Deterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel

@article{Harris2022DeterministicAF,
  title={Deterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel},
  author={David G. Harris},
  journal={ArXiv},
  year={2022},
  volume={abs/1909.08065}
}
  • David G. Harris
  • Published 17 September 2019
  • Computer Science, Mathematics
  • ArXiv
The Lovasz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its simplest "symmetric" form, it asserts that whenever a bad-event has probability $p$ and affects at most $d$ bad-events, and $e p d < 1$, then a configuration avoiding all $\mathcal B$ exists. A seminal algorithm of Moser & Tardos (2010) gives nearly-automatic… 
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References

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Parallel algorithms for the Lopsided Lovász Local Lemma
  • David G. Harris
  • Computer Science, Mathematics
    Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
  • 2019
TLDR
New parallel algorithms for most forms of LLLL are given, which are simpler, faster, and more general than the algorithms of Harris and Harris & Srinivasan, and generalizes an algorithm given by Blelloch, Fineman, Shun for undirected graphs.
Deterministic algorithms for the Lovász Local Lemma
TLDR
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TLDR
It is shown that the output distribution of the Moser-Tardos algorithm well-approximates the conditional LLL-distribution – the distribution obtained by conditioning on all bad events being avoided, and how a known bound on the probabilities of events in this distribution can be used for further probabilistic analysis and give new constructive and non-constructive results.
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TLDR
A new parallel algorithm is given that works under essentially the same conditions as the original algorithm of Moser and Tardos but uses only a single MIS computation, thus running in O(log2 n) time on an EREW PRAM.
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TLDR
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TLDR
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TLDR
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TLDR
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New bounds for the Moser-Tardos distribution
TLDR
New bounds on the MT-distribution are shown which are significantly stronger than those known to hold for the LLL-dist distribution for the variable-assignment setting and a tighter bound on the probability of a disjunctive event or singleton event is shown.
Moser and tardos meet Lovász
TLDR
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