IABFU Algorithms & Data Strcuture Bipartite Graph Questions
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Let ????=(????,????) 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 ??.
a)
Give a legitimate ????for a branch-and-bound (B&B) algorithm that finds a minimum-weight
complete matching in ????, and prove that your ???? is valid. Your ?? cannot be just the cost so far.
b)
Using your ????, apply B&B to find a minimum-weight complete matching in the following
weighted bipartite graph ????:????={1,2,3},????={4,5,6,7},
??={[(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),5]}.
Show the solution tree, the ????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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