Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel algorithms and concentration bounds for the Lovasz Local Lemma
  via witness DAGs   The Lov\'{a}sz Local Lemma (LLL) is a cornerstone principle in the
probabilistic method of combinatorics, and a seminal algorithm of Moser &
Tardos (2010) provides an efficient randomized algorithm to implement it. This
can be parallelized to give an algorithm that uses polynomially many processors
and runs in $O(\log^3 n)$ time on an EREW PRAM, stemming from $O(\log n)$
adaptive computations of a maximal independent set (MIS). Chung et al. (2014)
developed faster local and parallel algorithms, potentially running in time
$O(\log^2 n)$, but these algorithms require more stringent conditions than the
LLL.
  We give a new parallel algorithm that works under essentially the same
conditions as the original algorithm of Moser & Tardos but uses only a single
MIS computation, thus running in $O(\log^2 n)$ time on an EREW PRAM. This can
be derandomized to give an NC algorithm running in time $O(\log^2 n)$ as well,
speeding up a previous NC LLL algorithm of Chandrasekaran et al. (2013).
  We also provide improved and tighter bounds on the run-times of the
sequential and parallel resampling-based algorithms originally developed by
Moser & Tardos. These apply to any problem instance in which the tighter
Shearer LLL criterion is satisfied.

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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc