# The inverse maximum flow problem under weighted lk norm

## Keywords:

inverse combinatorial optimization, maximum flow, strongly polynomial time complexity## Abstract

The problem consists in modifying the lower and the upper bounds of a given feasible flow f in a network G so that the given flow becomes a maximum flow in *G* and the distance between the initial vector of bounds and the modified one is measured using weighted *L _{k}*norm

*(k ∈ N)*is minimum. We denote this problem by IMFWL

_{k}. IMFWL

_{k}is a generalization of the inverse maximum flow problem under the

*L*norm (denoted IMFL

_{k}_{k}, where the per unit cost of modification is equal to 1 on all arcs), which was previously studied and solved in polynomial time. In this paper, the algorithm for IMFLk is adapted to solve IMFWL

_{k}.