Abstract
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.
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Bilò, D., Zych, A. (2012). New Advances in Reoptimizing the Minimum Steiner Tree Problem. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_19
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DOI: https://doi.org/10.1007/978-3-642-32589-2_19
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