A strongly polynomial algorithm for the inverse shortest arborescence problem Original Research Article

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 v1 -arborescence of G, is the shortest one. It is found that only the cost of T needs modifying. An O(n3) combinatorial algorithm is then proposed. This algorithm also gives an optimal solution to the inverse weighted shortest path problem.