On the low-dimensional steiner minimum tree problem in hamming metric

Authors:
Ernst Althaus;Joschka Kupilas;Rouven Naujoks
Affiliations:
Johannes-Gutenberg-Universität Mainz;Max-Planck-Institut für Informatik;Max-Planck-Institut für Informatik
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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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 - 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.