Some inverse min-max network problems under weighted l1 and linfinity norms with bound constraints on changes

We consider some inverse min-max (or max-min) network problems. Such an inverse problem is to modify the weights with bound constraints so that a given feasible solution becomes an optimal solution of a min-max (or max-min) network problem, and the deviation of the weights, measured by the weighted l1 norm or weighted l∞ norm, is minimum. In this paper, we present strongly polynomial time algorithms to solve the inverse min-max spanning tree problem and the inverse maximum capacity path problem.