • Complete practice problems
  • Take an online practice test
Form a study group with classmates
Collaborate with peers to enhance understanding and learn from different perspectives.
Show steps
  • Reach out to classmates
  • Set up regular meeting times
  • Discuss the course material, ask questions, and solve problems together
Four other activities
Expand to see all activities and additional details
Show all seven activities
Follow a video tutorial series on network flows
Gain a deeper understanding of network flows.
Browse courses on Network Flows
Show steps
  • Find a tutorial series on network flows
  • Follow along with the tutorials
  • Take notes and ask questions
Solve practice problems on linear programming
Practice and improve your skills in solving linear programming problems.
Browse courses on Linear Programming
Show steps
  • Find a resource with practice problems
  • Attempt a few problems yourself
  • Check your solutions against the provided answers
Create a cheat sheet on NP-complete problems
Reinforce your knowledge of the key concepts and algorithms related to NP-complete problems.
Browse courses on NP-Complete Problems
Show steps
  • Gather your notes and resources
  • Organize the information into a concise and visually appealing format
  • Reference your cheat sheet during your studies
Contribute to an open-source project related to streaming algorithms
Gain hands-on experience with streaming algorithms and contribute to the community.
Show steps
  • Find an open-source project on Github or a similar platform
  • Identify an area where you can contribute
  • Make a pull request with your changes

Career center

Learners who complete Advanced Algorithms and Complexity will develop knowledge and skills that may be useful to these careers:
Applied Mathematician
Applied Mathematicians use mathematical techniques to solve problems in a variety of fields. They use a variety of techniques and tools to develop models and make recommendations that can help organizations solve problems. Network flows, linear programming, and NP-complete problems are all important techniques in applied mathematics, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Applied Mathematicians with a strong foundation in these techniques. The course may also be helpful for Applied Mathematicians who wish to develop new algorithms and methods for applied mathematics.
See salaries and explore the career path for Applied Mathematician
Computer Scientist
Computer Scientists research and develop new computer technologies. They use a variety of techniques and tools to create new algorithms and methods for solving problems. Network flows, linear programming, and NP-complete problems are all important techniques in computer science, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Computer Scientists with a strong foundation in these techniques. The course may also be helpful for Computer Scientists who wish to develop new algorithms and methods for computer science.
See salaries and explore the career path for Computer Scientist
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to solve problems in a variety of industries. They use a variety of techniques and tools to develop models and make recommendations that can help organizations improve their operations. Network flows, linear programming, and NP-complete problems are all important techniques in operations research, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Operations Research Analysts with a strong foundation in these techniques. The course may also be helpful for Operations Research Analysts who wish to develop new algorithms and methods for operations research.
See salaries and explore the career path for Operations Research Analyst
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They use a variety of techniques and tools to develop models and make recommendations that can help organizations manage risk. Network flows, linear programming, and NP-complete problems are all important techniques in actuarial science, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Actuaries with a strong foundation in these techniques. The course may also be helpful for Actuaries who wish to develop new algorithms and methods for actuarial science.
See salaries and explore the career path for Actuary
Financial Analyst
Financial Analysts use mathematical and financial techniques to analyze and evaluate investments. They use a variety of techniques and tools to develop models and make recommendations that can help organizations make investment decisions. Network flows, linear programming, and NP-complete problems are all important techniques in financial analysis, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Financial Analysts with a strong foundation in these techniques. The course may also be helpful for Financial Analysts who wish to develop new algorithms and methods for financial analysis.
See salaries and explore the career path for Financial Analyst
Market Researcher
Market Researchers use mathematical and statistical techniques to analyze and understand consumer behavior. They use a variety of techniques and tools to develop models and make recommendations that can help organizations develop marketing campaigns and products. Network flows, linear programming, and NP-complete problems are all important techniques in market research, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Market Researchers with a strong foundation in these techniques. The course may also be helpful for Market Researchers who wish to develop new algorithms and methods for market research.
See salaries and explore the career path for Market Researcher
Data Scientist
Data Scientists are responsible for analyzing data, building models, and making predictions to help organizations make informed decisions. They use a variety of techniques and tools to extract insights from data, including network flows, linear programming, and NP-complete problems. The Advanced Algorithms and Complexity course from University of California, San Diego can provide Data Scientists with a strong foundation in these techniques, as well as the ability to solve complex problems efficiently. The course may also be helpful for Data Scientists who wish to develop new algorithms and methods for data analysis.
See salaries and explore the career path for Data Scientist
Risk Manager
Risk Managers use mathematical and statistical techniques to assess and manage risk. They use a variety of techniques and tools to develop models and make recommendations that can help organizations mitigate risk. Network flows, linear programming, and NP-complete problems are all important techniques in risk management, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Risk Managers with a strong foundation in these techniques. The course may also be helpful for Risk Managers who wish to develop new algorithms and methods for risk management.
See salaries and explore the career path for Risk Manager
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze and evaluate financial data. They use a variety of techniques and tools to develop models and make recommendations that can help organizations make investment decisions. Network flows, linear programming, and NP-complete problems are all important techniques in quantitative analysis, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Quantitative Analysts with a strong foundation in these techniques. The course may also be helpful for Quantitative Analysts who wish to develop new algorithms and methods for quantitative analysis.
See salaries and explore the career path for Quantitative Analyst
Machine Learning Engineer
Machine Learning Engineers design, build, and maintain machine learning models. They use a variety of techniques and tools to develop models that can learn from data and make predictions. Network flows, linear programming, and NP-complete problems are all important techniques in machine learning, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Machine Learning Engineers with a strong foundation in these techniques. The course may also be helpful for Machine Learning Engineers who wish to develop new algorithms and methods for machine learning.
See salaries and explore the career path for Machine Learning Engineer
Database Administrator
Database Administrators manage and maintain databases. They use a variety of techniques and tools to ensure that databases are available and performant. Network flows, linear programming, and NP-complete problems are all important techniques in database administration, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Database Administrators with a strong foundation in these techniques. The course may also be helpful for Database Administrators who wish to develop new algorithms and methods for database administration.
See salaries and explore the career path for Database Administrator
Systems Analyst
Systems Analysts design and implement computer systems. They use a variety of techniques and tools to create systems that meet the needs of organizations. Network flows, linear programming, and NP-complete problems are all important techniques in systems analysis, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Systems Analysts with a strong foundation in these techniques. The course may also be helpful for Systems Analysts who wish to develop new algorithms and methods for systems analysis.
See salaries and explore the career path for Systems Analyst
Computer Programmer
Computer Programmers design, develop, and maintain computer programs. They use a variety of techniques and tools to create programs that meet the needs of organizations. Network flows, linear programming, and NP-complete problems are all important techniques in computer programming, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Computer Programmers with a strong foundation in these techniques. The course may also be helpful for Computer Programmers who wish to develop new algorithms and methods for computer programming.
See salaries and explore the career path for Computer Programmer
Data Architect
Data Architects design and manage data systems. They use a variety of techniques and tools to create data systems that meet the needs of organizations. Network flows, linear programming, and NP-complete problems are all important techniques in data architecture, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Data Architects with a strong foundation in these techniques. The course may also be helpful for Data Architects who wish to develop new algorithms and methods for data architecture.
See salaries and explore the career path for Data Architect
Software Engineer
Software Engineers design, develop, and maintain software applications. They use a variety of techniques and tools to create software that meets the needs of users. Network flows, linear programming, and NP-complete problems are all important techniques in software engineering, and the Advanced Algorithms and Complexity course from University of California, San Diego can provide Software Engineers with a strong foundation in these techniques. The course may also be helpful for Software Engineers who wish to develop new algorithms and methods for software development.
See salaries and explore the career path for Software Engineer

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 Advanced Algorithms and Complexity.
Cover image
Introduction to Programming in Java
Save
Provides a comprehensive overview of algorithms and data structures, with a focus on efficiency and correctness. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Introduction to Programming in Java: An...
Paperback
$$$
Introduction to Programming in Java: An...
Paperback
$$$
Introduction to Programming in Java: An...
Kindle Edition
$$
Cover image
Introduction to Algorithms, fourth edition
Save
This classic textbook provides a comprehensive introduction to algorithms, data structures, and their applications. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Introduction to Algorithms, fourth edition
Paperback
Check
Introduction to Algorithms, fourth edition
Kindle Edition
Check
Cover image
The Algorithm Design Manual
Save
Provides a practical guide to algorithm design, with a focus on problem-solving techniques and code optimization. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
The Algorithm Design Manual (Texts in Computer...
