Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Cubic-Time 2-Approximation Algorithm for rSPR Distance   Due to hybridization events in evolution, studying two different genes of a
set of species may yield two related but different phylogenetic trees for the
set of species. In this case, we want to measure the dissimilarity of the two
trees. The rooted subtree prune and regraft (rSPR) distance of the two trees
has been used for this purpose. The problem of computing the rSPR distance of
two given trees has many applications but is unfortunately NP-hard. The
previously best approximation algorithm for rSPR distance achieves a ratio of
2.5 and it was open whether a better approximation algorithm for rSPR distance
exists. In this paper, we answer this question in the affirmative by presenting
a cubic-time approximation algorithm for rSPR distance that achieves a ratio of
2. Our algorithm is based on the new notion of key and a number of new
structural lemmas. The algorithm is fairly simple and the proof of its
correctness is intuitively understandable albeit complicated.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org