Question

Assume that we have an algorithm A for computing a minimum spanning tree of a graph G that takes as an input the cost matrix C whose entries are positive numbers. We want to compute a maximum spanning tree of G using A, but are not allowed to modify A; instead we can modify the cost matrix C. Outline an algorithm for computing the maximum spanning tree of G.

Answer 1

If we are not allowed to modify algorithm, we can modify the cost matrix. Each value of cost matrix can be multiplied by -1 so that maximum cost edges become the minimum cost edges and then we can apply the above algorithm to the new cost matrix. After the creation of minimum spanning tree, multiply all weight by -1 again to get maximum spanning tree. This method can be used to create maximum spanning tree.