A note on upgrading the min–max weight of a base of a matroid

Abstract

A min–max spanning tree is a spanning tree minimizing the maximum weight of its edges. Sepasian and Monabbati (2017) introduced the problem of upgrading the maximum edge weight of a min–max spanning tree. Each edge weight can be decreased by paying a cost, and the objective is to minimize the maximum weight of a min–max spanning tree within a given budget. They designed a polynomial algorithm and a faster algorithm for a special case. In this paper, we extend their algorithm to matroids. Further, we show that the algorithm for the special case is applicable to a more general case.