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
Reconstructing minimal rooted trees
Discrete Applied Mathematics
Rooted Maximum Agreement Supertrees
Algorithmica
Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network
SIAM Journal on Computing
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
Constructing Level-2 Phylogenetic Networks from Triplets
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New results on optimizing rooted triplets consistency
Discrete Applied Mathematics
The complexity of inferring a minimally resolved phylogenetic supertree
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Phylogenetic Networks: Concepts, Algorithms and Applications
Phylogenetic Networks: Concepts, Algorithms and Applications
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A recursive algorithm by Aho et al. [SIAM J. Comput., 10 (1981), pp. 405-421] forms the basis for many modern rooted supertree methods employed in Phylogenetics. However, as observed by Bryant [Building Trees, Hunting for Trees, and Comparing Trees: Theory and Methods in Phylogenetic Analysis, Ph.D. thesis, University of Canterbury, Christchurch, New Zealand, 1997], 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). Furthermore, we show that the decision version of MinRS is NP-hard for any fixed positive integer $q\geq4$, where $q$ is the number of allowed internal nodes, but linear-time solvable for $q\leq3$. In contrast, MinRS becomes polynomial-time solvable for any $q$ when restricted to caterpillars. We also present an exponential-time algorithm based on tree separators for solving MinRS exactly. It runs in $2^{O(n\log p)}$ time when every node may have at most $p$ children that are internal nodes and where $n$ is the cardinality of the leaf label set. Finally, we demonstrate that augmenting the algorithm of Aho et al. with an algorithm for optimal graph coloring to help merge certain blocks of leaves during the execution does not improve the output solution much in the worst case.