Design & Analysis of Algorithms - Vol 1 | 28. Module – 03 by Abraham | Learn Smarter
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28. Module – 03

The chapter explores the Bellman-Ford algorithm as a method for finding the shortest paths in graphs, especially those containing negative edge weights. It discusses the limitations and assumptions of Dijkstra's algorithm and contrasts them with the reassurances provided by Bellman-Ford when negative cycles are not present. The emphasis is placed on the determination of shortest paths through systematic updates rather than greedy choices.

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Sections

  • 28.1

    Design And Analysis Of Algorithms, Chennai Mathematical Institute

    The section introduces the Bellman-Ford algorithm for finding the shortest paths in graphs with negative edge weights, distinguishing it from Dijkstra's algorithm.

    Learning Practice

  • 28.1.1

    Prof. Madhavan Mukund

    The section details the Bellman-Ford algorithm, which is designed to find the shortest paths in graphs with negative edge weights but no negative cycles.

    Learning Practice

  • 28.1.2

    Department Of Computer Science And Engineering

    The section introduces the Bellman-Ford Algorithm for finding the shortest paths in graphs with negative edge weights, emphasizing properties that differentiate it from Dijkstra's algorithm.

    Learning Practice

  • 28.1.3

    Module – 03

    This section explores the Bellman-Ford Algorithm for finding shortest paths in graphs that contain negative edge weights.

    Learning Practice

  • 28.1.4

    Lecture - 27

    This section discusses the Bellman-Ford algorithm, which computes shortest paths in graphs with negative edge weights but no negative cycles.

    Learning Practice

  • 28.2

    Negative Edges: Bellman-Ford Algorithm

    The Bellman-Ford Algorithm is designed to compute the shortest paths in graphs that may have negative edge weights, while ensuring no negative cycles exist.

    Learning Practice

  • 28.2.1

    Introduction To Negative Edges

    This section introduces the Bellman-Ford algorithm for finding shortest paths in graphs with negative edge weights, emphasizing the importance of avoiding negative cycles.

    Learning Practice

  • 28.2.2

    Properties Of Shortest Paths

    This section discusses the properties of shortest paths in graphs with negative edge weights, specifically elaborating on the Bellman-Ford algorithm.

    Learning Practice

  • 28.2.3

    Update Operation In Dijkstra's Algorithm

    This section discusses the update operation in Dijkstra's algorithm, especially in the context of handling graphs with negative edge weights.

    Learning Practice

  • 28.2.4

    Characteristics Of The Bellman-Ford Algorithm

    The Bellman-Ford algorithm calculates shortest paths in graphs with negative edge weights, distinguishing itself from Dijkstra's algorithm by allowing incomplete path evaluations.

    Learning Practice

  • 28.2.5

    Example Of Bellman-Ford Algorithm

    This section outlines the Bellman-Ford Algorithm, which calculates the shortest paths in graphs with negative edge weights, provided there are no negative cycles.

    Learning Practice

References

ch27.pdf

Class Notes

Memorization

What we have learnt

  • The Bellman-Ford algorithm ...
  • A shortest path will never ...
  • The update operation in the...

Final Test

Revision Tests