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For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimumtree problem asks for a minimum weight Steiner tree spanning $R$ such thatevery 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 forthe Steiner minimum tree problem. The result improves the previous bestapproximation ratio $2\rho+1$ for the problem. The ratio is not currently bestbut the algorithm is very simple.

A simple approximation algorithm for the internal Steiner minimum tree