Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Shellability of complexes of trees
Journal of Combinatorial Theory Series A
Regular Article: Geometry of the Space of Phylogenetic Trees
Advances in Applied Mathematics
Approximating geodesic tree distance
Information Processing Letters
Horoball hulls and extents in positive definite space
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Computing Geodesic Distances in Tree Space
SIAM Journal on Discrete Mathematics
Shortest path problem in rectangular complexes of global nonpositive curvature
Computational Geometry: Theory and Applications
Tree-space statistics and approximations for large-scale analysis of anatomical trees
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Dimension reduction in principal component analysis for trees
Computational Statistics & Data Analysis
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Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a euclidean-like structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained.