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Project: Within the framework of the valorization of the acquired knowledge, one wishes to carry out an algorithm manipulating classical procedures of the theory of the graphs. With regard to part 1 of the project, it is requested to file a report on the algorithm carried out as well as the various associated procedures by justifying the data structures used. For part 2, you are asked to submit the source files as well as a demonstration of the implementation via one or more execution scenarios depending on the type of graph entered by the user. Part 1: Write an algorithm that allows the acquisition of a graph G(X,E) by the user. The acquisition is performed by entering the adjacency matrix relative to G having the number n of vertices. 1. Undirected graph: each of the edges has a weight. 2. Directed graph: each of the arcs has a cost. • If the entered graph is undirected, the algorithm performs the following tasks: 1. Verification of graph connectivity. 2. Finding a spanning tree of minimum weight by applying the PRIM algorithm. 3. Search for a spanning tree of maximum weight by applying the PRIM algorithm. If the entered graph is oriented, the algorithm performs the following tasks: 1. Verification of the strong connectivity of the graph. If the graph is not strongly connected, you are asked to provide the reduced graph 2. Check for the existence of a root vertex 3. If there is a root vertex, it is requested to search for a tree structure of shortest paths resulting from this vertex by applying the most appropriate algorithm (BELLMAN algorithm, DIJKSTRA algorithm, BELLMAN-FORD algorithm).

Project: Within the framework of the valorization of the acquired knowledge, one wishes to carry out an algorithm manipulating classical procedures of the theory of the graphs. With regard to part 1 of the project, it is requested to file a report on the algorithm carried out as well as the various associated procedures by justifying the data structures used. For part 2, you are asked to submit the source files as well as a demonstration of the implementation via one or more execution scenarios depending on the type of graph entered by the user. Part 1: Write an algorithm that allows the acquisition of a graph G(X,E) by the user. The acquisition is performed by entering the adjacency matrix relative to G having the number n of vertices. 1. Undirected graph: each of the edges has a weight. 2. Directed graph: each of the arcs has a cost. • If the entered graph is undirected, the algorithm performs the following tasks: 1. Verification of graph connectivity. 2. Finding a spanning tree of minimum weight by applying the PRIM algorithm. 3. Search for a spanning tree of maximum weight by applying the PRIM algorithm. If the entered graph is oriented, the algorithm performs the following tasks: 1. Verification of the strong connectivity of the graph. If the graph is not strongly connected, you are asked to provide the reduced graph 2. Check for the existence of a root vertex 3. If there is a root vertex, it is requested to search for a tree structure of shortest paths resulting from this vertex by applying the most appropriate algorithm (BELLMAN algorithm, DIJKSTRA algorithm, BELLMAN-FORD algorithm).

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
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subject "graph and optimization"

Project: Within the framework of the valorization of the acquired knowledge, one wishes to carry out an algorithm manipulating classical procedures of the theory of the graphs. With regard to part 1 of the project, it is requested to file a report on the algorithm carried out as well as the various associated procedures by justifying the data structures used. For part 2, you are asked to submit the source files as well as a demonstration of the implementation via one or more execution scenarios depending on the type of graph entered by the user. Part 1: Write an algorithm that allows the acquisition of a graph G(X,E) by the user. The acquisition is performed by entering the adjacency matrix relative to G having the number n of vertices. 1. Undirected graph: each of the edges has a weight. 2. Directed graph: each of the arcs has a cost. • If the entered graph is undirected, the algorithm performs the following tasks: 1. Verification of graph connectivity. 2. Finding a spanning tree of minimum weight by applying the PRIM algorithm. 3. Search for a spanning tree of maximum weight by applying the PRIM algorithm. If the entered graph is oriented, the algorithm performs the following tasks: 1. Verification of the strong connectivity of the graph. If the graph is not strongly connected, you are asked to provide the reduced graph 2. Check for the existence of a root vertex 3. If there is a root vertex, it is requested to search for a tree structure of shortest paths resulting from this vertex by applying the most appropriate algorithm (BELLMAN algorithm, DIJKSTRA algorithm, BELLMAN-FORD algorithm).
Transcribed Image Text:Project: Within the framework of the valorization of the acquired knowledge, one wishes to carry out an algorithm manipulating classical procedures of the theory of the graphs. With regard to part 1 of the project, it is requested to file a report on the algorithm carried out as well as the various associated procedures by justifying the data structures used. For part 2, you are asked to submit the source files as well as a demonstration of the implementation via one or more execution scenarios depending on the type of graph entered by the user. Part 1: Write an algorithm that allows the acquisition of a graph G(X,E) by the user. The acquisition is performed by entering the adjacency matrix relative to G having the number n of vertices. 1. Undirected graph: each of the edges has a weight. 2. Directed graph: each of the arcs has a cost. • If the entered graph is undirected, the algorithm performs the following tasks: 1. Verification of graph connectivity. 2. Finding a spanning tree of minimum weight by applying the PRIM algorithm. 3. Search for a spanning tree of maximum weight by applying the PRIM algorithm. If the entered graph is oriented, the algorithm performs the following tasks: 1. Verification of the strong connectivity of the graph. If the graph is not strongly connected, you are asked to provide the reduced graph 2. Check for the existence of a root vertex 3. If there is a root vertex, it is requested to search for a tree structure of shortest paths resulting from this vertex by applying the most appropriate algorithm (BELLMAN algorithm, DIJKSTRA algorithm, BELLMAN-FORD algorithm).
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