The following method designed from a problem-solving strategy has been proposed for finding a minimum spanning tree (MST) in a connected weighted graph G: (i) Randomly divide the vertices in the graph into two subsets to form two connected weighted subgraphs with equal number of vertices or differing by at most one. Each subgraph contains all the edges whose vertices both belong to the subgraph's vertex set. (ii) Find a MST for each subgraph using Kruskal's algorithm. (iii) Connect the two MSTS by choosing an edge with minimum wight amongst those edges connecting them. Use the proposed method to find al MST in the connected weighted graph shown in Figure 2. Verify the correctness of your answer and draw a conclusion on the correctness of the proposed method from your verification,
The following method designed from a problem-solving strategy has been proposed for finding a minimum spanning tree (MST) in a connected weighted graph G: (i) Randomly divide the vertices in the graph into two subsets to form two connected weighted subgraphs with equal number of vertices or differing by at most one. Each subgraph contains all the edges whose vertices both belong to the subgraph's vertex set. (ii) Find a MST for each subgraph using Kruskal's algorithm. (iii) Connect the two MSTS by choosing an edge with minimum wight amongst those edges connecting them. Use the proposed method to find al MST in the connected weighted graph shown in Figure 2. Verify the correctness of your answer and draw a conclusion on the correctness of the proposed method from your verification,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The following method designed from a problem-solving strategy has been proposed for finding
a minimum spanning tree (MST) in a connected weighted graph G:
(i) Randomly divide the vertices in the graph into two subsets to form two
connected weighted subgraphs with equal number of vertices or differing
by at most one. Each subgraph contains all the edges whose vertices both
belong to the subgraph's vertex set.
(ii) Find a MST for each subgraph using Kruskal's algorithm.
(iii) Connect the two MSTS by choosing an edge with minimum wight amongst
those edges connecting them.
Use the proposed method to find al MST in the connected weighted graph shown in Figure 2.
Verify the correctness of your answer and draw a conclusion on the correctness of the proposed
method from your verification,
b
a
2
1
d
3
Figure 2. A connected weighted graph with four vertices
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