Algorithms on Graphs

Go to Course: https://www.coursera.org/learn/algorithms-on-graphs

Introduction

### Course Review: Algorithms on Graphs #### Overview In our increasingly interconnected world, the ability to efficiently navigate and analyze networks is invaluable. Coursera's course, **Algorithms on Graphs**, provides a comprehensive introduction to the powerful algorithms that govern everything from navigation services to social media analysis. Whether you're looking to optimize travel routes, design robust computer networks, or gain insights into social dynamics, this course equips you with the skills to tackle these challenges using graph theory and algorithms. #### Course Structure and Syllabus The course is structured into several modules, each building on the concepts of graph theory and its applications. Here's a brief overview of what you can expect: 1. **Decomposition of Graphs 1 & 2**: - Dive into the representation of graphs and basic decomposition algorithms. You will learn to work with both undirected and directed graphs through practical programming assignments that involve mazes, road networks, and analyzing computer science curricula. 2. **Paths in Graphs 1 & 2**: - This section focuses on finding shortest paths within graphs, a key application of graph theory. You will be introduced to fundamental algorithms such as Breadth-First Search, Dijkstra's Algorithm, and Bellman-Ford's Algorithm. These methods are not only pivotal for navigation applications but also for more complex scenarios like currency exchange optimization. 3. **Minimum Spanning Trees**: - In this module, two greedy algorithms — Kruskal's and Prim's — are examined for solving the minimum spanning tree problem. This part of the course is particularly useful for understanding how to build efficient road networks and clustering tasks in data mining. 4. **Advanced Shortest Paths Project (Optional)**: - For those eager to push their skills further, this optional module introduces advanced shortest path algorithms that enhance performance significantly compared to classical methods. As part of a project, you will find shortest paths on real-world maps and social networks, allowing for creativity and competitiveness in implementation strategies. #### Learning Experience The course strikes a good balance between theoretical concepts and practical applications. The programming assignments are particularly engaging, as they allow you to apply learned algorithms to real-world problems. This hands-on approach not only reinforces understanding but also makes the learning process enjoyable. The teaching style is clear and structured, with a well-paced delivery that helps both beginners and those with some prior knowledge of graph theory to follow along effectively. #### Recommendation **Algorithms on Graphs** is highly recommended for anyone interested in computer science, data analysis, or any field that relies on network structures. The skills learned in this course are universally applicable, making it a valuable addition to your professional toolkit. Whether you're a student gearing up for a career in tech or a professional seeking to enhance your analytical capabilities, this course provides the foundational knowledge and practical skills necessary to excel. The practical applications — from navigation systems to social network analysis — are not only relevant but also incredibly exciting, offering a glimpse into how algorithms shape our digital interactions and decision-making processes. **Final Thoughts** By the end of the course, you will have a robust understanding of graph algorithms and their applications. You will not only be prepared to implement these algorithms in programming tasks but also equipped with insights that can drive decisions in business and technology domains. Don't miss the chance to enhance your skills with this exceptional course on Coursera!

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.

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

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.

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.

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).

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 :)