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3. In this problem, you will show the execution of the minimum spanning tree algorithms that...
Question II - Graph Traversal and Minimum Spanning Trees [40 Points] Consider the following graph: B 10 1 4 1 H 9 4 a) Traverse the graph starting from vertex A, and using the Breadth-First Search algorithm. Show the traversal result and the data structure you are using. [10 Points] b) Traverse the graph starting from vertex A, and using the Depth-First Search (Post-order) algorithm. Show the traversal result and the data structure you are using. [10 Points] c) Apply...
6. (6 points) Trace the execution of Kruskal's algorithm to find the Minimum Spanning Tree of the graph shown below. 5 10
Consider the following weighted undirected graph. (a) Explain why edge (B, D) is safe. In other words, give a cut where the edge is the cheapest edge crossing the cut. (b) We would like to run the Kruskal's algorithm on this graph. List the edges appearing in the Minimum Spanning Tree (MST) in the order they are added to the MST. For simplicity, you can refer to each edge as its weight. (c) 1We would like to run the Prim's algorithm on this...
Problem A: Consider the following graph. (a). Find a minimum spanning tree of the graph using Kruskal's algorithm. List the edges in the order they are put into the tree. (b). Apply Prim's algorithm to the same graph starting with node A. List the edges, in order added to the MST. (c). Suppose the cost of every edge touching node A is increased by a constant. Are we guaranteed that the MST remains the MST? Explain.
2. Use Prim's algorithm to find a minimum spanning tree for the following graph 3. Use Kruskal's algorithm to find a minimum spanning tree for the graph given in question.
Run Prim (starting from vertex "f") and Kruskal algorithms on the graph below: 3 2 9 3 . (5 points) Prim's algorithm: draw a table that shows the vertices in the queue at each iteration, similar to example from the notes (2 points) Prim's algorithm: using the table from the first part, list the order in which edges are added to the tree (3 points) Kruskal's algorithm: list the order in which edges are added to the tree
1. Use Prim's algorithm to solve the minimum weight spanning tree problem for the following graph.2. Use Kruskal's algorithm to solve the minimum weight spanning tree problem for the following graph.
Question 3 Apply Kruskal's algorithm to find Minimum Spanning Tree for the following graph. (In the final exam, you might be asked about Prim's algorithm or both). Weight of edge(1,2) = 10 Weight of edge(2,4)= 5 Weight of edge(6,4)=10 Weight of edge(1,4) = 20 Weight of edge(2,3) = 3 Weight of edge(6,5)= 3 Weight of edge(1,6) = 2 Weight of edge(3,5) = 15 Weight of edge(4,5)= 11
Do prim's and kruskal's algorithms always generate a unique minimum spanning tree? Please discuss in terms of both the structure of the graph and its cost. 0 4 4 6
Please explain thoroughly: Find the minimum spanning tree of the following graph using either Kruskal's or Prim's algorithm. Show your setup and the first 3 iterations 4. 4 5 4