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Related papers: New Constructive Aspects of the Lovasz Local Lemma

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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 probabilistic method is a technique for proving combinatorial existence results by means of showing that a randomly chosen object has the desired properties with positive probability. A particularly powerful probabilistic tool is the…

Combinatorics · Mathematics 2022-02-08 Anton Bernshteyn

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

The Lovasz Local Lemma due to Erdos and Lovasz is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events,…

Data Structures and Algorithms · Computer Science 2007-05-23 Aravind Srinivasan

We consider the recent formulation of the Algorithmic Lov\'asz Local Lemma [10,2,3] for finding objects that avoid `bad features', or `flaws'. It extends the Moser-Tardos resampling algorithm [17] to more general discrete spaces. At each…

Data Structures and Algorithms · Computer Science 2018-09-05 Vladimir Kolmogorov

We consider recent formulations of the algorithmic Lovasz Local Lemma by Achlioptas-Iliopoulos-Kolmogorov [2] and by Achlioptas-Iliopoulos-Sinclair [3]. These papers analyze a random walk algorithm for finding objects that avoid undesired…

Data Structures and Algorithms · Computer Science 2020-08-17 Vladimir Kolmogorov

The Lov\'{a}sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works…

Data Structures and Algorithms · Computer Science 2025-09-09 David G. Harris , Fotis Iliopoulos , Vladimir Kolmogorov

The Lov\'asz Local Lemma (the LLL for short) is a powerful tool in probabilistic combinatorics that is used to verify the existence of combinatorial objects with desirable properties. Recent years saw the development of various…

Combinatorics · Mathematics 2026-05-29 Anton Bernshteyn , Jing Yu

We give an algorithmic local lemma by establishing a sufficient condition for the uniform random walk on a directed graph to reach a sink quickly. Our work is inspired by Moser's entropic method proof of the Lov\'{a}sz Local Lemma (LLL) for…

Combinatorics · Mathematics 2015-04-10 Dimitris Achlioptas , Fotis Iliopoulos

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

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 Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general…

Quantum Physics · Physics 2013-10-10 Andris Ambainis , Julia Kempe , Or Sattath

The constructive Lov\'{a}sz Local Lemma has become a central tool for designing efficient distributed algorithms. While it has been extensively studied in the classic LOCAL model that uses unlimited bandwidth, much less is known in the…

Data Structures and Algorithms · Computer Science 2024-05-14 Magnús M. Halldórsson , Yannic Maus , Saku Peltonen

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

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

We present a poly $\log \log n$ time randomized CONGEST algorithm for a natural class of Lovasz Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-06 Yannic Maus , Jara Uitto

The Lovasz Local Lemma [EL75] is a powerful tool to prove the existence of combinatorial objects meeting a prescribed collection of criteria. The technique can directly be applied to the satisfiability problem, yielding that a k-CNF formula…

Data Structures and Algorithms · Computer Science 2008-10-29 Robin A. Moser

The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of…

Logic · Mathematics 2024-06-19 Daniel Mourad

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