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… 
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References

SHOWING 1-10 OF 27 REFERENCES
Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees
TLDR
The problem of computing the minimum number of TBR operations required to transform one tree to another can be reduced to a problem whose size is a function just of the distance between the trees, and thereby establish that the problem is fixed-parameter tractable.
On the Combinatorics of Rooted Binary Phylogenetic Trees
AbstractWe study subtree-prune-and-regraft (SPR) operations on leaf-labelled rooted binary trees, also known as rooted binary phylogenetic trees. This study is motivated by the problem of
The maximum agreement subtree problem
On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance
TLDR
This paper shows that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard, and shows that this distance is fixed parameter tractable when parameterised by the distance between the two trees.
On agreement forests
Reconstructing evolution of sequences subject to recombination using parsimony.
  • J. Hein
  • Biology
    Mathematical biosciences
  • 1990
Calculating SPR distances between trees
  • P. Goloboff
  • Computer Science
    Cladistics : the international journal of the Willi Hennig Society
  • 2008
TLDR
A measure of tree‐similarity based on SPR distances is proposed, obtained by calculating the minimum number of weighted SPR moves (with moves to closer nodes being less costly), and the resulting measure of similarity is symmetric (i.e., Dij = Dji, for any two trees i,j).
...
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