Shortest Paths & NP-Complete Problems
Learn advanced algorithms focusing on shortest paths, NP-completeness, and strategies for intractable problems in this intermediate computer science course.
Learn advanced algorithms focusing on shortest paths, NP-completeness, and strategies for intractable problems in this intermediate computer science course.
This intermediate-level course explores advanced algorithms focusing on three key areas: shortest path algorithms, NP-completeness theory, and strategies for handling computationally intractable problems. You'll master fundamental algorithms like Bellman-Ford, Floyd-Warshall, and Johnson for solving shortest path problems in various graph scenarios. The course then delves into NP-completeness and its implications for algorithm design, equipping you with a theoretical framework to understand computational complexity. Finally, you'll explore practical approaches for dealing with intractable problems, including approximation algorithms, heuristics, local search techniques, and dynamic programming. Throughout the course, you'll apply these concepts through programming assignments and problem sets, gaining hands-on experience that reinforces theoretical understanding.
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What you'll learn
Implement and analyze the Bellman-Ford algorithm for single-source shortest paths
Master all-pairs shortest path algorithms like Floyd-Warshall and Johnson's algorithm
Understand NP-completeness and its implications for algorithm design
Design exact algorithms for NP-complete problems like Vertex Cover and Traveling Salesman
Develop approximation algorithms and heuristics for NP-complete problems
Implement and analyze local search algorithms for optimization problems
Skills you'll gain
This course includes:
7.75 Hours PreRecorded video
9 assignments
Access on Mobile, Tablet, Desktop
FullTime access
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There are 4 modules in this course
This course, part of the Algorithms Specialization, covers three main topics: shortest paths algorithms, NP-completeness theory, and strategies for handling computationally intractable problems. The shortest paths section explores Bellman-Ford, Floyd-Warshall, and Johnson's algorithms for single-source and all-pairs problems. The NP-completeness modules provide a theoretical framework for understanding problem complexity and its implications for algorithm design. The final sections focus on practical approaches to intractable problems, including approximation algorithms, heuristics, and local search techniques. Throughout the course, students apply concepts through programming assignments and problem sets, developing both theoretical understanding and practical implementation skills.
Week 1
Module 1 · 4 Hours to complete
Week 2
Module 2 · 3 Hours to complete
Week 3
Module 3 · 1 Hours to complete
Week 4
Module 4 · 4 Hours to complete
Fee Structure
Instructor
A Pioneering Computer Scientist and Game Theory Expert
Tim Roughgarden has established himself as a leading figure in theoretical computer science, particularly at the intersection of algorithms and economics. Born July 20, 1975, he earned his Ph.D. from Cornell University in 2002 under Éva Tardos's supervision, followed by a postdoc at UC Berkeley. He served as a professor in Stanford University's Computer Science department from 2004 to 2018 before joining Columbia University. His research focuses on algorithm design, game theory, and their applications to networks, auctions, and blockchains. His contributions have earned him numerous prestigious honors, including the Grace Murray Hopper Award, the Presidential Early Career Award for Scientists and Engineers, the Gödel Prize, and a Guggenheim Fellowship. As an educator, he has developed widely-used online courses in algorithms through Coursera and authored several influential textbooks including "Algorithms Illuminated" and "Twenty Lectures on Algorithmic Game Theory." Currently serving as a Professor at Columbia University and Head of Research at a16z crypto, he continues to advance the field through his work on the boundary of computer science and economics.
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