Gain insights into key graph algorithms, including depth-first search, shortest paths, and flow networks. Explore their applications and foundational role in advanced computing disciplines.

This technology-agnostic course will teach you about many classical graph algorithms essential for a well-rounded software engineer. 

You will begin with an introduction to the running-time analysis of algorithms and the representation and structure of graphs. You’ll cover the depth-first search algorithm and its many applications, like detecting cycles, topological sorting, and identifying cut-vertices and strongly connected components. You will then cover algorithms for finding shortest paths and minimum spanning trees. You’ll also learn about the Ford-Fulkerson algorithm and its use in finding a maximum flow and minimum cut in networks. Moreover, you will adapt it to find maximum matchings and minimum vertex covers in bipartite graphs. Finally, you will learn about the Gale-Shapley algorithm for finding stable matchings.

The material in this course serves as a basis for other advanced algorithms, like parallel and distributed algorithms, and has many diverse applications in other computing disciplines.

Mastering Graph Algorithms

# The task at hand

Grab some paper and a pen, and use the Ford-Fulkerson algorithm on the flow network given below to figure out the value of a maximum flow and the capacity of a minimum cut. Assume that the vertex $v_1$ is the source and the vertex $v_7$ is the sink.  

You can verify your solution by clicking the “Run Ford-Fulkerson” button. 

> **Note:** 
> - You can also experiment on a different flow network using these #concept=instructions#instructions.#concept# 
> - If you choose to add a new edge, its weight will be generated randomly. 
> - If the automatically generated labels overlap with vertices or edges, you may view them more clearly by dragging the vertices of the given digraph (after selecting the “Drag vertices” checkbox).

 

Test your understanding of the Ford-Fulkerson algorithm.

Introduction

Review: Asymptotic Notation and Math Prerequisites

Working with Graphs

Depth-First Search and Applications

Prelude: Shortest Paths

Single-source Shortest Paths in Weighted Digraphs

All Pairs Shortest Paths

Minimum Spanning Tree

Flows

Matchings and Vertex Covers

Conclusion

Use Simulated Annealing for the Traveling Salesman Problem

Exercise: The Ford-Fulkerson Algorithm

The task at hand