Upgrading min-max spanning tree problem under various cost functions

This paper addresses upgrading min-max spanning tree problem (MMST). Given a graph G(V,E), the aim of this problem is to modify edge weights under certain limits and given budget so that the MMST with respect to perturbed graph improves as much as possible. We present a complexity result for general non-decreasing cost functions. In special case, it is shown that the problem under linear and sum-type Hamming cost function can be solved in O(|E|2) and O(|E|log⁡|E|log⁡|V|) time, respectively.