A supertree method for rooted trees
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Rooted Maximum Agreement Supertrees
Algorithmica
Using Max Cut to Enhance Rooted Trees Consistency
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Analytic solutions for three taxon ML trees with variable rates across sites
Discrete Applied Mathematics
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
Computing a Smallest Multilabeled Phylogenetic Tree from Rooted Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The Complexity of Inferring A Minimally Resolved Phylogenetic Supertree
SIAM Journal on Computing
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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 log k) 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.