Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees

@article{Allen2001SubtreeTO,
  title={Subtree Transfer Operations and Their Induced Metrics on Evolutionary Trees},
  author={Benjamin Allen and Mike A. Steel},
  journal={Annals of Combinatorics},
  year={2001},
  volume={5},
  pages={1-15}
}
Abstract. Leaf-labelled trees are widely used to describe evolutionary relationships, particularly in biology. In this setting, extant species label the leaves of the tree, while the internal vertices correspond to ancestral species. Various techniques exist for reconstructing these evolutionary trees from data, and an important problem is to determine how "far apart" two such reconstructed trees are from each other, or indeed from the true historical tree. To investigate this question requires… 
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References

SHOWING 1-10 OF 23 REFERENCES
On the Nearest Neighbour Interchange Distance Between Evolutionary Trees
TLDR
An upper bound on the nni-distance between two arbitrary n-node trees is improved and a polynomial-time approximation algorithm is presented that, given two trees, finds a transformation between them of length O(log n) times their distance.
The discovery and importance of multiple islands of most
TLDR
The set of most-parsimonious trees for a data matrix may include several distinct classes (islands) of trees, and trees in different islands may have different implications for character evolution, and for this reason should be sought.
On the similarity of dendrograms.
Parameterized complexity: A framework for systematically confronting computational intractability
TLDR
An improved FPT ker-nelization algorithm for Vertex Cover, a practical FPT algorithm for the Maximum Agreement Subtree problem parameterized by the number of species to be deleted, and new general heuristics for these problems based on FPT techniques are described.
...
...