Problem A: Consider the following graph.
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.
Homework Answers
Hope u understand the answer.
For any doubt please comment.Consider the following weighted undirected graph.
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...
Given a graph below draw MST in BOLD using either Kruskal's or Prim's algorithm. How many...
Given a graph below draw MST in BOLD using either Kruskal's or Prim's algorithm. How many edges are in MST? _ What is the length of MST? _ What are the neighbors in the minimum spanning tree (MST) of the node a _ and the node f _
Problem E: For each of the following parts, state True or False. If true, give a short proof. If ...
Problem E: For each of the following parts, state True or False. If true, give a short proof. If false, givera counterexample: (1). Using Kruskal's algorithm, edges are (always) inserted into the MST in the same order as using Prim's (2). If an edge e is part of a TSP tour found by the quick TSP method then it must also be part of the (3). If an edge e is part of a Shortest Path Tree rooted at A...
3. In this problem, you will show the execution of the minimum spanning tree algorithms that...
3. In this problem, you will show the execution of the minimum spanning tree algorithms that you studied in class on the following graph: START 10 40 5 20 35 15 6 30 62 12 (a) (5 points) Trace the execution of Prim's algorithm to find the minimum spanning tree for this graph. At each step, you should show the vertex and the edge added to the tree and the resulting values of D after the relaxation operation. Use START...
Consider the following weighted graph G:
Consider the following weighted graph G: Use Prim's algorithm to find a minimal spanning tree T of this graph starting at the vertex s. You do not need to show every step of the algorithm, but to receive full credit you should: list the edges of T in the order in which they're added; redraw G and indicate which edges belong to T; compute the cost of T.
Question II - Graph Traversal and Minimum Spanning Trees [40 Points] Consider the following graph: B...
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...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
Run Prim (starting from vertex "f") and Kruskal algorithms on the graph below: 3 2 9...
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
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST)...
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST) with node 1 as the "root". List the vertices in the order in which the algorithm adds them to the solution, along with the edge and its weight used to make the selection, one per line. Each line should look like this: add vertex y: edge = (x,y), weight = 5 When the algorithm ends there are, generally, edges left in the heap. List...
Use Kruskal's algorithm to find a minimum spanning tree for the graph. Indicate the order in which edges are added to form the tree.
Use Kruskal's algorithm to find a minimum spanning tree for the graph. Indicate the order in which edges are added to form the tree. In what order were the edges added? (Enter your answer as a comma-separated list of sets.)
Given a graph below draw MST in BOLD using either Kruskal's or Prim's algorithm. How many edges are in MST? _ What is the length of MST? _ What are the neighbors in the minimum spanning tree (MST) of the node a _ and the node f _
Problem E: For each of the following parts, state True or False. If true, give a short proof. If false, givera counterexample: (1). Using Kruskal's algorithm, edges are (always) inserted into the MST in the same order as using Prim's (2). If an edge e is part of a TSP tour found by the quick TSP method then it must also be part of the (3). If an edge e is part of a Shortest Path Tree rooted at A...
3. In this problem, you will show the execution of the minimum spanning tree algorithms that you studied in class on the following graph: START 10 40 5 20 35 15 6 30 62 12 (a) (5 points) Trace the execution of Prim's algorithm to find the minimum spanning tree for this graph. At each step, you should show the vertex and the edge added to the tree and the resulting values of D after the relaxation operation. Use START...
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...
Consider the weighted graph below: Demonstrate Prim's algorithm starting from vertex A. Write the edges in the order they were added to the minimum spanning tree. Demonstrate Dijkstra's algorithm on the graph, using vertex A as the source. Write the vertices in the order which they are marked and compute all distances at each step.
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
Given the following weighted graph G. use Prim's algorithm to determine the Minimum-Cost Spanning Tree (MCST) with node 1 as the "root". List the vertices in the order in which the algorithm adds them to the solution, along with the edge and its weight used to make the selection, one per line. Each line should look like this: add vertex y: edge = (x,y), weight = 5 When the algorithm ends there are, generally, edges left in the heap. List...
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