Abstract
Three results on the Steiner tree problem are presented: (i) Computing optimum k-restricted Steiner tree is APX-complete for k≥4, (ii) the minimum-cost k-restricted Steiner tree problem in phylogeny is APX-complete for k≥4, and (iii) the k-Steiner ratio for the Steiner tree problem in phylogeny matches the corresponding ratio for metric spaces defined on graphs. The results are significant because k-restricted trees are used in various approximation algorithms for the Steiner tree problem, and (i) and (ii) suggest that there is a limit to the approximability of the optimum solution. The k-Steiner ratio, which establishes a relation between the size of the optimum Steiner tree and the optimum k-restricted tree, arises in the analysis of many of the same algorithms.
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Supported in part by the National Science Foundation under grants CCR-9211262 and CCR-9520946.
Supported by grants from NFR and TFR.
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Fernández-Baca, D., Lagergren, J. (1996). On the approximability of the Steiner tree problem in phylogeny. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009482
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DOI: https://doi.org/10.1007/BFb0009482
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