Problem 7: Consider the following weighted graph: 5 2 3. 3 7 e 3 4. 1. Use Prim's algorithm to find a minimum spanning tree for the above weighted graph. 2. Use Kruskal's algorithm to find a minimum spanning tree for the above weighted graph. 3. Compare between Prim's algorithm and Kruskal's algorithm. 00

Problem 7: Consider the following weighted graph: 5 2 3. 3 7 e 3 4. 1. Use Prim's algorithm to find a minimum spanning tree for the above weighted graph. 2. Use Kruskal's algorithm to find a minimum spanning tree for the above weighted graph. 3. Compare between Prim's algorithm and Kruskal's algorithm. 00

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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PLEASE SHOW WRITTEN WORK ON PAPER!!! PLEASE HELP
1. Use Prim's algorithm to compute a minimum spanning tree for the following weighted graph. 2 5 (b) 7 6. 3 1 f 7 8 4 8 8 9. 2 5 2. 3.
b) Consider graph G=(V, E) with six nodes and eight edges. The edges have distinct integer weights. a 17 b 10 7 2 f 6 The minimum spanning tree of G is constructed by Kruskal's algorithm and is shown in tree MST below: a 17 101 10 7 C f d 6 The edge weights of only those edges that are in the MST are given in graph G. What is the minimum possible summation of edge weights for the edges (a, b), (e, d), (c, d)? (5 points) As you justify your answer for edge weights, please use graph G and apply Kruskal's algorithm to obtain the MST step by step (5 points). Show and explain all your work.
Question 8. A connected graph G has 4 vertices and 4 edges of costs 1, 2, 3 and respectively 4. (a) Show that G is not a tree. (b) Show that G has a single minimum spanning tree. (Hint: For example, think how Prim's algorithm constructs the minimum spanning tree). (c) Draw a connected graph G with 4 nodes and 4 edges of costs 1, 2, 3, 4, respectively, so that the minimum spanning tree contains the edge of cost 4. The 4 nodes are below, you need to draw the 4 edges and indicate their cost. a O b d
b. Using Kruskal's algorithm find the minimum spanning tree of the given graph. 70 B 20 30 50 D 60 10 C 40 E
7 a) Use Dijkstra's algorithm to find the shortest path tree rooted at node B for the graph below. Label the vertices according to the algorithm. F 3 1 2 E B 6 8 A 1 3 زرا 1 10 5 b). Suppose the cost of every edge touching node B is increased by a non-negative constant. Are we guaranteed that the shortest path tree rooted at B remains the same? Explain.
Consider the following graph. b Q 17 3 6 5 3 7 d 3 QU 2 g 7 h $ برا 3 N نی k 1 (i) Using either Prim's or Kruskal's algorithms, determine the minimum spanning tree of the tree given below. State which algorithm you used. (ii) Find the shortest path of the graph below from A to L. Use Dijsktra's algorithm and show all working.
() Write the difference between Spanning Tree and Minimum Spanning Tree (MST)? (ii) Calculate the cost of the MST for the below graph using (a) Prim's Algorithm. (b) Kruskal's Algorithm, Cleary write the steps in the algorithm and solve the problem. 17 20 10 25 6. K 10 F 12 10 H E.
2. Use the Bellman-Ford algorithm to calculate the shortest paths from node A to every other node in the graph. Write the solution ir le and show every step. 4 7 2 -3 -1 -1 10 4 F 5
2 в 22 A 6 3 D E 20 9 11 5. G 12 H Figure 4: Directed, weighted graph a) Write an adjacency matrix OR adjacency list to represent the graph in Figure 4. b) Use Dijkstra's algorithm to calculate the single-source shortest paths from vertex A to every other vertex. i Show your steps in the table below. As the algorithm proceeds, cross out old values and write in new ones, from left to right in each cell. If during your algorithm two unvisited vertices have the same distance, use alphabetical order to determine which one is selected first. i. List the vertices in the order in which Dijkstra's algorithm marks them known. 4.
a) Which edges would you keep for the minimum-weight spanning tree? (Indicate as vertex-vertex — eg. “K-P”... if there were vertices K and P.) b) Describe the algorithm you used to determine the minimum-weight spanning tree above. Did you face any challenges in applying this algorithm?
Q2: Apply Kruskal's algorithm and find the minimum cost-spanning tree for the given graph. Show each step clearly. 7 8 1 A U 9 6 4 3 B 2 D 5 2 T