# Extremal Distances for Subtree Transfer Operations in Binary Trees

@article{Atkins2018ExtremalDF, title={Extremal Distances for Subtree Transfer Operations in Binary Trees}, author={Ross Atkins and Colin McDiarmid}, journal={Annals of Combinatorics}, year={2018}, volume={23}, pages={1-26} }

Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection (TBR), subtree prune and regraft (SPR), and rooted subtree prune and regraft (rSPR). We show that for a pair of leaf-labelled binary trees with n leaves, the maximum number of such moves required to transform one into the other is $$n-\Theta (\sqrt{n})$$n-Θ(n), extending a result of Ding, Grünewald, and Humphries, and this holds also if one of the trees is…

## 11 Citations

Reflections on kernelizing and computing unrooted agreement forests

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Five new reduction rules are proposed and shown to be the first reduction rules that strictly enhance the reductive power of the subtree and chain reduction rules.

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A kernel of size 9k − 8 is described for the NP-hard problem of computing the Tree Bisection and Reconnect distance k between two unrooted binary phylogenetic trees by extending the existing portfolio of reduction rules with three novel new reduction rules.

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This work shows that any two rooted phylogenetic networks of the same complexity are connected by a sequence of either rSPR or rNNI moves, and gives bounds on the number of (distance-1) tail moves necessary to turn one network into another.

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Calculating the Unrooted Subtree Prune-and-Regraft Distance

- Computer ScienceIEEE/ACM Transactions on Computational Biology and Bioinformatics
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A “progressive A*” search algorithm is developed using multiple heuristics, including the TBR and replug distances, to exactly compute the unrooted SPR distance, which is nearly two orders of magnitude faster than previous methods on small trees.

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