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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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The image depicts a weighted graph with ten vertices, labeled from \( V_0 \) to \( V_9 \). These vertices are interconnected with edges, each marked with weights representing numeric values. The graph forms a structure with visible triangles and quadrilaterals due to the connections. **Key Features:** - **Vertices:** There are ten vertices, each denoted by a circle and labeled with \( V_0 \), \( V_1 \), ..., \( V_9 \). - **Edges and Weights:** - The edge between \( V_0 \) and \( V_1 \) has a weight of 9. - The edge between \( V_0 \) and \( V_5 \) has a weight of 4. - The edge between \( V_0 \) and \( V_6 \) has a weight of 5. - The edge between \( V_0 \) and \( V_8 \) has a weight of 6. - The edge between \( V_1 \) and \( V_2 \) has a weight of 3. - The edge between \( V_1 \) and \( V_5 \) has a weight of 4. - The edge between \( V_1 \) and \( V_6 \) has a weight of 4. - The edge between \( V_2 \) and \( V_3 \) has a weight of 4. - The edge between \( V_2 \) and \( V_6 \) has a weight of 3. - The edge between \( V_2 \) and \( V_7 \) has a weight of 5. - The edge between \( V_3 \) and \( V_4 \) has a weight of 8. - The edge between \( V_3 \) and \( V_7 \) has a weight of 4. - The edge between \( V_3 \) and \( V_9 \) has a weight of 6. - The edge between \( V_4 \) and \( V_9 \) has a weight of 3. - The edge between \( V_5 \) and \( V_6 \) has a weight of 3. - The edge between \( V_5 \) and \( V_8
Transcribed Image Text:The image depicts a weighted graph with ten vertices, labeled from \( V_0 \) to \( V_9 \). These vertices are interconnected with edges, each marked with weights representing numeric values. The graph forms a structure with visible triangles and quadrilaterals due to the connections. **Key Features:** - **Vertices:** There are ten vertices, each denoted by a circle and labeled with \( V_0 \), \( V_1 \), ..., \( V_9 \). - **Edges and Weights:** - The edge between \( V_0 \) and \( V_1 \) has a weight of 9. - The edge between \( V_0 \) and \( V_5 \) has a weight of 4. - The edge between \( V_0 \) and \( V_6 \) has a weight of 5. - The edge between \( V_0 \) and \( V_8 \) has a weight of 6. - The edge between \( V_1 \) and \( V_2 \) has a weight of 3. - The edge between \( V_1 \) and \( V_5 \) has a weight of 4. - The edge between \( V_1 \) and \( V_6 \) has a weight of 4. - The edge between \( V_2 \) and \( V_3 \) has a weight of 4. - The edge between \( V_2 \) and \( V_6 \) has a weight of 3. - The edge between \( V_2 \) and \( V_7 \) has a weight of 5. - The edge between \( V_3 \) and \( V_4 \) has a weight of 8. - The edge between \( V_3 \) and \( V_7 \) has a weight of 4. - The edge between \( V_3 \) and \( V_9 \) has a weight of 6. - The edge between \( V_4 \) and \( V_9 \) has a weight of 3. - The edge between \( V_5 \) and \( V_6 \) has a weight of 3. - The edge between \( V_5 \) and \( V_8
### Graph Problem: Shortest Path Using Dijkstra’s Algorithm #### Objective Use Dijkstra's algorithm to find the shortest path from node \( \alpha \) (α) to node \( \zeta \) (z) in the given weighted graph. **Please show your steps to receive any credit.** #### Graph Structure The graph is a weighted, undirected graph structured as follows: 1. **Nodes:** - The nodes are labeled with Greek letters from α to ζ. 2. **Edges and Weights:** - The edges connect the nodes and are labeled with their respective weights. 3. **Node and Edge Details:** - Node \( \alpha \) (α) has edges connected to: - Node \( \beta \) (β) with a weight of 1 - Node \( \gamma \) (γ) with a weight of 3 - Node \( \beta \) (β) connects to: - Node \( \delta \) (δ) with a weight of 3 - Node \( \kappa \) (κ) with a weight of 5 - Node \( \gamma \) (γ) connects to: - Node \( \theta \) (θ) with a weight of 4 - Node \( \lambda \) (λ) with a weight of 1 - Node \( \delta \) (δ) connects to: - Node \( \alpha \) (α) with a weight of 2 - Node \( \epsilon \) (ε) with a weight of 2 - Node \( \epsilon \) (ε) connects to: - Node \( \gamma \) (γ) with a weight of 3 - Node \( \zeta \) (ζ) with a weight of 6 - Node \( \theta \) (θ) connects to: - Node \( \lambda \) (λ) with a weight of 1 - Node \( \iota \) (ι) with a weight of 4 - Node \( \lambda \) (λ) connects to: - Node \( \zeta \) (ζ) with a weight of 5 - Node \( \zeta \) (ζ) is the target node, connected back to nodes as mentioned above. 4
Transcribed Image Text:### Graph Problem: Shortest Path Using Dijkstra’s Algorithm #### Objective Use Dijkstra's algorithm to find the shortest path from node \( \alpha \) (α) to node \( \zeta \) (z) in the given weighted graph. **Please show your steps to receive any credit.** #### Graph Structure The graph is a weighted, undirected graph structured as follows: 1. **Nodes:** - The nodes are labeled with Greek letters from α to ζ. 2. **Edges and Weights:** - The edges connect the nodes and are labeled with their respective weights. 3. **Node and Edge Details:** - Node \( \alpha \) (α) has edges connected to: - Node \( \beta \) (β) with a weight of 1 - Node \( \gamma \) (γ) with a weight of 3 - Node \( \beta \) (β) connects to: - Node \( \delta \) (δ) with a weight of 3 - Node \( \kappa \) (κ) with a weight of 5 - Node \( \gamma \) (γ) connects to: - Node \( \theta \) (θ) with a weight of 4 - Node \( \lambda \) (λ) with a weight of 1 - Node \( \delta \) (δ) connects to: - Node \( \alpha \) (α) with a weight of 2 - Node \( \epsilon \) (ε) with a weight of 2 - Node \( \epsilon \) (ε) connects to: - Node \( \gamma \) (γ) with a weight of 3 - Node \( \zeta \) (ζ) with a weight of 6 - Node \( \theta \) (θ) connects to: - Node \( \lambda \) (λ) with a weight of 1 - Node \( \iota \) (ι) with a weight of 4 - Node \( \lambda \) (λ) connects to: - Node \( \zeta \) (ζ) with a weight of 5 - Node \( \zeta \) (ζ) is the target node, connected back to nodes as mentioned above. 4
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