Algorithms on Graphs from Coursera

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 a 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 online 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.

What's inside

Syllabus

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.

Decomposition of Graphs 2

This week we continue to study graph decomposition algorithms, but now for directed graphs.

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.

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.

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).

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 :)

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Taught by Neil Rhodes, Michael Levin, Alexander S. Kulikov, Daniel M Kane; they are experienced algorithm scientists and instructors

Covers shortest pathfinding, a core skill for programmers in Tech

Develops problem-solving skills in the context of graphs and their applications

Provides a strong theoretical foundation for exploring many topics in Computer Science

Touches on topics heavily used in Industry (fastest routes in navigation systems, efficient network design)

Reviews summary

Algorithms on graphs: highly recommended

Learners say that Algorithms on Graphs is a superb course with engaging assignments. According to students, this course is well structured, with clear explanations, thought-provoking discussions, and helpful programming assignments that aid in understanding the material. Overall, learners strongly recommend this course.

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 Algorithms on Graphs with these activities:

Review Matrix Representation of Graphs

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Review matrix representation of graphs to enhance your understanding of graph theory.

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Go over notes or resources from previous coursework
Solve practice problems involving matrix representation of graphs

Read Introduction to Algorithms by Cormen et al.

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Strengthen your foundational understanding of algorithms by reading a classic textbook in the field.

View Introduction to Algorithms, fourth edition on Amazon

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Read selected chapters related to graph algorithms
Solve practice problems from the book

Join a Study Group for Graph Algorithms

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Engage with peers to discuss and reinforce concepts related to graph algorithms.

Browse courses on Graphs

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Find a study group or create one with classmates
Schedule regular meetings
Discuss course materials, solve problems, and share insights

Six other activities

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Create a Visualization of Breadth-First Search

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Create a visual representation of Breadth-First Search to solidify your understanding of graph traversal algorithms.

Browse courses on Breadth-First Search

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Choose a tool for creating visualizations
Implement Breadth-First Search algorithm
Visualize the execution of the algorithm

Attend a Workshop on Advanced Graph Algorithms

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Deepen your understanding by attending a workshop tailored to advanced graph algorithms.

Browse courses on Graphs

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Research and identify relevant workshops
Register and attend the workshop
actively participate and engage with experts

Practice Dijkstra's Algorithm

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Practice Dijkstra's Algorithm to strengthen your understanding of finding the shortest paths in graphs.

Browse courses on Shortest Paths

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Learn Dijkstra's Algorithm
Find practice problems
Solve practice problems using Dijkstra's Algorithm

Participate in Coding Contests on Graph Algorithms

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Challenge yourself by participating in coding contests that focus on graph algorithms.

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Identify coding platforms that host contests
Solve contest problems related to graph algorithms
Analyze your solutions and learn from others

Practice Creating Minimum Spanning Trees

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Practice creating minimum spanning trees to improve your understanding of network optimization.

Browse courses on Minimum Spanning Trees

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Understand the concept of minimum spanning trees
Learn algorithms like Kruskal's and Prim's
Practice creating minimum spanning trees using these algorithms

Practice Finding Shortest Paths with Advanced Algorithms

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Enhance your understanding of advanced shortest path algorithms and their practical applications.

Browse courses on Graphs

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Learn algorithms like A* and Dijkstra's with Fibonacci heap
Implement these algorithms
Apply them to real-world problems like finding shortest routes

Career center

Learners who complete Algorithms on Graphs will develop knowledge and skills that may be useful to these careers:

Management Consultant

Management Consultants help organizations improve their performance by providing advice on strategy, operations, and technology. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to analyze business problems, identify solutions, and communicate findings to stakeholders.

See salaries and explore the career path for Management Consultant

Marketing Manager

Marketing Managers are responsible for developing and executing marketing campaigns. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to develop and execute marketing campaigns, as well as how to manage marketing teams. This course is the right fit for Marketing Managers who want to learn about the use of graphs to map out customer and marketing data.

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Data Scientist

Data Scientists use their knowledge of mathematics, statistics, and computer science to analyze data and solve problems. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to analyze data, identify trends, and draw conclusions. Data scientists often use graph algorithms to find patterns and trends in datasets. This course offers a great foundation for that line of work.

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Business Analyst

Business Analysts use their knowledge of business and technology to analyze business problems and identify solutions. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to analyze business problems, identify solutions, and communicate findings to stakeholders.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve problems in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to use mathematical and analytical techniques to solve problems, as well as how to communicate findings to stakeholders. This course helps build a foundation for those looking to work with graphs to develop optimal solutions for business problems.

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Software Engineer

Software Engineers design, develop, and maintain software systems. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to design and develop software systems, as well as how to test and debug code. Many Google Maps developers rely on an advanced understanding of algorithms on graphs. This course is the right fit for a software engineer seeking such knowledge.

See salaries and explore the career path for Software Engineer

Customer Success Manager

Customer Success Managers are responsible for ensuring that customers are satisfied with their products and services. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to ensure that customers are satisfied with their products and services.

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Systems Analyst

Systems Analysts are responsible for analyzing business systems and recommending improvements. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to analyze business systems and recommend improvements.

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Data Analyst

Data Analysts use their knowledge of mathematics, statistics, and computer science to analyze data and solve business problems. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to analyze data, identify trends, and draw conclusions. Many Data Analysts also need to gain familiarity with graph algorithms. This course provides a foundation in this area.

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Financial Analyst

Financial Analysts use their knowledge of finance and economics to analyze financial data and make investment recommendations. They may work in a variety of industries, including investment banking, asset management, and hedge funds. This course would be helpful in learning how to analyze financial data, make investment recommendations, and communicate findings to stakeholders.

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Product Manager

Product Managers are responsible for the development and launch of new products. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to develop and launch new products, as well as how to manage product teams.

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Project Manager

Project Managers are responsible for planning, executing, and closing projects. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to plan, execute, and close projects.

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Sales Manager

Sales Managers are responsible for managing sales teams and generating revenue. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to manage sales teams and generate revenue.

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Data Engineer

Data Engineers are responsible for the design, construction, and maintenance of data pipelines and systems. They may work in a variety of industries, including finance, healthcare, and retail. This course would be helpful in learning how to design and build data pipelines, as well as how to manage and analyze data. Data Engineers also rely on graph algorithms to help process data. Knowledge of these algorithms can be applied to working in this field.

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Business Development Manager

Business Development Managers are responsible for generating new business for their companies. They may work in a variety of industries, including technology, retail, and manufacturing. This course would be helpful in learning how to generate new business, as well as how to manage sales teams.

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