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

Abstract

Given a network [Formula: see text] and an [Formula: see text] cut [Formula: see text] with the capacity [Formula: see text] and the constant value [Formula: see text], an inverse minimum [Formula: see text] cut problem with value constraint is to modify the vector capacity [Formula: see text] as little as possible to make the [Formula: see text] cut [Formula: see text] become a minimum [Formula: see text] cut with the capacity [Formula: see text]. 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 [Formula: see text]. In this paper, we investigate the inverse minimum [Formula: see text] 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 [Formula: see text] and [Formula: see text]. In this algorithm, we first modify the capacity vector such that the given cut becomes a minimum [Formula: see text] cut in the network and then, by preserving optimality this [Formula: see text] cut, adjust it to satisfy value constraint.