Partial inverse min–max spanning tree problem

This paper addresses a partial inverse combinatorial optimization problem, called the partial inverse min–max spanning tree problem. For a given weighted graph G and a forest F of the graph, the problem is to modify weights at minimum cost so that a bottleneck (min–max) spanning tree of G contains the forest. In this paper, the modifications are measured by the weighted Manhattan distance. The main contribution is to present two algorithms to solve the problem in polynomial time. This result is considerable because the partial inverse minimum spanning tree problem, which is closely related to this problem, is proved to be NP-hard in the literature. Since both the algorithms have the same worse-case complexity, some computational experiments are reported to compare their running time.