Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Polynomial Permanent Mod Powers of 2 and Shortest Disjoint
  Cycles   We present a parallel algorithm for permanent mod 2^k of a matrix of
univariate integer polynomials. It places the problem in ParityL subset of
NC^2. This extends the techniques of [Valiant], [Braverman, Kulkarni, Roy] and
[Bj\"orklund, Husfeldt], and yields a (randomized) parallel algorithm for
shortest 2-disjoint paths improving upon the recent result from (randomized)
polynomial time.
  We also recognize the disjoint paths problem as a special case of finding
disjoint cycles, and present (randomized) parallel algorithms for finding a
shortest cycle and shortest 2-disjoint cycles passing through any given fixed
number of vertices or edges.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex