Posted: January 8th, 2017

Let G be a weighted graph of n nodes,and k an integer, 3≤????≤????.A k-node cycle in G is a cycle that has k distinct nodes, and the weight (or length) of a cycle is the sum of the weights of the edges that make up the cycle. Give an approximate cost function ???? (other than the “cost so far”) for a branch-and-bound algorithm that takes as input G and k, and returns a minimum-weight k-node cycle.

b. Apply your algorithm to derive a minimum-weight 3-node cycle in the following graph G=(V,E): V={1, 2, 3, 4, 5, 6}, E={[(1,3) 2], [(1,4) 4], [(1,6) 3], [3,4) 4], [(3,6) 3], [(3,5) 5],[(6,4) 3], [(6,5) 4], [(6,2) 2], [(2,4) 1]}. Make sure you show the solution tree and the ???? of each generated node.

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