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Related papers: Directed Lov\'asz Local Lemma and Shearer's Lemma

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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

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

Shearer gave a general theorem characterizing the family $\LLL$ of dependency graphs labeled with probabilities $p_v$ which have the property that for any family of events with a dependency graph from $\LLL$ (whose vertex-labels are upper…

Combinatorics · Mathematics 2012-04-27 Wesley Pegden

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

In a seminal paper (Moser and Tardos, JACM'10), Moser and Tardos developed a simple and powerful algorithm to find solutions to combinatorial problems in the variable Lov{\'a}sz Local Lemma (LLL) setting. Kolipaka and Szegedy (STOC'11)…

Data Structures and Algorithms · Computer Science 2021-11-15 Kun He , Qian Li , Xiaoming Sun

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

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

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

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) says that, given a set of bad events that depend on the values of some random variables and where each event happens with probability at most $p$ and depends on at most $d$ other events, there is an…

Data Structures and Algorithms · Computer Science 2019-08-21 Sebastian Brandt , Yannic Maus , Jara Uitto

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

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

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 (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 2019-09-20 David G. Harris

The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to show the existence of a variety of combinatorial structures with good "local" properties. The "LLL-distribution" can be used to show that the resulting structures…

Combinatorics · 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

The Lov\'asz Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of $n$ `bad events', each occurring with probability at most $p$ and dependent on a set of underlying random variables,…

Data Structures and Algorithms · Computer Science 2025-02-18 Peter Davies-Peck

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 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\'{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
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