Design & Analysis of Algorithms - Vol 1 | 25. DAGs: Longest Paths by Abraham | Learn Smarter
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25. DAGs: Longest Paths

The chapter covers the concept of Directed Acyclic Graphs (DAGs) and focuses on identifying the longest path within them. It discusses practical applications, such as scheduling courses based on prerequisites. The chapter emphasizes the use of topological sorting to determine the longest path efficiently, showcasing the relationship between longest paths and task scheduling with dependencies.

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Sections

  • 25.1

    Dags: Longest Paths

    This section explores the longest path problem in Directed Acyclic Graphs (DAGs), identifying how to calculate the longest path using topological ordering.

    Learning Practice

  • 25.1.1

    Introduction To Dags

    This section discusses Directed Acyclic Graphs (DAGs) and how to identify the longest path in a DAG, which corresponds to various dependency-related problems.

    Learning Practice

  • 25.1.2

    Topological Sorting

    Topological sorting provides a way to order the vertices of a Directed Acyclic Graph (DAG) based on their dependencies, which is crucial for solving problems like determining the minimum number of semesters needed to complete a set of tasks.

    Learning Practice

  • 25.1.3

    Example With Courses And Prerequisites

    This section explores the problem of finding the Longest Path in a Directed Acyclic Graph (DAG), particularly in the context of scheduling courses based on prerequisites.

    Learning Practice

  • 25.1.4

    Setting Up The Longest Path Problem

    This section discusses the identification of the longest path in Directed Acyclic Graphs (DAGs) and its significance in solving practical problems, such as scheduling courses.

    Learning Practice

  • 25.1.5

    Computing Longest Path Using Topological Order

    This section discusses the process of determining the longest path in a Directed Acyclic Graph (DAG) through topological ordering.

    Learning Practice

  • 25.1.6

    Naive Vs. Incremental Computation

    This section explores the concept of finding the longest path in Directed Acyclic Graphs (DAGs) and compares naive versus incremental computation methods.

    Learning Practice

  • 25.1.7

    Step-By-Step Example Of Longest Path Computation

    This section explores how to compute the longest path in a directed acyclic graph (DAG), highlighting its significance and method of calculation.

    Learning Practice

  • 25.1.8

    Pseudo Code For Longest Path

    This section discusses finding the longest path in a Directed Acyclic Graph (DAG) and its application in modeling dependencies like course prerequisites.

    Learning Practice

  • 25.1.9

    Complexity Analysis

    This section discusses how to analyze the longest path in a Directed Acyclic Graph (DAG), focusing on topological sorting and dependency management.

    Learning Practice

  • 25.1.10

    Importance Of Dags And Efficiency In Longest Path

    This section delves into Directed Acyclic Graphs (DAGs) and the significance of efficiently identifying the longest path in them, particularly in practical scenarios like course scheduling.

    Learning Practice

  • 25.1.11

    Challenges With Arbitrary Graphs

    This section discusses the concept of identifying the longest path in Directed Acyclic Graphs (DAGs) and contrasts it with arbitrary graphs where finding the longest path poses significant challenges.

    Learning Practice

References

ch24.pdf

Class Notes

Memorization

Final Test

Revision Tests