  We introduce the parametric matroid one-interdiction problem. Given a
matroid, each element of its ground set is associated with a weight that
depends linearly on a real parameter from a given parameter interval. The goal
is to find, for each parameter value, one element that, when being removed,
maximizes the weight of a minimum weight basis. The complexity of this problem
can be measured by the number of slope changes of the piecewise linear function
mapping the parameter to the weight of the optimal solution of the parametric
matroid one-interdiction problem. We provide two polynomial upper bounds as
well as a lower bound on the number of these slope changes. Using these, we
develop algorithms that require a polynomial number of independence tests and
analyse their running time in the special case of graphical matroids.
