Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic divide-and-conquer: deterministic second half   We present a probabilistic divide-and-conquer (PDC) method for \emph{exact}
sampling of conditional distributions of the form $\mathcal{L}( {\bf X}\, |\,
{\bf X} \in E)$, where ${\bf X}$ is a random variable on $\mathcal{X}$, a
complete, separable metric space, and event $E$ with $\mathbb{P}(E) \geq 0$ is
assumed to have sufficient regularity such that the conditional distribution
exists and is unique up to almost sure equivalence. The PDC approach is to
define a decomposition of $\mathcal{X}$ via sets $\mathcal{A}$ and
$\mathcal{B}$ such that $\mathcal{X} = \mathcal{A} \times \mathcal{B}$, and
sample from each separately. The deterministic second half approach is to
select the sets $\mathcal{A}$ and $\mathcal{B}$ such that for each element
$a\in \mathcal{A}$, there is only one element $b_a \in \mathcal{B}$ for which
$(a,b_a)\in E$. We show how this simple approach provides non-trivial
improvements to several conventional random sampling algorithms in
combinatorics, and we demonstrate its versatility with applications to sampling
from sufficiently regular conditional distributions.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph