Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-time algorithms for the curve graph   We describe a polynomial-time algorithm to compute a (tight) geodesic between
two curves in the curve graph. As well as enabling us to compute the distance
between a pair of curves, this has several applications to mapping classes. For
example, we can use these geodesics to compute the asymptotic translation
length, Nielsen--Thurston type, and canonical curve system of a mapping class
in polynomial time in its word length.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an