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Daniel Kane,
Alexander S. Kulikov,
and
Michael Levin
If you have ever used a navigation service to find the 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, water and electricity supply 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.
Read more
If you have ever used a navigation service to find the 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, water and electricity supply 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.
Read more
If you have ever used a navigation service to find the 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, water and electricity supply 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, part of the Algorithms and Data Structures MicroMasters program, you will learn what a graph is and its most important properties. You’ll learn several ways to traverse graphs and how you can do useful things while traversing the graph in some order. We will also talk about shortest paths algorithms. 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.
Register for this course and see more details by visiting:
OpenCourser.com/course/6agtij/graph
What's inside
Learning objectives
- Graph exploration and decomposition into connected components
- Shortest paths algorithms, including breadth-first search, dijkstra’s algorithm and bellman-ford algorithm
- Minimum spanning tree algorithms
- Graph exploration and decomposition into connected components
- Shortest paths algorithms, including breadth-first search, dijkstra’s algorithm and bellman-ford algorithm
- Minimum spanning tree algorithms
Syllabus
Modules 1 and 2: Decomposition of GraphsGraphs 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.
Read more
Syllabus
Modules 1 and 2: Decomposition of GraphsGraphs 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.
Read more
Modules 3 and 4: Shortest PathsIn 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 earn 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.
Module 5: Minimum Spanning TreesIn 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).
Module 6: Flows in NetworksNetwork 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.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Teaches algorithms for finding shortest paths, which is a valuable skill in many industries as well as in academia
Taught by recognized experts in algorithms, including Alexander S. Kulikov, Michael Levin, and Daniel Kane
Develops minimum spanning trees, a fundamental data structure that is highly relevant to a variety of applications in computer science
Requires no prior knowledge of algorithms, making it accessible to beginners
Provides hands-on programming assignments that allow learners to apply the algorithms they learn to real-world problems
Covers advanced topics such as flows in networks, which are relevant to areas such as transportation and logistics
Save this course
Save Graph Algorithms to your list so you can find it easily later:
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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 Graph Algorithms with these
activities:
Review Graphs
Show steps
Start by reviewing the basics of graphs and data structures before taking this course to strengthen your understanding and knowledge
Browse courses on
Graph
Show steps
-
Read through lecture notes and textbook sections on graphs and data structures
-
Complete practice problems and exercises on graphs and data structures
Algorithms, 4th Edition
Show steps
Review the textbook to supplement your learning of algorithms and data structures, providing a broader perspective on the topics covered in the course
View
Introduction to Programming in Java: An...
on Amazon
Show steps
-
Read through relevant chapters and sections on graphs and algorithms
-
Solve practice problems and exercises from the book
Study Group
Show steps
Join a study group to discuss course concepts, exchange ideas, and enhance your understanding through collaborative learning
Show steps
-
Find or create a study group with fellow students
-
Set regular meeting times and discuss assigned topics
Five other activities
Expand to see all activities and additional details
Show all eight activities
Dijkstra's Tutorial
Show steps
Follow a tutorial to enhance your understanding of Dijkstra's algorithm for finding the shortest path in a graph, as covered in Module 3
Show steps
-
Find a tutorial that explains Dijkstra's algorithm in detail
-
Follow the tutorial steps to implement the algorithm in your preferred programming language
LeetCode Practice
Show steps
Enhance your problem-solving skills by completing challenges on LeetCode related to graph algorithms, such as finding shortest paths and minimum spanning trees
Show steps
-
Sign up for a LeetCode account
-
Solve problems tagged with graph algorithms
Maze Solver
Show steps
This course teaches various algorithms for traversing graphs, try implementing a maze solver using these algorithms to test your understanding
Show steps
-
Design a representation for the maze
-
Implement a graph traversal algorithm, such as breadth-first search
-
Validate and test your implementation with different maze configurations
Graph Visualization
Show steps
Create a visual representation of graphs to deepen your understanding of their structure and relationships
Show steps
-
Choose a graph data structure
-
Implement functions to add nodes and edges
-
Develop a visualization algorithm to display the graph
Graph Theory Workshop
Show steps
Attend a workshop to engage with experts in graph theory, learn about advanced concepts, and enhance your practical skills
Show steps
-
Find and register for a relevant workshop
-
Actively participate in discussions and exercises
Review Graphs
Show steps
Start by reviewing the basics of graphs and data structures before taking this course to strengthen your understanding and knowledge
Browse courses on
Graph
Show steps
Show steps
Show steps
- Read through lecture notes and textbook sections on graphs and data structures
- Complete practice problems and exercises on graphs and data structures
Algorithms, 4th Edition
Show steps
Review the textbook to supplement your learning of algorithms and data structures, providing a broader perspective on the topics covered in the course
View
Introduction to Programming in Java: An...
