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Step 0 3 8 2 X N' u 4 2 6 -W- 3 D(v),p(v) (a) Z W D(w),p(w) (b) X D(x).p(x) (c) Z D(y).p(y) D(z).p(z) (d) 00

Step 0 3 8 2 X N' u 4 2 6 -W- 3 D(v),p(v) (a) Z W D(w),p(w) (b) X D(x).p(x) (c) Z D(y).p(y) D(z).p(z) (d) 00

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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5.01-1. Dijkstra's Algorithm (1, part 1).  Consider the network shown below, and Dijkstra’s link-state algorithm to find the least cost path from source node U to all other destinations.  Using the algorithm statement and its visual representation used in the textbook, complete the first row in the table below showing the link state algorithm’s execution by matching the table entries (a), (b), (c), and (d) with their values. 

The image depicts a directed weighted graph alongside a table, likely illustrating an example of Dijkstra's algorithm for finding the shortest path in a graph. ### Description #### Graph: - The graph consists of six nodes labeled U, V, W, X, Y, and Z. - Edges have various weights as follows: - U to V: 2 - U to X: 3 - V to W: 4 - V to Y: 2 - W to Z: 1 - X to V: 2 - X to W: 3 - X to Y: 6 - X to Z: 3 - Y to W: 2 - Y to Z: 1 #### Table: - The table is set up to track steps in the algorithm: - **Step:** Current step number in the algorithm, starting at 0. - **N':** Node under consideration, starting with U. - **D(v), p(v):** Distance to node V and its predecessor node. - **D(w), p(w):** Distance to node W and its predecessor node. - **D(x), p(x):** Distance to node X and its predecessor node. - **D(y), p(y):** Distance to node Y and its predecessor node. - **D(z), p(z):** Distance to node Z and its predecessor node (initially infinity). #### Dropdowns: - Four dropdown menus, each corresponding to a column (a, b, c, d) in the table, allow for choosing the distance and predecessor for nodes V, W, X, and Y. Possible values are provided, such as "1,U", "3,U", "6,V", etc., which represent the distance and the predecessor node. This setup suggests an interactive problem-solving task for understanding how Dijkstra’s algorithm progresses at each step to update the shortest path estimates for each node.
Transcribed Image Text:The image depicts a directed weighted graph alongside a table, likely illustrating an example of Dijkstra's algorithm for finding the shortest path in a graph. ### Description #### Graph: - The graph consists of six nodes labeled U, V, W, X, Y, and Z. - Edges have various weights as follows: - U to V: 2 - U to X: 3 - V to W: 4 - V to Y: 2 - W to Z: 1 - X to V: 2 - X to W: 3 - X to Y: 6 - X to Z: 3 - Y to W: 2 - Y to Z: 1 #### Table: - The table is set up to track steps in the algorithm: - **Step:** Current step number in the algorithm, starting at 0. - **N':** Node under consideration, starting with U. - **D(v), p(v):** Distance to node V and its predecessor node. - **D(w), p(w):** Distance to node W and its predecessor node. - **D(x), p(x):** Distance to node X and its predecessor node. - **D(y), p(y):** Distance to node Y and its predecessor node. - **D(z), p(z):** Distance to node Z and its predecessor node (initially infinity). #### Dropdowns: - Four dropdown menus, each corresponding to a column (a, b, c, d) in the table, allow for choosing the distance and predecessor for nodes V, W, X, and Y. Possible values are provided, such as "1,U", "3,U", "6,V", etc., which represent the distance and the predecessor node. This setup suggests an interactive problem-solving task for understanding how Dijkstra’s algorithm progresses at each step to update the shortest path estimates for each node.
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