About this course: If you have ever used a navigation service to find optimal route and estimate time to destination, you've used algorithms on graphs. 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 in Facebook, you're going to work with graphs and algorithms on graphs. In this course, you will first learn what a graph is and what are some of the most important properties. Then you'll learn several ways to traverse graphs and how you can do useful things while traversing the graph in some order. We will then talk about shortest paths algorithms — from the basic ones to those which open door for 1000000 times faster algorithms used in Google Maps and other navigational services. You will use these algorithms if you choose to work on our Fast Shortest Routes industrial capstone project. We will finish with minimum spanning trees which are used to plan road, telephone and computer networks and also find applications in clustering and approximate algorithms.
Created by: University of California San Diego, National Research University Higher School of Economics
Taught by: Alexander S. Kulikov, Visiting Professor
Department of Computer Science and Engineering
Taught by: Michael Levin, Lecturer
Computer Science
Taught by: Daniel M Kane, Assistant Professor
Department of Computer Science and Engineering / Department of Mathematics
Taught by: Neil Rhodes, Adjunct Faculty
Computer Science and Engineering
| Basic Info | Course 3 of 6 in the 数据结构与算法 Specialization |
| Level | Intermediate |
| Commitment | 5 weeks of study, 3-4 hours/week |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
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, 3 readings
- Reading: Welcome
- Video: Representing Graphs
- Reading: Slides and External References
- Video: Exploring Graphs
- Video: Connectivity
- Video: Previsit and Postvisit Orderings
- Reading: Slides and External References
Graded: Programming Assignment 1: Decomposition of Graphs
WEEK 2
Decomposition of Graphs 2
This week we continue to study graph decomposition algorithms, but now for directed graphs.
4 videos, 1 reading
- Video: Topological Sort
- Video: Strongly Connected Components
- Video: Computing Strongly Connected Components
- Reading: Slides and External References
Graded: Programming Assignment 2: Decomposition of Graphs
WEEK 3
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, 1 reading
- Video: Breadth-First Search
- Video: Breadth-First Search (continued)
- Video: Implementation and Analysis
- Video: Proof of Correctness
- Video: Proof of Correctness (continued)
- Video: Shortest-Path Tree
- Video: Reconstructing the Shortest Path
- Reading: Slides and External References
Graded: Programming Assignment 3: Paths in Graphs
WEEK 4
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, 2 readings
- Video: Naive Algorithm
- Video: Dijkstra's Algorithm: Intuition and Example
- Video: Dijkstra's Algorithm: Implementation
- Video: Dijkstra's Algorithm: Proof of Correctness
- Video: Dijkstra's Algorithm: Running Time
- Reading: Slides and External References
- Video: Currency Exchange
- Video: Currency Exchange: Reduction to Shortest Paths
- Video: Bellman-Ford Algorithm
- Video: Bellman-Ford Algorithm: Proof of Correctness
- Video: Negative Cycles
- Video: Infinite Arbitrage
- Reading: Slides and External References
Graded: Programming Assignment 4: Paths in Graphs
WEEK 5
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, 1 reading
- Video: Greedy Algorithms
- Video: Cut Property
- Video: Kruskal's Algorithm
- Video: Prim's Algorithm
- Reading: Slides and External References
Graded: Programming Assignment 5: Minimum Spanning Trees
WEEK 6
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, 3 readings, 1 practice quiz
- Video: Bidirectional Search
- Video: Six Handshakes
- Video: Bidirectional Dijkstra
- Video: Finding Shortest Path after Meeting in the Middle
- Video: Computing the Distance
- Reading: Slides and External References
- Video: A* Algorithm
- Video: Performance of A*
- Video: Bidirectional A*
- Video: Potential Functions and Lower Bounds
- Video: Landmarks (Optional)
- Reading: Slides and External References
- Video: Highway Hierarchies and Node Importance
- Video: Preprocessing
- Video: Witness Search
- Video: Query
- Video: Proof of Correctness
- Video: Node Ordering
- Reading: Slides and External Refernces
- Practice Quiz: Bidirectional Dijkstra, A* and Contraction Hierarchies
- Ungraded Programming: Advanced Shortest Paths
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University of California San Diego
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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 communications, IT, mathematics, engineering, and more.
Learn more on www.hse.ru
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Ratings and Reviews
Amazing class that helped me understand graph algorithms.
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.
Excellent materials on graphs. Thanks to the instructors.
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OA
Excellent course. Like with the other courses in the series the programming assignment are a great help for understanding the material.