The steiner problem with edge lengths 1 and 2,
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In this paper we improve the results in the literature concerning the problem of computing the minimum Steiner tree given the minimum Steiner tree for a similar problem instance. Using a σ-approximation algorithm computing the minimum Steiner tree from scratch, we provide a $\left(\frac{3 \sigma-1}{2 \sigma-1}+\epsilon\right)$ and a $\left(\frac{2 \sigma-1}{\sigma}+\epsilon\right)$ -approximation algorithm for altering the instance by removing a vertex from the terminal set and by increasing the cost of an edge, respectively. If we use the best up to date σ=ln 4+ε, our ratios equal 1.218 and 1.279 respectively.