1. Plans that Span (MSTs) 0 6 4 9 3 3 6 1 2 2 2 5 3 7 8 8 6 5 5

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
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**1.4 What's the order of edges visited by Kruskal's? Include edges that are skipped (put "skipped" next to the edge), and assume we stop after picking 6 edges.**

In this exercise, apply Kruskal's algorithm to determine the sequence in which edges are considered. Ensure to identify skipped edges clearly and note that the process concludes once 6 edges are chosen.
Transcribed Image Text:**1.4 What's the order of edges visited by Kruskal's? Include edges that are skipped (put "skipped" next to the edge), and assume we stop after picking 6 edges.** In this exercise, apply Kruskal's algorithm to determine the sequence in which edges are considered. Ensure to identify skipped edges clearly and note that the process concludes once 6 edges are chosen.
# 1. Plans that Span (MSTs)

## Graph Description:

The image presents a weighted, undirected graph with seven nodes labeled from 0 to 6. The connections (edges) between these nodes have varying weights, representing the edge costs. This type of graph is often used to demonstrate the concept of a Minimum Spanning Tree (MST) in computer science and optimization.

### Detailed Breakdown:

- **Nodes and Edges:**
  - **Node 0:** Connected to Node 1 (weight 3) and Node 3 (weight 6).
  - **Node 1:** Connected to Node 0 (weight 3), Node 2 (weight 2), Node 3 (weight 4), and Node 4 (weight 6).
  - **Node 2:** Connected to Node 1 (weight 2), Node 3 (weight 5), Node 5 (weight 8), and Node 6 (weight 3).
  - **Node 3:** Connected to Node 0 (weight 6), Node 1 (weight 4), Node 2 (weight 5), and Node 6 (weight 2).
  - **Node 4:** Connected to Node 1 (weight 6) and Node 5 (weight 7).
  - **Node 5:** Connected to Node 2 (weight 8), Node 4 (weight 7), and Node 6 (weight 5).
  - **Node 6:** Connected to Node 2 (weight 3), Node 3 (weight 2), and Node 5 (weight 5).

### Concept Explanation:

In graph theory, a Minimum Spanning Tree is a subset of the edges of a connected, edge-weighted graph that connects all the vertices with the minimum possible total edge weight. The goal is to minimize the sum of the weights while ensuring all nodes remain connected. MSTs are used in network design, circuit design, and various optimization problems.

Understanding MSTs involves algorithms like Kruskal's and Prim's, which systematically select edges to form a tree ensuring minimal total edge weight. This graph illustration serves as a practical depiction of such problems and the methodology for solving them.
Transcribed Image Text:# 1. Plans that Span (MSTs) ## Graph Description: The image presents a weighted, undirected graph with seven nodes labeled from 0 to 6. The connections (edges) between these nodes have varying weights, representing the edge costs. This type of graph is often used to demonstrate the concept of a Minimum Spanning Tree (MST) in computer science and optimization. ### Detailed Breakdown: - **Nodes and Edges:** - **Node 0:** Connected to Node 1 (weight 3) and Node 3 (weight 6). - **Node 1:** Connected to Node 0 (weight 3), Node 2 (weight 2), Node 3 (weight 4), and Node 4 (weight 6). - **Node 2:** Connected to Node 1 (weight 2), Node 3 (weight 5), Node 5 (weight 8), and Node 6 (weight 3). - **Node 3:** Connected to Node 0 (weight 6), Node 1 (weight 4), Node 2 (weight 5), and Node 6 (weight 2). - **Node 4:** Connected to Node 1 (weight 6) and Node 5 (weight 7). - **Node 5:** Connected to Node 2 (weight 8), Node 4 (weight 7), and Node 6 (weight 5). - **Node 6:** Connected to Node 2 (weight 3), Node 3 (weight 2), and Node 5 (weight 5). ### Concept Explanation: In graph theory, a Minimum Spanning Tree is a subset of the edges of a connected, edge-weighted graph that connects all the vertices with the minimum possible total edge weight. The goal is to minimize the sum of the weights while ensuring all nodes remain connected. MSTs are used in network design, circuit design, and various optimization problems. Understanding MSTs involves algorithms like Kruskal's and Prim's, which systematically select edges to form a tree ensuring minimal total edge weight. This graph illustration serves as a practical depiction of such problems and the methodology for solving them.
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