Design & Analysis of Algorithms - Vol 1 | 24. Topological Ordering of Directed Acyclic Graphs (DAG) by Abraham | Learn Smarter
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24. Topological Ordering of Directed Acyclic Graphs (DAG)

The chapter focuses on the topological sorting of directed acyclic graphs (DAGs), detailing the process of labeling vertices by their in-degrees and demonstrating the elimination of vertices to determine a valid sequence of tasks. A specific algorithm involving adjacency lists is discussed, highlighting how it improves efficiency to linear time complexity for identifying in-degrees and processing vertices. The chapter concludes with pseudocode to illustrate the implemented algorithm and its complexity analysis.

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Sections

  • 24.1

    Topological Ordering Of Directed Acyclic Graphs (Dag)

    This section explains the process of topologically ordering vertices in directed acyclic graphs (DAGs) using in-degree counts.

    Learning Practice

  • 24.1.1

    Introduction To In Degrees

    This section introduces the concept of 'in degrees' in directed acyclic graphs (DAGs), detailing how vertices are labeled and how in degrees are calculated during topological sorting.

    Learning Practice

  • 24.1.2

    Elimination Process

    This section outlines the elimination process for vertices in a Directed Acyclic Graph (DAG), focusing on in-degree updates and topological ordering.

    Learning Practice

  • 24.1.3

    Valid Topological Ordering

    This section discusses the process of performing a topological sort on a directed acyclic graph (DAG), highlighting how to determine valid ordering based on in-degrees.

    Learning Practice

  • 24.1.4

    Pseudo Code For Algorithm

    This section explains how to derive a pseudo code for performing topological sorting on a Directed Acyclic Graph (DAG) by calculating in-degrees and iteratively eliminating vertices.

    Learning Practice

  • 24.1.5

    Algorithm Complexity

    The section discusses algorithm complexity, specifically focusing on topological sorting in directed acyclic graphs (DAGs).

    Learning Practice

  • 24.1.6

    Using Adjacency List

    This section describes the process of implementing a topological sort on a Directed Acyclic Graph (DAG) using an adjacency list, focusing on the computation of in-degrees and the elimination of vertices.

    Learning Practice

  • 24.1.6.1

    Implementation Steps

    This section outlines the implementation steps of a topological sorting algorithm for Directed Acyclic Graphs (DAG).

    Learning Practice

References

ch23 part b.pdf

Class Notes

Memorization

What we have learnt

  • Topological sorting is esse...
  • The in-degree of a vertex i...
  • Using an adjacency list enh...

Final Test

Revision Tests