A weighted inverse minimum cut problem under the bottleneck type Hamming distance

An inverse optimization problem is defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost (capacity) vector, and x⁰ ∈ S. We want to perturb the cost (capacity) vector c to d so that x⁰ is an optimal solution of P with respect to the cost (capacity) vector d, and to minimize some objective function. In this paper, we consider the weighted inverse minimum cut problem under the bottleneck type Hamming distance. For the general case, we present a combinatorial algorithm that runs in strongly polynomial time.