Design & Analysis of Algorithms - Vol 1 | 26. Shortest Paths in Weighted Graphs by Abraham | Learn Smarter
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26. Shortest Paths in Weighted Graphs

The chapter focuses on the computation of shortest paths in weighted graphs, detailing techniques like Dijkstra's algorithm that efficiently determine minimum cost routes between vertices. It contrasts the single-source shortest path problem with the all-pairs shortest path problem and highlights practical applications in transportation and logistics. Understanding these algorithms is essential for problem-solving in various graph-related applications.

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Sections

  • 26.1

    Shortest Paths In Weighted Graphs

    This section discusses the computation of shortest paths in weighted graphs, distinguishing it from unweighted graphs and highlighting the applications and algorithms used to solve these problems.

    Learning Practice

  • 26.1.1

    Introduction To Weighted Graphs

    This section introduces weighted graphs, exploring the computation of shortest paths across them.

    Learning Practice

  • 26.1.2

    Exploration Of Graphs

    This section introduces the concept of weighted graphs and discusses methods for computing shortest paths between vertices.

    Learning Practice

  • 26.1.3

    Cost Of Edges In Graphs

    This section discusses the concept of weighted graphs, where edges have associated costs, primarily focusing on computing shortest paths.

    Learning Practice

  • 26.1.4

    Total Cost Calculation

    This section discusses the computation of shortest paths in weighted graphs, focusing on the significance of edge costs and the methods used to determine minimal travel costs.

    Learning Practice

  • 26.1.5

    Types Of Shortest Path Problems

    This section introduces weighted graphs and their significance in computing shortest paths, detailing single-source and all-pairs shortest path problems.

    Learning Practice

  • 26.1.5.1

    Single Source Shortest Path Problem

    This section covers the Single Source Shortest Path Problem in weighted graphs, detailing how to compute the shortest paths from a single source vertex to all other vertices in the graph.

    Learning Practice

  • 26.1.5.2

    All Pairs Shortest Path Problem

    This section examines the All Pairs Shortest Path Problem in weighted graphs, including concepts such as edge weights, shortest path determination, and algorithms like Dijkstra's for shortest paths.

    Learning Practice

  • 26.1.6

    Algorithm Analogy

    This section introduces the concept of weighted graphs and explores the algorithms used to compute the shortest paths through analogies.

    Learning Practice

  • 26.1.7

    Algorithm Execution

    This section explores the computation of shortest paths in weighted graphs using various algorithms and methodologies.

    Learning Practice

  • 26.1.7.1

    Describing The Burning Process

    This section discusses the process of finding the shortest path in weighted graphs using a burning analogy to illustrate the concept of edge weights and path costs.

    Learning Practice

  • 26.1.7.2

    Formal Algorithm Description

    This section focuses on algorithms for finding the shortest paths in weighted graphs, extending the principles of breadth-first search and depth-first search.

    Learning Practice

  • 26.1.8

    Dijkstra's Algorithm

    This section discusses Dijkstra's Algorithm for finding shortest paths in weighted graphs, highlighting its principles and applications.

    Learning Practice

References

ch25.pdf

Class Notes

Memorization

What we have learnt

  • Weighted graphs assign cost...
  • Dijkstra's algorithm is a s...
  • The shortest path in a weig...

Final Test

Revision Tests