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how to find the minimum weighted cycle containing two given nodes in a weighted using -'algorithm,graph,cycle,shortest-path'


how to find the minimum weighted cycle containing two given nodes in a weighted  using -'algorithm,graph,cycle,shortest-path'

Given a weighted undirected graph G = (V, E) and a set of nodes P.

Given two nodes, n1 and n2.

I want to find two separate (non-overlapping) paths from n1 to n2, so that the sum of the weights of the two paths is minimum. And I paraphrase the problem to what the title describes, that is the minimum weighted cycle containing n1 and n2.

Obviously it's not correct to find a first minimum weighted path p1 from n1 to n2 and then remove the edges in p1 from the graph and then find a second minimum weighted path p2.

How can I find such a cycle?
    

asked Sep 7, 2015 by rajesh
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