Let G = (V,E) be a bipartite graph, but this time it is a weighted graph. The weight of a complete matching is the sum of the weights of its edges. We are interested in finding a minimum-weight complete matching in G. a) Give a legitimate C for a branch-and-bound (B&B) algorithm that finds a minimum-weight complete matching in G, and prove that your C is valid. Your C cannot be just the cost so far. b) Using your C, apply B&B to find a minimum-weight complete matching in the following weighted bipartite graph G: A = (1,2,3), B = (4,5,6,7) E = (((1,4), 3]. [(1,5), 4]. [(1,7). 15]. ((2,4), 1]. |(2,5), 8]. [(2,6), 3]. |(3,4), 3]. [(3,5), 9]. [ (3,6). 51). Show the solution tree. the C of every tree node generated, and the optimal solution. Also, mark the order in which each node in the solution tree is visited
Let G = (V,E) be a bipartite graph, but this time it is a weighted graph. The weight of a complete matching is the sum of the weights of its edges. We are interested in finding a minimum-weight complete matching in G. a) Give a legitimate C for a branch-and-bound (B&B) algorithm that finds a minimum-weight complete matching in G, and prove that your C is valid. Your C cannot be just the cost so far. b) Using your C, apply B&B to find a minimum-weight complete matching in the following weighted bipartite graph G: A = (1,2,3), B = (4,5,6,7) E = (((1,4), 3]. [(1,5), 4]. [(1,7). 15]. ((2,4), 1]. |(2,5), 8]. [(2,6), 3]. |(3,4), 3]. [(3,5), 9]. [ (3,6). 51). Show the solution tree. the C of every tree node generated, and the optimal solution. Also, mark the order in which each node in the solution tree is visited
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Let G = (V,E) be a bipartite graph, but this time it is a weighted graph. The weight of a
complete matching is the sum of the weights of its edges. We are interested in finding a
minimum-weight complete matching in G.
a) Give a legitimate C for a branch-and-bound (B&B)
complete matching in G, and prove that your C is valid. Your C cannot be just the cost so
far.
b) Using your C, apply B&B to find a minimum-weight complete matching in the following
weighted bipartite graph G: A = (1,2,3), B = (4,5,6,7)
E = (((1,4), 3]. [(1,5), 4]. [(1,7). 15]. ((2,4), 1]. |(2,5), 8]. [(2,6), 3]. |(3,4), 3]. [(3,5), 9]. [ (3,6). 51).
Show the solution tree. the C of every tree node generated, and the optimal solution. Also,
mark the order in which each node in the solution tree is visited.
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