The Geometry of the NeighborJoining Algorithm for Small Trees
Abstract
In 2007, Eickmeyer et al. showed that the tree topologies outputted by the NeighborJoining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of the space of dissimilarity maps ${\R}^{n \choose 2}$, where $n$ is the number of taxa. In this paper, we will analyze the behavior of the NeighborJoining algorithm on five and six taxa and study the geometry and combinatorics of the polyhedral subdivision of the space of dissimilarity maps for six taxa as well as hyperplane representations of each polyhedral subdivision. We also study simulations for one of the questions stated by Eickmeyer et al., that is, the robustness of the NJ algorithm to small perturbations of tree metrics, with tree models which are known to be hard to be reconstructed via the NJ algorithm.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 DOI:
 10.48550/arXiv.0908.0098
 arXiv:
 arXiv:0908.0098
 Bibcode:
 2009arXiv0908.0098E
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 15 pages