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A fast algorithm for computing geodesic distances in tree space.

Megan Owen¹, J Scott Provan

¹Department of Mathematics, University of California, Berkeley, MC 3840, Berkeley, CA 94720-0432, USA. maowen@berkeley.edu

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|November 13, 2010

Summary

This study introduces a polynomial-time algorithm for computing geodesic distances between phylogenetic trees. The new method efficiently finds shortest paths in continuous tree space, aiding evolutionary biology research.

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Area of Science:

Computational Biology
Evolutionary Biology
Phylogenetics

Background:

Comparing phylogenetic trees with edge lengths is crucial in evolutionary studies.
The Billera-Holmes-Vogtmann tree space offers a continuous framework for tree comparison.
Calculating geodesic distances (shortest paths) in this space is computationally challenging.

Purpose of the Study:

To develop a polynomial-time algorithm for computing geodesic distances between phylogenetic trees.
To address the open problem of efficient geodesic computation in tree space.
To facilitate optimization problems and comparisons of evolutionary trees.

Main Methods:

Introduced a novel polynomial-time algorithm for geodesic path computation.
The algorithm iteratively refines an initial path through successively shorter paths.
Leverages the Euclidean-like structure of the Billera-Holmes-Vogtmann tree space.

Main Results:

A practical algorithm for finding geodesics in phylogenetic tree space is presented.
The algorithm guarantees convergence to the shortest path.
Demonstrates the feasibility of efficient geodesic computation.

Conclusions:

The developed algorithm provides an efficient solution for computing geodesic distances.
This advancement simplifies comparative analyses of phylogenetic trees.
Enables new possibilities for optimization problems in phylogenetics.