on Amazon
Show steps
Show steps
Show steps
- Read through relevant chapters and sections on graphs and algorithms
- Solve practice problems and exercises from the book
Study Group
Show steps
Join a study group to discuss course concepts, exchange ideas, and enhance your understanding through collaborative learning
Show steps
Show steps
Show steps
- Find or create a study group with fellow students
- Set regular meeting times and discuss assigned topics
Five other activities
Expand to see all activities and additional details
Show all eight activities
Dijkstra's Tutorial
Show steps
Follow a tutorial to enhance your understanding of Dijkstra's algorithm for finding the shortest path in a graph, as covered in Module 3
Show steps
Show steps
Show steps
- Find a tutorial that explains Dijkstra's algorithm in detail
- Follow the tutorial steps to implement the algorithm in your preferred programming language
LeetCode Practice
Show steps
Enhance your problem-solving skills by completing challenges on LeetCode related to graph algorithms, such as finding shortest paths and minimum spanning trees
Show steps
Show steps
Show steps
- Sign up for a LeetCode account
- Solve problems tagged with graph algorithms
Maze Solver
Show steps
This course teaches various algorithms for traversing graphs, try implementing a maze solver using these algorithms to test your understanding
Show steps
Show steps
Show steps
- Design a representation for the maze
- Implement a graph traversal algorithm, such as breadth-first search
- Validate and test your implementation with different maze configurations
Graph Visualization
Show steps
Create a visual representation of graphs to deepen your understanding of their structure and relationships
Show steps
Show steps
Show steps
- Choose a graph data structure
- Implement functions to add nodes and edges
- Develop a visualization algorithm to display the graph
Graph Theory Workshop
Show steps
Attend a workshop to engage with experts in graph theory, learn about advanced concepts, and enhance your practical skills
Show steps
Show steps
Show steps
- Find and register for a relevant workshop
- Actively participate in discussions and exercises
Career center
Learners who complete Graph Algorithms will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
A Data Scientist knows a great deal about modeling and data analysis, which are skills that can help you solve real problems faster and understand complex systems more quickly. By taking this course, you will learn foundational algorithms and techniques that Data Scientists need in order to succeed.
Data Analyst
Data Analyst
Data Analysts must be skilled in data collection, analysis, interpretation, and visualization. The knowledge you'll learn in this course will help you build a foundation for your work as a Data Analyst.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software. The algorithms and data structures skills you'll learn in this course will give you a leg up in many software development roles.
Business Analyst
Business Analyst
A Business Analyst studies and evaluates the structure of an organization and defines business requirements. This course can help you build the skills to perform analysis that allows you to recommend changes and act as a liaison between management and technical staff.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers deploy models to increase programmatic efficiency. Your work will help companies stay competitive. This course will help you build foundational knowledge to get you started.
Quantitative Analyst
Quantitative Analyst
As a Quantitative Analyst, you will use statistical and mathematical modeling to solve complex problems on Wall Street or in other fields. This course gives you an edge in these fields.
Actuary
Actuary
Actuaries combine mathematical and statistical skills to assess financial risk, which makes taking this course a valuable addition to your skillset.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts apply advanced analytical methods to help organizations make better decisions. Taking this course may help you build foundational skills for this role.
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data. This course may help you to develop critical thinking skills which can be beneficial for working as a Statistician.
Data Engineer
Data Engineer
Data Engineers build, maintain, and manage data pipelines and databases. Taking this course will help you develop the necessary skills to succeed in this role.
