Design & Analysis of Algorithms - Vol 2 | 2. Minimum Cost Spanning Trees by Abraham | Learn Smarter
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2. Minimum Cost Spanning Trees

The chapter discusses the concept of Minimum Cost Spanning Trees in graph theory, highlighting the importance of connectivity and cost-effectiveness in restoring road networks after disasters. It introduces examples of spanning trees, the criteria for formation, and presents Prim’s and Kruskal’s algorithms as solutions for finding minimum cost spanning trees. The properties and definitions of trees are explored, establishing their fundamental characteristics such as connectivity and acyclicity.

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Sections

  • 2

    Minimum Cost Spanning Trees

    This section discusses the concept of Minimum Cost Spanning Trees, emphasizing the connection and cost optimization in graph algorithms.

    Learning Practice

  • 2.1

    Problem Motivation

    This section introduces the concept of Minimum Cost Spanning Trees through a real-world context involving road restoration after a cyclone.

    Learning Practice

  • 2.2

    Spanning Trees

    This section introduces Minimum Cost Spanning Trees, highlighting their definition, properties, and illustrative algorithms like Prim's and Kruskal's.

    Learning Practice

  • 2.3

    Cost Of Spanning Trees

    The section discusses Minimum Cost Spanning Trees, focusing on algorithms to ensure connectivity in graphs while minimizing costs.

    Learning Practice

  • 2.4

    Properties Of Trees

    This section introduces the concept of Minimum Cost Spanning Trees in graph theory, highlighting their properties and algorithms.

    Learning Practice

  • 2.4.1

    Number Of Edges In A Tree

    This section explains the properties of trees in graph theory, particularly focusing on the number of edges in a tree and their significance in constructing minimum cost spanning trees.

    Learning Practice

  • 2.4.2

    Adding Edges To A Tree

    This section covers the concept of Minimum Cost Spanning Trees and the characteristics of trees in graph theory, including the implications of adding edges.

    Learning Practice

  • 2.4.3

    Unique Path Property

    This section introduces the concept of Minimum Cost Spanning Trees, explaining the criteria for ensuring connectivity in graphs while minimizing costs.

    Learning Practice

  • 2.4.4

    Implications Of Properties

    This section discusses the concept and importance of Minimum Cost Spanning Trees in the context of graph theory and algorithms.

    Learning Practice

  • 2.5

    Building A Minimum Cost Spanning Tree

    This section introduces the concept of Minimum Cost Spanning Trees, explaining their significance in ensuring connectivity while minimizing costs in a graph.

    Learning Practice

  • 2.5.1

    Prim's Algorithm

    Prim's Algorithm finds a minimum cost spanning tree in a weighted graph by incrementally connecting vertices based on the smallest edge weight.

    Learning Practice

  • 2.5.2

    Kruskal's Algorithm

    Kruskal's Algorithm is a greedy approach used to find the minimum cost spanning tree of a graph by adding edges in ascending order of weight while avoiding cycles.

    Learning Practice

References

ch29.pdf

Class Notes

Memorization

What we have learnt

  • A tree is defined as a conn...
  • Any tree with n vertices ha...
  • Minimum Cost Spanning Trees...

Final Test

Revision Tests