1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

1. Consider the following weighted graph. F B 10 5 G 15 E 30 D 5 10 5 15 20 A (a) Apply Dijkstra's Algorithm to the graph with A as the source/root and draw the graph for EACH step of the algorithm (include the initial state!). (b) Draw the minimum distance spanning tree associated with the algorithm with A as the root. Label the vertices! (c) Suppose a new graph is formed by deleting the edge between D and E. Run Dijkstra's Algorithm on this new graph with A as the source/root. You only need to provide the final graph produced by the algorithm.

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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1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?
Consider the following graph. d a g b h (a) Without adding new vertices, add a single edge to the graph so that the new graph will have an Euler path. Which vertices does your new edge connect? O b and h O i and d Od and h Oh and f O a and e (b) In addition to the edge from part (a), add a second edge (using the existing vertices) so that the resulting graph will have an Euler circuit. Which vertices does your second new edge connect? O d and c O g and b O c and e O b and i O g and f
Build a weighted graph that models a section of your home state. Use Dijkstra’s algorithm to determine the shortest path from a starting vertex to the last vertex.
1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not? Please provide graphs if possible.
Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.
Given the following graph, A C 3 1 E 4 В F 7 D 5 What is the next edge and vertex(s) to be included in the solution if a. we are using Prim's algorithm to find a minimum spanning tree and we have started with vertex E? Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if b. we are using Kruskal's algorithm to find a minimum spanning tree Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if c. we are using Dijkstra's shortest path algorithm to find shortest paths and we have started with vertex E, with C and F already included in the shortest path tree? Edge: Vertex(s):
Graph Theory, please I need answers from questions D to F. Thank you
3. Given the directed Graph as below. B A 10 C 8 2 D E Using A as the source, illustrate the Dijkstra algorithm to find the shortest path from vertex A to any other vertex. Make sure to show all the steps.
) Find the strongly connected components of the given graph using Kosaraju’s algorithm.Graph: A → B B → C B → E C → F D → B D → G E → AE → D E → F F → H G → E G → H H → I I → FHint: Graph LayoutA B CD E FG H I Answer: DFS on Reverse Graph starting on A: Labels 1 2 3 4 5 6 7 8 9 DFS on Original Graph, based on descending label order: Format: DFS starting from {node} (label = {node_label} ) = {nodes_discovered} DFS starting from ____ (label = ___ ): _____________________ DFS starting from ____ (label = ___ ): _____________________ DFS starting from ____ (label = ___ ): _____________________ Strongly Connected Components: _______________________________________
1. Use the graph below to answer the following questions. A B H 10 G 10 25 20 5 50 5 5 30 5 15 C 20 D F 15 E (a) Use Kruskal's Algorithm to produce a minimum spanning tree. Write down the edges that you choose in order of the algorithm. (b) Use Prim's Algorithm to produce a minimum spanning tree (assume A is the root/source). Write down the edges that you choose in order of the algorithm.