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 a paper and a pen, and figure out what are the stack contents right before each SSC of the following graph is identified by Tarjan’s algorithm. Assume that depth-first search is implemented to visit the vertices with smaller subscripts first.

You may verify your solution by clicking the “Run Tarjan’s Algorithm” button.  

> **Note:** 
> - You may also try experimenting on a different digraph that can be created following these #concept=instructions#instructions.#concept# 
> - 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 Tarjan’s 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: Practice Tarjan’s Algorithm

The task at hand