Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs
  with Prescribed Degrees   The uniform sampling of simple graphs matching a prescribed degree sequence
is an important tool in network science, e.g., to construct graph generators or
null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice.
Given an arbitrary simple graph with the required degree sequence, ES-MC
carries out a large number of small changes involving at most four edges to
eventually obtain a uniform sample. In practice, reasonably short runs
efficiently yield approximate uniform samples.
  We first engineer a simple sequential ES-MC implementation representing the
graph in a hash-set. Despite its simplicity and to the best of our knowledge,
our implementation significantly outperforms all openly available solutions.
  Secondly, we propose the Global Edge Switching Markov Chain (G-ES-MC) and
show that it, too, converges to a uniform distribution. We provide empirical
evidence that G-ES-MC requires not more switches than ES-MC (and often fewer).
  Thirdly, we engineer shared-memory parallel algorithms for ES-MC and G-ES-MC;
we find that they benefit from the easier dependency structure of the G-ES-MC.
In an empirical evaluation, we demonstrate the scalability of our
implementations.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex