Suppose we are given a directed network G = (V, E) with a root node r and a set of terminals T ⊆ V. We'd like to disconnect many terminals from r, while cutting relatively few edges.
We make this trade-off precise as follows. For a set of edges F c E, let q(F) denote the number of nodes v e T such that there is no r-v path in the subgraph (V, E – F). Give a polynomial-time algorithm to find a set F of edges that maximizes the quantity q(F) –|F|. (Note that setting F equal to the empty set is an option.)
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