About this Course
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Intermediate Level

Approx. 17 hours to complete

Suggested: 5 weeks of study, 3-4 hours/week...

English

Subtitles: English

Skills you will gain

Graph TheoryGraphsGraph Algorithms

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

Approx. 17 hours to complete

Suggested: 5 weeks of study, 3-4 hours/week...

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
4 hours to complete

Decomposition of Graphs 1

Graphs arise in various real-world situations as there are road networks, computer networks and, most recently, social networks! If you're looking for the fastest time to get to work, cheapest way to connect set of computers into a network or efficient algorithm to automatically find communities and opinion leaders hot in Facebook, you're going to work with graphs and algorithms on graphs. In this module, you will learn ways to represent a graph as well as basic algorithms for decomposing graphs into parts. In the programming assignment of this module, you will apply the algorithms that you’ve learned to implement efficient programs for exploring mazes, analyzing Computer Science curriculum, and analyzing road networks. In the first week of the module, we focus on undirected graphs....
5 videos (Total 43 min), 3 readings, 1 quiz
5 videos
Representing Graphs9m
Exploring Graphs14m
Connectivity5m
Previsit and Postvisit Orderings7m
3 readings
Welcome10m
Slides and External References10m
Slides and External References10m
Week
2
4 hours to complete

Decomposition of Graphs 2

This week we continue to study graph decomposition algorithms, but now for directed graphs....
4 videos (Total 36 min), 1 reading, 1 quiz
4 videos
Topological Sort9m
Strongly Connected Components7m
Computing Strongly Connected Components10m
1 reading
Slides and External References10m
Week
3
4 hours to complete

Paths in Graphs 1

In this module you will study algorithms for finding Shortest Paths in Graphs. These algorithms have lots of applications. When you launch a navigation app on your smartphone like Google Maps or Yandex.Navi, it uses these algorithms to find you the fastest route from work to home, from home to school, etc. When you search for airplane tickets, these algorithms are used to find a route with the minimum number of plane changes. Unexpectedly, these algorithms can also be used to determine the optimal way to do currency exchange, sometimes allowing to earh huge profit! We will cover all these applications, and you will learn Breadth-First Search, Dijkstra's Algorithm and Bellman-Ford Algorithm. These algorithms are efficient and lay the foundation for even more efficient algorithms which you will learn and implement in the Shortest Paths Capstone Project to find best routes on real maps of cities and countries, find distances between people in Social Networks. In the end you will be able to find Shortest Paths efficiently in any Graph. This week we will study Breadth-First Search algorithm....
8 videos (Total 55 min), 1 reading, 1 quiz
8 videos
Breadth-First Search7m
Breadth-First Search (continued)6m
Implementation and Analysis9m
Proof of Correctness7m
Proof of Correctness (continued)5m
Shortest-Path Tree6m
Reconstructing the Shortest Path3m
1 reading
Slides and External References10m
Week
4
5 hours to complete

Paths in Graphs 2

This week we continue to study Shortest Paths in Graphs. You will learn Dijkstra's Algorithm which can be applied to find the shortest route home from work. You will also learn Bellman-Ford's algorithm which can unexpectedly be applied to choose the optimal way of exchanging currencies. By the end you will be able to find shortest paths efficiently in any Graph....
12 videos (Total 86 min), 2 readings, 1 quiz
12 videos
Naive Algorithm10m
Dijkstra's Algorithm: Intuition and Example7m
Dijkstra's Algorithm: Implementation3m
Dijkstra's Algorithm: Proof of Correctness4m
Dijkstra's Algorithm: Running Time7m
Currency Exchange6m
Currency Exchange: Reduction to Shortest Paths8m
Bellman-Ford Algorithm6m
Bellman-Ford Algorithm: Proof of Correctness6m
Negative Cycles7m
Infinite Arbitrage10m
2 readings
Slides and External References10m
Slides and External References10m
Week
5
4 hours to complete

Minimum Spanning Trees

In this module, we study the minimum spanning tree problem. We will cover two elegant greedy algorithms for this problem: the first one is due to Kruskal and uses the disjoint sets data structure, the second one is due to Prim and uses the priority queue data structure. In the programming assignment for this module you will be computing an optimal way of building roads between cities and an optimal way of partitioning a given set of objects into clusters (a fundamental problem in data mining)....
5 videos (Total 53 min), 1 reading, 1 quiz
5 videos
Greedy Algorithms4m
Cut Property9m
Kruskal's Algorithm15m
Prim's Algorithm13m
1 reading
Slides and External References10m
Week
6
34 hours to complete

Advanced Shortest Paths Project (Optional)

In this module, you will learn Advanced Shortest Paths algorithms that work in practice 1000s (up to 25000) of times faster than the classical Dijkstra's algorithm on real-world road networks and social networks graphs. You will work on a Programming Project based on these algorithms. You will find the shortest paths on the real maps of parts of US and the shortest paths connecting people in the social networks. We encourage you not only to use the ideas from this module's lectures in your implementations, but also to come up with your own ideas for speeding up the algorithm! We encourage you to compete on the forums to see whose implementation is the fastest one :)...
17 videos (Total 130 min), 3 readings, 2 quizzes
17 videos
Bidirectional Search10m
Six Handshakes6m
Bidirectional Dijkstra5m
Finding Shortest Path after Meeting in the Middle9m
Computing the Distance2m
A* Algorithm11m
Performance of A*2m
Bidirectional A*6m
Potential Functions and Lower Bounds5m
Landmarks (Optional)10m
Highway Hierarchies and Node Importance7m
Preprocessing7m
Witness Search10m
Query8m
Proof of Correctness9m
Node Ordering14m
3 readings
Slides and External References10m
Slides and External References10m
Slides and External Refernces10m
1 practice exercise
Bidirectional Dijkstra, A* and Contraction Hierarchiess
4.7
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Top Reviews

By SKApr 24th 2018

This course is very much helpful for the graph beginners. As a suggestion, i would like to say that add some extra contents on the data structures which is to be used in the algorithm.

By EMSep 23rd 2017

Great!\n\nHard concepts explained clearly and in depth, in the same fashion as the previous two courses (Algo Toolbox and Data Structure).\n\nGood job!

Instructors

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Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering
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Michael Levin

Lecturer
Computer Science
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Daniel M Kane

Assistant Professor
Department of Computer Science and Engineering / Department of Mathematics
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Neil Rhodes

Adjunct Faculty
Computer Science and Engineering

About University of California San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

About National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

About the Data Structures and Algorithms Specialization

This specialization is a mix of theory and practice: you will learn algorithmic techniques for solving various computational problems and will implement about 100 algorithmic coding problems in a programming language of your choice. No other online course in Algorithms even comes close to offering you a wealth of programming challenges that you may face at your next job interview. To prepare you, we invested over 3000 hours into designing our challenges as an alternative to multiple choice questions that you usually find in MOOCs. Sorry, we do not believe in multiple choice questions when it comes to learning algorithms...or anything else in computer science! For each algorithm you develop and implement, we designed multiple tests to check its correctness and running time — you will have to debug your programs without even knowing what these tests are! It may sound difficult, but we believe it is the only way to truly understand how the algorithms work and to master the art of programming. The specialization contains two real-world projects: Big Networks and Genome Assembly. You will analyze both road networks and social networks and will learn how to compute the shortest route between New York and San Francisco (1000 times faster than the standard shortest path algorithms!) Afterwards, you will learn how to assemble genomes from millions of short fragments of DNA and how assembly algorithms fuel recent developments in personalized medicine....
Data Structures and Algorithms

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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