A Strongly Polynomial Algorithm for the Inverse Shortest Arborescence Problem

In this paper an inverse problem of the weighted shortest arborescence problem is discussed. That is. given a directed graph G and a set of nonnegative costs on its arcs. we need to modify those costs as little as possible to ensure that T, a given (.I-arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(rz”) combinatorial algorithm is then proposed. This algorithm also gives an optimal solution to the inverse weighted shortest path problem.