Increasing the weight of minimum spanning trees

Abstract The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NP-hard and an Ω(1/log  k )-approximation algorithm is presented for it, where (input parameter) k  > 1 is the number of edges to be removed. The second problem is studied, assuming that the increase in the weight of an edge has an associated cost proportional to the magnitude of the change. An O ( n 3 m 2  log( n 2 / m )) time algorithm is presented to solve it.

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