Reconstructing trees from subtree weights

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Abstract

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is an extension of the tree-metric theorem to more general dissimilarity maps. In particular, we show that a tree with n leaves is reconstructible from the weights of the m-leaf subtrees provided that n ≥ 2m — 1.

Keywords

Phylogenetics
Tree
Reconstruction
Algorithm
Tropical

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L. Pachter was partially supported by a Grant from the NIH (R01-HG02362-02).