Inverse Multicast Quality of Service Routing Problem with Bandwidth and Delay Under the Weighted $$l_1$$ Norm

Quality of Service (QoS) Routing problem has been attracting considerable attention thanks to the rapid development of the high-speed communication network, image processing and computer science. In the past decades, many Quality of Service Routing algorithms were presented based on the QoS requirements and the resource constraints. The idea of the inverse optimization problem is to modify the given or estimated parameters such that the given feasible solution became an optimal solution. The modification costs are measured by different norms, such as $$l_1$$ norm, $$l_2$$ norm, $$l_\infty $$ norm, Hamming distance and so on. In this paper, we consider the inverse multicast quality of service routing problems under the weighted $$l_1$$ norm. We present combinatorial algorithms which can be finished in strongly polynomial time.