Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Neighbor-Net Algorithm   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 begin by describing the output of neighbor-net in terms of the
tessellation of $\bar{\MM}_{0}^n(\mathbb{R})$ by associahedra. This highlights
the fact that neighbor-net outputs a tree in addition to a circular ordering
and we explain when the neighbor-net tree is the neighbor-joining tree. A key
observation is that the tree constructed in existing implementations of
neighbor-net is not a neighbor-joining tree. Next, we show that neighbor-net is
a greedy algorithm for finding circular split systems of minimal balanced
length. This leads to an interpretation of neighbor-net as a greedy algorithm
for the traveling salesman problem. The algorithm is optimal for Kalmanson
matrices, from which it follows that neighbor-net is consistent and has optimal
radius 1/2. We also provide a statistical interpretation for the balanced
length for a circular split system as the length based on weighted least
squares estimates of the splits. We conclude with applications of these results
and demonstrate the implications of our theorems for a recently published
comparison of Papuan and Austronesian languages.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess