A Note on "A Faster Approximation Algorithm for the Steiner Problem in Graphs"

Abstract Mehlhorn (1988) has presented an improved implementation of the Kou, Markowsky and Berman Steiner tree approximation algorithm (1981). By replacing one step of the original algorithm the complexity reduces from O (| S |⋯(| E |+| V |;⋯ log | V |) to O (| E |+| V |⋯ log | V |), where S is the set of terminals, E the set of all edges and V the set of all vertices in the graph. In this paper we will show that due to the improvement two steps of the algorithm may be omitted. This does not reduce the complexity of the algorithm but it makes it simpler.