Financial Analyst
Financial Analyst
Financial Analysts analyze and interpret financial data to make investment recommendations. The mathematical and analytical skills you'll learn in this course with help you build your foundation.
Market Researcher
Market Researcher
Market Researchers study market conditions, customer behavior, and industry trends to help businesses make better decisions. This course may provide some foundational knowledge that can be helpful in this career.
Computer Scientist
Computer Scientist
Computer Scientists are theoretically inclined individuals who research computing and information technology. This course will help you gain a deeper understanding of computing.
Mathematician
Mathematician
Mathematicians use logic, reasoning, and symbols to develop and apply mathematical theories. This course may be useful as you work to build the skills you need to succeed as a Mathematician.
Economist
Economist
Economists study the production, distribution, and consumption of goods and services. This course may be useful as you develop the skills required to be an Economist.
For more career information including salaries, visit:
OpenCourser.com/course/6agtij/graph
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
Graph Algorithms.
Provides a comprehensive introduction to the algorithms discussed in this course. It provides detailed explanations and examples, making it a valuable reference for students.
Save
Provides an in-depth coverage of graph algorithms, including the topics covered in this course. It includes detailed pseudocode and Java code, making it a useful reference for students.
Provides a comprehensive introduction to data structures and algorithms, including the topics covered in this course. It uses Java code throughout, making it a valuable reference for students.
Provides a concise and elegant introduction to the fundamental concepts of algorithms and data structures. It valuable resource for students who want to understand the theoretical foundations of graph algorithms.
Save
Provides a comprehensive introduction to graph theory, including the topics covered in this course. It provides a solid foundation for understanding the theoretical aspects of graph algorithms.
Provides a comprehensive introduction to combinatorial optimization, including the topics covered in this course. It provides advanced algorithms and techniques, making it a valuable reference for students interested in pursuing further studies in optimization.
Provides a comprehensive treatment of network flows, including the topics covered in this course. It provides advanced algorithms and applications, making it a valuable reference for students interested in pursuing further studies in network flows.
Save
Provides a comprehensive introduction to graph algorithms, including the topics covered in this course. It provides detailed pseudocode and examples, making it a valuable reference for students.
Provides a practical guide to designing and implementing algorithms, including the topics covered in this course. It includes real-world examples and case studies, making it a valuable reference for students.
Provides a comprehensive reference on graph theory, including the topics covered in this course. It provides a wide range of topics and applications, making it a valuable reference for students interested in pursuing further studies in graph theory.
Provides a comprehensive introduction to graph theory, including the topics covered in this course. It includes applications to engineering and computer science, making it a valuable reference for students interested in these fields.
Provides a comprehensive introduction to algorithmic graph theory, including the topics covered in this course. It includes advanced algorithms and techniques, making it a valuable reference for students interested in pursuing further studies in graph algorithms.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/6agtij/graph
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Effort
8 to 10 hours per week for 6 weeks
Level
Intermediate
Via
edX
Institution
The University of California, San Diego
Instructors
Daniel Kane
Alexander S. Kulikov
Michael Levin
Language
English
Transcript
English
This course belongs to a
collection
called
Algorithms and Data Structures. It's comprised of nine courses:
- Algorithmic Design and Techniques
- Data Structures Fundamentals
- Graph Algorithms (viewing)
- NP-Complete Problems
- String Processing and Pattern Matching Algorithms
- Dynamic Programming: Applications In Machine Learning and Genomics
- Graph Algorithms in Genome Sequencing
- Algorithms and Data Structures Capstone
- Introduction to Algorithms
Good to know
Teaches algorithms for finding shortest paths, which is a valuable skill in many industries as well as in academia
Taught by recognized experts in algorithms, including Alexander S. Kulikov, Michael Levin, and Daniel Kane
Develops minimum spanning trees, a fundamental data structure that is highly relevant to a variety of applications in computer science
Requires no prior knowledge of algorithms, making it accessible to beginners
Provides hands-on programming assignments that allow learners to apply the algorithms they learn to real-world problems
Covers advanced topics such as flows in networks, which are relevant to areas such as transportation and logistics
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