# Solving group Steiner problems as Steiner problems: the rigorous proof

## TL;DR

This paper rigorously proves a transformation from the group Steiner tree problem to the Steiner tree problem, clarifying the conditions under which the transformation is valid, which was previously only intuitively suggested.

## Contribution

It provides the first rigorous proof of the transformation with a specific large M value, solidifying the theoretical foundation of this widely-used approach.

## Key findings

- The transformation is valid for a specific large M value.
- The proof clarifies the conditions needed for the transformation.
- This work strengthens the theoretical basis for solving group Steiner problems.

## Abstract

The Steiner tree problems are well-known NP-hard problems that have diverse applications. Duin et al. (2004) have intuitively proposed the widely-used transformation from the classical group Steiner tree problem to the classical Steiner tree problem in graphs. This transformation has not been rigorously proven so far. Specifically, the large M value that is used in this transformation has not been specified. In this paper, we address this issue by rigorously prove this transformation for a specific large M value.