Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel and sequential in-place permuting and perfect shuffling using
  involutions   We show that any permutation of ${1,2,...,N}$ can be written as the product
of two involutions. As a consequence, any permutation of the elements of an
array can be performed in-place in parallel in time O(1). In the case where the
permutation is the $k$-way perfect shuffle we develop two methods for
efficiently computing such a pair of involutions.
  The first method works whenever $N$ is a power of $k$; in this case the time
is O(N) and space $O(\log^2 N)$. The second method applies to the general case
where $N$ is a multiple of $k$; here the time is $O(N \log N)$ and the space is
$O(\log^2 N)$. If $k=2$ the space usage of the first method can be reduced to
$O(\log N)$ on a machine that has a SADD (population count) instruction.

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics