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Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Title: Implementing Kruskal's Algorithm** **Objective:** Run Kruskal’s algorithm from vertex 0 on the following graph. Show a sequence of diagrams in which the tree gradually grows. **Graph Description:** The provided graph consists of 7 vertices (0 to 6) and the following edges with weights: - Vertex 0 is connected to: - Vertex 1 with a weight of 7 - Vertex 3 with a weight of 5 - Vertex 1 is connected to: - Vertex 2 with a weight of 8 - Vertex 3 with a weight of 9 - Vertex 4 with a weight of 7 - Vertex 2 is connected to: - Vertex 4 with a weight of 5 - Vertex 3 is connected to: - Vertex 4 with a weight of 15 - Vertex 5 with a weight of 6 - Vertex 4 is connected to: - Vertex 5 with a weight of 8 - Vertex 6 with a weight of 9 - Vertex 5 is connected to: - Vertex 6 with a weight of 11 **Instructions:** The objective is to use Kruskal’s algorithm to find the Minimum Spanning Tree (MST) of the graph. Begin with sorting all the edges in non-decreasing order of their weights and then pick the smallest ones ensuring no cycles are formed until all vertices are included in the MST.
Transcribed Image Text:**Title: Implementing Kruskal's Algorithm** **Objective:** Run Kruskal’s algorithm from vertex 0 on the following graph. Show a sequence of diagrams in which the tree gradually grows. **Graph Description:** The provided graph consists of 7 vertices (0 to 6) and the following edges with weights: - Vertex 0 is connected to: - Vertex 1 with a weight of 7 - Vertex 3 with a weight of 5 - Vertex 1 is connected to: - Vertex 2 with a weight of 8 - Vertex 3 with a weight of 9 - Vertex 4 with a weight of 7 - Vertex 2 is connected to: - Vertex 4 with a weight of 5 - Vertex 3 is connected to: - Vertex 4 with a weight of 15 - Vertex 5 with a weight of 6 - Vertex 4 is connected to: - Vertex 5 with a weight of 8 - Vertex 6 with a weight of 9 - Vertex 5 is connected to: - Vertex 6 with a weight of 11 **Instructions:** The objective is to use Kruskal’s algorithm to find the Minimum Spanning Tree (MST) of the graph. Begin with sorting all the edges in non-decreasing order of their weights and then pick the smallest ones ensuring no cycles are formed until all vertices are included in the MST.
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