A simple approximation algorithm for the internal Steiner minimum tree

TL;DR

This paper presents a simple polynomial-time approximation algorithm for the internal Steiner minimum tree problem, improving the approximation ratio over previous methods by leveraging the Steiner minimum tree approximation ratio.

Contribution

It introduces a straightforward $2 ho$-approximation algorithm that simplifies previous approaches and improves the approximation ratio for the internal Steiner minimum tree problem.

Findings

Achieves a $2 ho$-approximation ratio, better than previous $2 ho+1$

Provides a simple polynomial-time algorithm

Improves theoretical bounds for the problem

Abstract

For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time $2\rho$-approximation algorithm, in which $\rho$ is the approximation ratio for the Steiner minimum tree problem. The result improves the previous best approximation ratio $2\rho+1$ for the problem. The ratio is not currently best but the algorithm is very simple.