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Related papers: Moser-Tardos Algorithm: Beyond Shearer's Bound

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The Lopsided Lov\'{a}sz Local Lemma (LLLL) is a powerful probabilistic principle which has been used in a variety of combinatorial constructions. While originally a general statement about probability spaces, it has recently been…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

Moser and Tardos (2010) gave an algorithmic proof of the lopsided Lov\'asz local lemma (LLL) in the variable framework, where each of the undesirable events is assumed to depend on a subset of a collection of independent random variables.…

Combinatorics · Mathematics 2020-06-16 Lefteris Kirousis , John Livieratos , Kostas I. Psaromiligkos

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…

Discrete Mathematics · Computer Science 2023-10-13 Bernhard Haeupler , David G. Harris

The Lov\'asz Local Lemma (LLL) is a very powerful tool in combinatorics and probability theory to show the possibility of avoiding all bad events under some weakly dependent conditions. In a seminal paper, Ambainis, Kempe, and Sattath (JACM…

Computational Complexity · Computer Science 2024-09-30 Kun He , Qian Li , Xiaoming Sun , Jiapeng Zhang

The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…

Combinatorics · Mathematics 2019-09-13 Anton Bernshteyn

Moser & Tardos have developed a powerful algorithmic approach (henceforth "MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its variants is a search for "bad" events in a current configuration. In the initial stage…

Discrete Mathematics · Computer Science 2023-10-13 David G. Harris , Aravind Srinivasan

The resampling algorithm of Moser \& Tardos is a powerful approach to develop constructive versions of the Lov\'{a}sz Local Lemma (LLL). We generalize this to partial resampling: when a bad event holds, we resample an appropriately-random…

Combinatorics · Mathematics 2023-10-13 David G. Harris , Aravind Srinivasan

Following the groundbreaking Moser-Tardos algorithm for the Lovasz Local Lemma (LLL), a series of works have exploited a key ingredient of the original analysis, the witness tree lemma, in order to: derive deterministic, parallel and…

Discrete Mathematics · Computer Science 2019-06-11 Fotis Iliopoulos

A tight criterion under which the abstract version Lov\'asz Local Lemma (abstract-LLL) holds was given by Shearer decades ago. However, little is known about that of the variable version LLL (variable-LLL) where events are generated by…

Discrete Mathematics · Computer Science 2017-09-18 Kun He , Liang Li , Xingwu Liu , Yuyi Wang , Mingji Xia

The Lopsided Lovasz Local Lemma (LLLL) is a cornerstone probabilistic tool for showing that it is possible to avoid a collection of "bad" events as long as their probabilities and interdependencies are sufficiently small. The strongest…

Probability · Mathematics 2023-10-13 David G. Harris

The Lov\'{a}sz Local Lemma (LLL) states that the probability that none of a set of "bad" events happens is nonzero if the probability of each event is small compared to the number of bad events it depends on. A series of results have…

Data Structures and Algorithms · Computer Science 2011-10-04 Bernhard Haeupler , Barna Saha , Aravind Srinivasan

We study a variant of the parallel Moser-Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm…

Combinatorics · Mathematics 2026-04-27 Endre Csóka , Łukasz Grabowski , András Máthé , Oleg Pikhurko , Konstantinos Tyros

The Lov\'{a}sz Local Lemma is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive…

Combinatorics · Mathematics 2026-04-30 Igal Sason

The Lov\'{a}sz 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…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…

Combinatorics · Mathematics 2017-05-08 Anton Bernshteyn

We consider the task of designing Local Computation Algorithms (LCA) for applications of the Lov\'{a}sz Local Lemma (LLL). LCA is a class of sublinear algorithms proposed by Rubinfeld et al.~\cite{Ronitt} that have received a lot of…

Data Structures and Algorithms · Computer Science 2020-07-08 Dimitris Achlioptas , Themis Gouleakis , Fotis Iliopoulos

Given a collection of independent events each of which has strictly positive probability, the probability that all of them occur is also strictly positive. The Lov\'asz local lemma (LLL) asserts that this remains true if the events are not…

Probability · Mathematics 2021-11-18 Dimitris Achlioptas , Kostas Zampetakis

Following the groundbreaking algorithm of Moser and Tardos for the Lovasz Local Lemma (LLL), there has been a plethora of results analyzing local search algorithms for various constraint satisfaction problems. The algorithms considered fall…

Discrete Mathematics · Computer Science 2020-08-20 Dimitris Achlioptas , Fotis Iliopoulos , Alistair Sinclair

The Lovasz Local Lemma (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that…

Data Structures and Algorithms · Computer Science 2019-08-07 Karthekeyan Chandrasekaran , Navin Goyal , Bernhard Haeupler

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…

Data Structures and Algorithms · Computer Science 2020-06-09 Sebastian Brandt , Christoph Grunau , Václav Rozhoň
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