A Weighted Inverse Minimum s−t Cut Problem with Value Constraint Under the Bottleneck-Type Hamming Distance
Abstract
Given a network G=(N,A,c) and an s−t cut [S,ˉS] with the capacity β and the constant value α, 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,ˉS] become a minimum s−t cut with the capacity α. 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 α. 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 β>α and β<α. 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.
