HomeCoursesMastering Graph Algorithms

4.3

Beginner

15h

Updated 2 months ago

Mastering Graph Algorithms

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.

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Overview

Content

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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.

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

WHAT YOU'LL LEARN

An understanding of classical graph algorithms

The ability to think and visualize in terms of graph structures

An inside-out understanding of what makes each algorithm work the way it does

Cultivation of a broader perspective that informs other computing disciplines

An understanding of classical graph algorithms

Content

91 Lessons50 Quizzes

Introduction

1 Lessons

Get familiar with the fundamentals and applications of graph algorithms across disciplines.

What Is This Course About?

Review: Asymptotic Notation and Math Prerequisites

11 Lessons

Grasp the fundamentals of logarithms, running time, and big-O notation for algorithm analysis.

Getting Started with Logarithms

Food for Thought: Running Time

Running Time as a Function of Input Size

Comparing Running times

Big-O Notation

Ruminating on Constants in Big-O Notation

Some Useful Facts

A Big-O Drill

Leveraging the Proof by Contradiction Technique

Exercise: Order of Growth

Quiz: Big-O Notation

Working with Graphs

9 Lessons

Work your way through understanding and representing graphs, including adjacency matrices, lists, and special graph types.

Depth-First Search and Applications

16 Lessons

Grasp the fundamentals of Depth-First Search and its applications in graph traversal and analysis.

Prelude: Shortest Paths

7 Lessons

Explore shortest-path strategies, BFS for unweighted digraphs, and apply graph traversal concepts.

Single-source Shortest Paths in Weighted Digraphs

12 Lessons

Focus on solving the single-source shortest paths problem using various algorithms in weighted digraphs.

All Pairs Shortest Paths

5 Lessons

Practice using Johnson's and Floyd-Warshall algorithms for efficient all-pairs shortest paths.

Minimum Spanning Tree

12 Lessons

Learn how to use Minimum Spanning Trees via Prim's and Kruskal's algorithms effectively.

Flows

6 Lessons

Walk through network flows, the Ford-Fulkerson algorithm, and practical exercises.

10.

Matchings and Vertex Covers

11 Lessons

Examine matchings, vertex covers, the Ford-Fulkerson algorithm, and the Gale-Shapley algorithm.

11.

Conclusion

1 Lessons

Grasp the fundamentals of graph algorithms' applications, utility, and practical significance in various fields.

Use Simulated Annealing for the Traveling Salesman Problem

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