Relative Merits of Minimum Cost Spanning Trees and Steiner Trees

This paper discusses about the concepts of Minimum cost spanning tree and what happens if it is used in place of Steiner tree. We show that the MSTP is equivalent to a Steiner Tree Problem (STP) in an adequate layered graph. We also adapt the proposed approach for the Diameter-Constrained Minimum Spanning Tree Problem (DMSTP). Although the HMSTP and the DMSTP have symmetric edge costs, we will focus on so-called directed formulations.