Abstract
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps R(n2)+ to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n ≤ 8. This requires the measurement of volumes of spherical polytopes in high dimension, which we obtain using a combination of Monte Carlo methods and polyhedral algorithms. Our results include a demonstration that highly unrelated trees can be co-optimal in BME reconstruction, and that NJ regions are not convex. We obtain the l2 radius for neighbor-joining for n = 5 and we conjecture that the ability of the neighbor-joining algorithm to recover the BME tree depends on the diameter of the BME tree.
Document Type
Article
Publication Date
4-30-2008
Digital Object Identifier (DOI)
http://dx.doi.org/10.1186/1748-7188-3-5
Repository Citation
Eickmeyer, Kord; Huggins, Peter; Pachter, Lior; and Yoshida, Ruriko, "On the optimality of the neighbor-joining algorithm" (2008). Statistics Faculty Publications. 7.
https://uknowledge.uky.edu/statistics_facpub/7
Notes/Citation Information
Published in Algorithms for Molecular Biology, v. 3, 5.
© 2008 Eickmeyer et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.