Homework Graph Algorithms Dijkstra's and Bellman Ford(1)

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Dec 6, 2023

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Homework – Graph Concepts and Algorithms A. Dijkstra’s algorithm

B. Graph Concepts For each of the following graph-based computational tasks, specify the type of graph most appropriate for the data in question in terms of undirected or directed, and unweighted or weighted. In addition, choose the graph algorithm from the following list best suited to computing a solution: • Breadth-First Search • Depth-First Search • Dijkstra’s Algorithm • Topological Sort  N/A to DFS, BFS, TOPO, or shortest path a) You want to model a collection of Java files in a project. You know which files exist and which other Java files they depend on using. You want to determine the order that the files have to be compiled in before a given file f can be compiled and run. b) You want to model how a tweet gets re-tweeted by followers on Twitter. You have data on who the users of Twitter are and all the followers of each user. Given a source, a tweet can be re- tweeted by any follower of that source. If a tweet gets arbitrarily re-tweeted k times, you want to know which users could have seen the tweet. c) You have locations and the distances between them. You want to know the shortest cost path from one source location to all other locations. C. Bellman-Ford algorithm

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a) Given a graph G = (V, E) with positive edge weights, the Bellman-Ford algorithm and Dijkstra’s algorithm can produce different shortest-path trees despite always producing the same shortest- path weights. Explanation: b) Perform Bellman-Ford Algorithm on the following graph showing the edges list, d and p tables as discussed in class (see the excel sheet available on eLearning) D. Floyd-Warshall Algorithm

Apply Floyd-Warshall, all sources shortest path algorithm on the following graph:

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