The Complexity of Inferring a Minimally Resolved Phylogenetic Supertree
A recursive algorithm by Aho, Sagiv, Szymanski, and Ullman  forms the basis for many modern rooted supertree methods employed in Phylogenetics. However, as observed by Bryant , 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 2 O(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.
KeywordsPhylogenetic tree rooted triplet minimally resolved supertree NP-hardness tree separator
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