You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We show that any randomised Monte Carlo distributed algorithm for the Lov 'asz local lemma requires @math communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of @math , where @math is the maximum degree of the dependency graph. By prior work, there are distributed algorithms for the Lov 'asz local lemma with a running time of @math rounds in bounded-degree graphs, and the best lower bound before our work was @math rounds [ 2014].

Cited Abstract(s):
[1]: 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 @math time on an EREW PRAM, stemming from @math adaptive computations of a maximal independent set (MIS). (2014) developed faster local and parallel algorithms, potentially running in time @math , 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 @math time on an EREW PRAM. This can be derandomized to give an NC algorithm running in time @math as well, speeding up a previous NC LLL algorithm of (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.
While there are numerous positive results, only a few lower bounds for LLL are known. Moser and Tardos point out that in their resampling approach, @math expected iterations of resampling are needed. Recently, Haeupler and Harris [1] conjectured that parallel resampling algorithms need @math time.