Abstract
It is known that the d-dimensional Steiner Minimum Tree Problem in Hamming metric is NP-complete if d is considered to be a part of the input. On the other hand, it was an open question whether the problem is also NP-complete in fixed dimensions. In this paper we answer this question by showing that the problem is NP-complete for any dimension strictly greater than 2. We also show that the Steiner ratio is \(2-\frac{2}{d}\) for d ≥ 2. Using this result, we tailor the analysis of the so-called k-LCA approximation algorithm and show improved approximation guarantees for the special cases d = 3 and d = 4.
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© 2011 Springer-Verlag Berlin Heidelberg
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Althaus, E., Kupilas, J., Naujoks, R. (2011). On the Low-Dimensional Steiner Minimum Tree Problem in Hamming Metric. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_31
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DOI: https://doi.org/10.1007/978-3-642-20877-5_31
Publisher Name: Springer, Berlin, Heidelberg
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