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Dijkstra's Algorithm (1, part 3).  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 third row in the table below showing the link state algorithm’s execution by matching the table entries (a), (b), (c), (d) and (e) with their values

Dijkstra's Algorithm (1, part 3).  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 third row in the table below showing the link state algorithm’s execution by matching the table entries (a), (b), (c), (d) and (e) with their values

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
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5.01-3. Dijkstra's Algorithm (1, part 3).  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 third row in the table below showing the link state algorithm’s execution by matching the table entries (a), (b), (c), (d) and (e) with their values

The image contains a graph and a partially completed table for Dijkstra's algorithm, a method for finding the shortest paths between nodes in a weighted graph. ### Graph Details: - The graph has six nodes labeled U, V, W, X, Y, and Z. - The edges between these nodes have weights indicated by numbers on the lines connecting the nodes. - U to V: 2 - U to X: 3 - V to W: 2 - V to Y: 2 - W to Z: 1 - X to Y: 6 - X to W: 1 - Y to Z: 1 ### Table Details: The table is used to track the progress of Dijkstra's algorithm. - **Columns:** - Step: Indicates the iteration step of the algorithm. - N': Lists nodes processed up to that step. - D(v), p(v): The estimated shortest distance to node V and its predecessor. - D(w), p(w): The estimated shortest distance to node W and its predecessor. - D(x), p(x): The estimated shortest distance to node X and its predecessor. - D(y), p(y): The estimated shortest distance to node Y and its predecessor. - D(z), p(z): The estimated shortest distance to node Z and its predecessor. - **Row 0 (Initial Setup):** - Step 0: Start from node U. - Nodes marked with an asterisk (*) indicate that their distances are initially unknown. - D(z), p(z) is initially marked as infinity (∞), suggesting the node is unreachable initially. - **Row 1 (Step 1):** - Node U is included in N' (processed nodes). - There are blanks (a), (b), (c), (d), and (e) that correspond to the distances and predecessors that need to be filled in for Step 1. ### Dropdown Options: At the bottom, there are dropdown menus for each blank (a) to (e), providing options to fill in the table: - infinity - Combinations of numbers and node labels, e.g. "9,w", "4,v", "3,u". These selections help in completing the table accurately as per Dijkstra's algorithm.
Transcribed Image Text:The image contains a graph and a partially completed table for Dijkstra's algorithm, a method for finding the shortest paths between nodes in a weighted graph. ### Graph Details: - The graph has six nodes labeled U, V, W, X, Y, and Z. - The edges between these nodes have weights indicated by numbers on the lines connecting the nodes. - U to V: 2 - U to X: 3 - V to W: 2 - V to Y: 2 - W to Z: 1 - X to Y: 6 - X to W: 1 - Y to Z: 1 ### Table Details: The table is used to track the progress of Dijkstra's algorithm. - **Columns:** - Step: Indicates the iteration step of the algorithm. - N': Lists nodes processed up to that step. - D(v), p(v): The estimated shortest distance to node V and its predecessor. - D(w), p(w): The estimated shortest distance to node W and its predecessor. - D(x), p(x): The estimated shortest distance to node X and its predecessor. - D(y), p(y): The estimated shortest distance to node Y and its predecessor. - D(z), p(z): The estimated shortest distance to node Z and its predecessor. - **Row 0 (Initial Setup):** - Step 0: Start from node U. - Nodes marked with an asterisk (*) indicate that their distances are initially unknown. - D(z), p(z) is initially marked as infinity (∞), suggesting the node is unreachable initially. - **Row 1 (Step 1):** - Node U is included in N' (processed nodes). - There are blanks (a), (b), (c), (d), and (e) that correspond to the distances and predecessors that need to be filled in for Step 1. ### Dropdown Options: At the bottom, there are dropdown menus for each blank (a) to (e), providing options to fill in the table: - infinity - Combinations of numbers and node labels, e.g. "9,w", "4,v", "3,u". These selections help in completing the table accurately as per Dijkstra's algorithm.
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