The most vital edges in the minimum spanning tree problem

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Abstract

Let G(N; A) be a connected, undirected and weighted network with node set N and edge set A. Suppose that there is an available budget to spend on removing edges and there is a removal cost associated with each edge. The most vital edges problem is to find a set of edges such that the total removal cost is not greater than the available budget and whose removal from G(N; A) results in the greatest increase in the total weight of a minimum spanning tree. We show that this problem is NP-hard and propose a branch and bound algorithm to solve it.

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