Abstract
We present a new graph-based approach to the following basic problem in phylogenetic tree construction. Let \(\mathcal {P}= \{T_1, \ldots , T_k\}\) be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks whether there is a phylogenetic tree T with the following property: for each \(i \in \{1, \dots , k\}\), \(T_i\) can be obtained from the restriction of T to the species set of \(T_i\) by contracting zero or more edges. If such a tree T exists, we say that \(\mathcal {P}\) is compatible and that T displays \(\mathcal {P}\). Our approach leads to a \(O(M_\mathcal {P}\log ^2 M_\mathcal {P})\) algorithm for the tree compatibility problem, where \(M_\mathcal {P}\) is the total number of nodes and edges in \(\mathcal {P}\). Our algorithm either returns a tree that displays \(\mathcal {P}\) or reports that \(\mathcal {P}\) is incompatible. Unlike previous algorithms, the running time of our method does not depend on the degrees of the nodes in the input trees. Thus, our algorithm is equally fast on highly resolved and highly unresolved trees.
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Notes
The name of our algorithm is intended to reflect its connection with \(\textsc {Build}\)–the “ST” stands for “supertree”.
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A preliminary version of this paper appeared in the proceedings of the 27th Annual Symposium on Combinatorial Pattern Matching, Tel Aviv, Israel, June 27–29, 2016 [9]. Yun Deng: Supported in part by the National Science Foundation under Grant CCF-1422134. David Fernández-Baca: Supported in part by the National Science Foundation under Grants CCF-1017189 and CCF-1422134.
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Deng, Y., Fernández-Baca, D. Fast Compatibility Testing for Rooted Phylogenetic Trees. Algorithmica 80, 2453–2477 (2018). https://doi.org/10.1007/s00453-017-0330-4
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DOI: https://doi.org/10.1007/s00453-017-0330-4