Selected partial inverse combinatorial optimization problems with forbidden elements

We study the computational complexity of some special partial inverse combinatorial optimization problems where the goal is to change a parameter at minimum cost such that there exists an optimal solution for the underlying combinatorial optimization problem with respect to the modified parameter that does not contain a prespecified set of forbidden elements. We show that the partial inverse problems that arise for the shortest path, minimum cut and assignment problem where the modification cost is measured by the weighted L1or weighted L∞-norm are strongly NP-hard.