A Weighted Inverse Minimum s - t Cut Problem with Value Constraint Under the Bottleneck-Type Hamming Distance

Given a network G = (N, A, c) and an s - t cut [S, (S) over bar] with the capacity beta and the constant value alpha, an inverse minimum s - t cut problem with value constraint is to modify the vector capacity c as little as possible to make the s - t cut [S, (S) over bar] become a minimum s- t cut with the capacity alpha. The distinctive feature of this problem with the inverse minimum cut problems is the addition of a constraint in which the capacity of the given cut has to equal to the preassumed value alpha. In this paper, we investigate the inverse minimum s- t cut problem with value constraint under the bottleneck weighted Hamming distance. We propose two strongly polynomial time algorithms based on a binary search to solve the problem. At each iteration of the first one, we solve a feasible flow problem. The second algorithm considers the problem in two cases beta > alpha and beta < alpha. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum s - t cut in the network and then, by preserving optimality this s - t cut, adjust it to satisfy value constraint.