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The Neighbor-Joining algorithm is a recursive procedure for reconstructing trees that is based on a transformation of pairwise distances between leaves. We present a generalization of the neighbor-joining transformation, which uses…

In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of…

The neighbor-joining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbor-net algorithm is an extension of the neighbor-joining algorithm and is used for constructing split networks. We…

Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…

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…

Recent theoretical work has demonstrated that Neighbor Joining applied to concatenated DNA sequences is a statistically consistent method of species tree reconstruction. This brief note compares the accuracy of this approach to other…

The Neighbor Joining Algorithm is among the most fundamental algorithmic results in computational biology. However, its definition and correctness proof are not straightforward. In particular, ''the question ''what does the NJ method seek…

Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…

In this paper, we will analyze the behavior of the Neighbor Joining algorithm on five taxa and we will show that the partition of the sample (data) space for estimation of a tree topology with five taxa into subspaces, within each of which…

Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…

We show that the neighbor-joining algorithm is a robust quartet method for constructing trees from distances. This leads to a new performance guarantee that contains Atteson's optimal radius bound as a special case and explains many cases…

Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighbourhood, that is, the number of trees exactly one operation from a given tree. We…

A variety of algorithms have been proposed for reconstructing trees that show the evolutionary relationships between species by comparing differences in genetic data across present-day taxa. If the leaf-to-leaf distances in a tree can be…

In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…

Among the distance based algorithms in phylogenetic tree reconstruction, the neighbor-joining algorithm has been a widely used and effective method. We propose a new algorithm which counts the number of consistent quartets for cherry…

The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…

Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…

A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These formulas have proved useful for the development of efficient…

Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2000, Pauplin showed that the BME method is equivalent to optimizing a linear…

We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…