Preventing Small (𝐬,𝐭)-Cuts by Protecting Edges
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We introduce and study Weighted Min (s,t)-Cut Prevention, where we are given a graph G=(V,E) with vertices s and t and an edge cost function and the aim is to choose an edge set D of total cost at most d such that G has no (s,t)-edge cut of capacity at most a that is disjoint from D. We show that Weighted Min (s,t)-Cut Prevention is NP-hard even on subcubcic graphs when all edges have capacity and cost one and provide a comprehensive study of the parameterized complexity of the problem. We show, for example W[1]-hardness with respect to d and an FPT algorithm for a.
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