Inverse Maximum Dynamic Flow Problem under the Sum-Type Weighted Hamming Distance

Inverse maximum flow (IMDF), is among the most important problems in the field ofdynamic network flow, which has been considered the Euclidean norms measure in previousresearches. However, recent studies have mainly focused on the inverse problems under theHamming distance measure due to their practical and important applications. In this paper,we studies a general approach for handling the inverse maximum dynamic flow problemunder the weighted sum-type Hamming distance. We assume that a dynamic network flow,and a desired feasible dynamic flow on the network is given. We try to adjust the current arccapacity vector to maximize the dynamic flow and minimize the changes. The motivationfor this study stems from the Hamming distance that is made practically important in thesituation where we only care about the change, disregarding its magnitude. In this paper,first we prove some preliminary results, then we show that this problem (IMDF) can betransformed to a minimum dynamic cut problem. So, we proposed a combinatorialalgorithm for solving the IMDF in strongly polynomial time. Ultimately, the proposedalgorithm, is illustrated by a numerical example on a dynamic network.