Abstract
A recursive algorithm by Aho, Sagiv, Szymanski, and Ullman [1] forms the basis for many modern rooted supertree methods employed in Phylogenetics. However, as observed by Bryant [4], the tree output by the algorithm of Aho et al. is not always minimal; there may exist other trees which contain fewer nodes yet are still consistent with the input. In this paper, we prove strong polynomial-time inapproximability results for the problem of inferring a minimally resolved supertree from a given consistent set of rooted triplets (MinRS). We also present an exponential-time algorithm for solving MinRS exactly which is based on tree separators. It runs in 2O(n logk) time when every node is required to have at most k children which are internal nodes and where n is the cardinality of the leaf label set of the input trees.
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References
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Jansson, J., Lemence, R.S., Lingas, A. (2010). The Complexity of Inferring a Minimally Resolved Phylogenetic Supertree. In: Moulton, V., Singh, M. (eds) Algorithms in Bioinformatics. WABI 2010. Lecture Notes in Computer Science(), vol 6293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15294-8_22
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DOI: https://doi.org/10.1007/978-3-642-15294-8_22
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