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onsider the network shown below, and Dijkstra’s link-state algorithm. Here, we are interested in computing the leas

onsider the network shown below, and Dijkstra’s link-state algorithm. Here, we are interested in computing the leas

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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5.03-1. Dijkstra's Algorithm (3, part 1).  Consider the network shown below, and Dijkstra’s link-state algorithm. Here, we are interested in computing the least cost path from node E (note: the start node here is E) to all other nodes using Dijkstra's algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the "Step 0" row in the table below showing the link state algorithm’s execution by matching the table entries (i), (ii), (iii), and (iv) with their values.

The image depicts a directed graph with six nodes labeled U, V, W, X, Y, and Z. The edges connecting these nodes have different weights, representing distances or costs between nodes. Here's a description of the graph and accompanying table: ### Graph Structure - Node U connects to: - V with weight 2 - X with weight 3 - Node V connects to: - W with weight 8 - Y with weight 4 - Node W connects to: - Z with weight 1 - Node X connects to: - V with weight 2 - Y with weight 6 - Node Y connects to: - Z with weight 1 ### Table Explanation The table shown is typical of Dijkstra’s algorithm, which is used to find the shortest path from a starting node to all other nodes in a graph. - **Step Column**: Indicates the iteration step of the algorithm. - **N' Column**: Represents the set of nodes whose shortest path from the source node has been determined. - **D(v), p(v), D(w), p(w), ... D(z), p(z) Columns**: Represent the shortest known distance from the starting node to nodes V, W, X, Y, and Z at each step and the corresponding predecessor node. ### Initial Values At Step 0: - **N'** is {U}. - Initially, distances (D) to nodes V, W, X, Y, Z are unknown (denoted by asterisks), except for node Z, which is set to infinity. ### Drop-down Options These correspond to possible values for the shortest paths and predecessors to be filled in the table: - **Infinity**: Represents unreachable nodes. - Specific values such as "9,w" or "2,u": Represent the shortest distance to a node and its predecessor. This setup is used to illustrate how Dijkstra’s algorithm proceeds in calculating the shortest path by iteratively updating the table with known shortest paths and updating nodes in the set N'.
Transcribed Image Text:The image depicts a directed graph with six nodes labeled U, V, W, X, Y, and Z. The edges connecting these nodes have different weights, representing distances or costs between nodes. Here's a description of the graph and accompanying table: ### Graph Structure - Node U connects to: - V with weight 2 - X with weight 3 - Node V connects to: - W with weight 8 - Y with weight 4 - Node W connects to: - Z with weight 1 - Node X connects to: - V with weight 2 - Y with weight 6 - Node Y connects to: - Z with weight 1 ### Table Explanation The table shown is typical of Dijkstra’s algorithm, which is used to find the shortest path from a starting node to all other nodes in a graph. - **Step Column**: Indicates the iteration step of the algorithm. - **N' Column**: Represents the set of nodes whose shortest path from the source node has been determined. - **D(v), p(v), D(w), p(w), ... D(z), p(z) Columns**: Represent the shortest known distance from the starting node to nodes V, W, X, Y, and Z at each step and the corresponding predecessor node. ### Initial Values At Step 0: - **N'** is {U}. - Initially, distances (D) to nodes V, W, X, Y, Z are unknown (denoted by asterisks), except for node Z, which is set to infinity. ### Drop-down Options These correspond to possible values for the shortest paths and predecessors to be filled in the table: - **Infinity**: Represents unreachable nodes. - Specific values such as "9,w" or "2,u": Represent the shortest distance to a node and its predecessor. This setup is used to illustrate how Dijkstra’s algorithm proceeds in calculating the shortest path by iteratively updating the table with known shortest paths and updating nodes in the set N'.
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