Hardcover
$$$
The Algorithm Design Manual
Paperback
$$$
The Algorithm Design Manual (Texts in Computer...
Kindle Edition
$$
The Algorithm Design Manual
Kindle Edition
$$$
Network Flows
Save
Provides a comprehensive overview of network flows, with a focus on theory, algorithms, and applications. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Network Flows
Paperback
Check
Network Flows
Kindle Edition
Check
Cover image
Linear Programming
Save
Provides a comprehensive overview of linear programming, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Linear Programming: Foundations and Extensions...
Kindle Edition
$$$
Cover image
Introduction to Applied Linear Algebra
Save
Provides a comprehensive overview of convex optimization, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Introduction to Applied Linear Algebra: Vectors,...
Hardcover
$$
Introduction to Applied Linear Algebra: Vectors,...
Kindle Edition
$$
Cover image
Machine Learning, revised and updated edition
Save
Provides a comprehensive overview of machine learning, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Machine Learning, revised and updated edition (The...
Paperback
$$
Machine Learning, revised and updated edition (The...
Kindle Edition
$$
Data Mining
Save
Provides a comprehensive overview of data mining, with a focus on concepts and techniques. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Data Mining: Concepts and Techniques (The Morgan...
Kindle Edition
$$$
Data Mining: Concepts and Techniques (The Morgan...
Hardcover
$$$
Data Mining: Concepts and Techniques, Second...
Hardcover
$$
Data Mining: Know It All
Hardcover
$$$
Cover image
Principles of Database Management
Save
Provides a comprehensive overview of big data analytics, with a focus on a practical approach to solving big data problems. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Principles of Database Management: The Practical...
Hardcover
$$$
Principles of Database Management: The Practical...
Kindle Edition
$$$
Cover image
Deep Learning
Save
Provides a comprehensive overview of deep learning, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Deep Learning
Paperback
$$$
Deep Learning (Adaptive Computation and Machine...
Hardcover
$$$
Deep Learning (Adaptive Computation and Machine...
Kindle Edition
$$$
Cover image
Reinforcement Learning, second edition
Save
Provides a comprehensive overview of reinforcement learning, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Reinforcement Learning, second edition: An...
Hardcover
$$$
Reinforcement Learning, second edition: An...
Kindle Edition
$$$
Pattern Recognition and Machine Learning
Save
Provides a comprehensive overview of pattern recognition and machine learning, with a focus on theory and algorithms. It valuable resource for students and practitioners alike, and it can serve as a reference or textbook for the course.
Pattern Recognition and Machine Learning...
Hardcover
$$$
Pattern Recognition and Machine Learning...
Paperback
$$$
Pattern Recognition and Machine Learning (text...
Unknown Binding
$$$$

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Effort
4 weeks of study, 4-8 hours/week
Level
Advanced
Via
Coursera
Institution
University of California San Diego
Instructors
Alexander S. Kulikov
Michael Levin
Daniel M Kane
Neil Rhodes
Language
English
Transcripts
Español Français Português Deutsch Italiano 中文 العربية 한국어 日本語 हिंदी Nederlands Svenska Pусский Türkçe Polski Ελληνικά українська мова magyar nyelv Bahasa Indonesia ไทย қазақша اُردُو, فارسی বাংলা tiếng Việt پښتو آذربایجان دیلی
This course belongs to a collection called Data Structures and Algorithms. It's comprised of six courses:
  1. Algorithmic Toolbox
  2. Advanced Algorithms and Complexity (viewing)
  3. Algorithms on Graphs
  4. Data Structures
  5. Algorithms on Strings
  6. Genome Assembly Programming Challenge
Traffic lights
Read about what's good
what should give you pause
and possible dealbreakers
Provides a thorough foundation for intermediate learners in the field of algorithms
Delves into advanced algorithms, which are essential for solving complex problems
Taught by reputable instructors with expertise in advanced algorithms
Covers topics such as network flows and linear programming, which are highly relevant in industry
Introduces streaming algorithms commonly used in data analysis
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