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Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?
- a)a path from s to t in the minimum weighted spanning tree
- b)a weighted shortest path from s to t
- c)an Euler walk from s to t
- d)a Hamiltonian path from s to
Correct answer is option 'A'. Can you explain this answer?
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Let s and t be two vertices in a undirected graph G + (V, E) having di...
Suppose shortest path from A->B is 6, but in MST, we have A->C->B (A->C = 4, C->B = 3), then along the path in MST, we have minimum congestion, i.e 4
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Let s and t be two vertices in a undirected graph G + (V, E) having di...
Introduction:
We are given an undirected graph G with vertices V and edges E. The edges have distinct positive weights. We need to find the path from vertex s to vertex t that has the minimum congestion. The congestion on an edge is defined as the weight of that edge, and the congestion on a path is defined as the maximum congestion on any edge of the path.
Explanation:
To find the path with minimum congestion from s to t, we can use the concept of a minimum weighted spanning tree.
1. Minimum Weighted Spanning Tree:
- A minimum weighted spanning tree is a tree that connects all the vertices of a graph with the minimum total weight.
- It is a subset of the edges of the graph that form a tree and has the minimum sum of edge weights.
- The minimum weighted spanning tree can be found using algorithms like Kruskal's algorithm or Prim's algorithm.
2. Path in Minimum Weighted Spanning Tree:
- Since the minimum weighted spanning tree connects all the vertices of the graph, there exists a path from s to t in the minimum weighted spanning tree.
- This path will have a congestion equal to the weight of the edge with minimum weight among all the edges that have one vertex in X and one vertex in Y.
- Any other path from s to t will have a congestion greater than or equal to this congestion.
3. Proof:
- Let's assume there exists a path P from s to t in the graph G that has a congestion less than the congestion of the path in the minimum weighted spanning tree.
- Since the path P is not in the minimum weighted spanning tree, there must exist at least one edge e on the path P that is not in the minimum weighted spanning tree.
- If we replace this edge e with the edge with minimum weight connecting one vertex in X and one vertex in Y, the congestion of the path P will increase.
- This contradicts the assumption that the path P has a congestion less than the congestion of the path in the minimum weighted spanning tree.
- Therefore, the path in the minimum weighted spanning tree is the path with minimum congestion from s to t.
Conclusion:
Thus, the path from s to t in the minimum weighted spanning tree is always the path with minimum congestion. Therefore, option 'A' is the correct answer.
We are given an undirected graph G with vertices V and edges E. The edges have distinct positive weights. We need to find the path from vertex s to vertex t that has the minimum congestion. The congestion on an edge is defined as the weight of that edge, and the congestion on a path is defined as the maximum congestion on any edge of the path.
Explanation:
To find the path with minimum congestion from s to t, we can use the concept of a minimum weighted spanning tree.
1. Minimum Weighted Spanning Tree:
- A minimum weighted spanning tree is a tree that connects all the vertices of a graph with the minimum total weight.
- It is a subset of the edges of the graph that form a tree and has the minimum sum of edge weights.
- The minimum weighted spanning tree can be found using algorithms like Kruskal's algorithm or Prim's algorithm.
2. Path in Minimum Weighted Spanning Tree:
- Since the minimum weighted spanning tree connects all the vertices of the graph, there exists a path from s to t in the minimum weighted spanning tree.
- This path will have a congestion equal to the weight of the edge with minimum weight among all the edges that have one vertex in X and one vertex in Y.
- Any other path from s to t will have a congestion greater than or equal to this congestion.
3. Proof:
- Let's assume there exists a path P from s to t in the graph G that has a congestion less than the congestion of the path in the minimum weighted spanning tree.
- Since the path P is not in the minimum weighted spanning tree, there must exist at least one edge e on the path P that is not in the minimum weighted spanning tree.
- If we replace this edge e with the edge with minimum weight connecting one vertex in X and one vertex in Y, the congestion of the path P will increase.
- This contradicts the assumption that the path P has a congestion less than the congestion of the path in the minimum weighted spanning tree.
- Therefore, the path in the minimum weighted spanning tree is the path with minimum congestion from s to t.
Conclusion:
Thus, the path from s to t in the minimum weighted spanning tree is always the path with minimum congestion. Therefore, option 'A' is the correct answer.
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Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer?
Question Description
Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer?.
Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let s and t be two vertices in a undirected graph G + (V, E) having distinct positive edge weights. Let [X, Y] be a partition of V such that s ∈ X and t ∈ Y. Consider the edge e having the minimum weight amongst all those edges that have one vertex in X and one vertex in Y. Let the weight of an edge e denote the congestion on that edge. The congestion on a path is defined to be the maximum of the congestions on the edges of the path. We wish to find the path from s to t having minimum congestion. Which one of the following paths is always such a path of minimum congestion?a)a path from s to t in the minimum weighted spanning treeb)a weighted shortest path from s to tc)an Euler walk from s to td)a Hamiltonian path from s toCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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