Regular Article: Geometry of the Space of Phylogenetic Trees
Advances in Applied Mathematics
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The Bergman complex of a matroid and phylogenetic trees
Journal of Combinatorial Theory Series B
Approximating geodesic tree distance
Information Processing Letters
Distance computation in the space of phylogenetic trees
Distance computation in the space of phylogenetic trees
A Fast Algorithm for Computing Geodesic Distances in Tree Space
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann [Adv. Appl. Math., 27 (2001), pp. 733-767]. We show that the possible combinatorial types of shortest paths between two trees can be compactly represented by a partially ordered set. We calculate the shortest distance along each candidate path by converting the problem into one of finding the shortest path through a certain region of Euclidean space. In particular, we show there is a linear time algorithm for finding the shortest path between a point in the all-positive orthant and a point in the all-negative orthant of $\mathbb{R}^k$ contained in the subspace of $\mathbb{R}^k$ consisting of all orthants with the first $i$ coordinates nonpositive and the remaining coordinates nonnegative for $0 \leq i \leq k$.