Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A faster implementation of the pivot algorithm for self-avoiding walks   The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating
the self-avoiding walk. At each iteration a pivot which produces a global
change in the walk is proposed. If the resulting walk is self-avoiding, the new
walk is accepted; otherwise, it is rejected. Past implementations of the
algorithm required a time O(N) per accepted pivot, where N is the number of
steps in the walk. We show how to implement the algorithm so that the time
required per accepted pivot is O(N^q) with q<1. We estimate that q is less than
0.57 in two dimensions, and less than 0.85 in three dimensions. Corrections to
the O(N^q) make an accurate estimate of q impossible. They also imply that the
asymptotic behavior of O(N^q) cannot be seen for walk lengths which can be
simulated. In simulations the effective q is around 0.7 in two dimensions and
0.9 in three dimensions. Comparisons with simulations that use the standard
implementation of the pivot algorithm using a hash table indicate that our
implementation is faster by as much as a factor of 80 in two dimensions and as
much as a factor of 7 in three dimensions. Our method does not require the use
of a hash table and should also be applicable to the pivot algorithm for
off-lattice models.

2
The categories of this paper are: math
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol