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Related papers: Extensions of the Algorithmic Lovasz Local Lemma

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The Lovasz Local Lemma is a seminal result in probabilistic combinatorics. It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events.…

Data Structures and Algorithms · Computer Science 2015-11-19 Nicholas Harvey , Jan Vondrak

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 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

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

The Lov\'asz Local Lemma is a classic result in probability theory that is often used to prove the existence of combinatorial objects via the probabilistic method. In its simplest form, it states that if we have $n$ `bad events', each of…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-10-20 Peter Davies

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

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

We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These are algorithms that search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a…

Discrete Mathematics · Computer Science 2018-09-06 Dimitris Achlioptas , Fotis Iliopoulos , Vladimir Kolmogorov

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…

Data Structures and Algorithms · Computer Science 2023-03-10 Kun He , Chunyang Wang , Yitong Yin

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

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

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

Lov\'asz Local Lemma (LLL) is a probabilistic tool that allows us to prove the existence of combinatorial objects in the cases when standard probabilistic argument does not work (there are many partly independent conditions). LLL can be…

Data Structures and Algorithms · Computer Science 2010-12-03 Andrey Rumyantsev

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

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 propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new…

Data Structures and Algorithms · Computer Science 2019-01-16 Heng Guo , Mark Jerrum , Jingcheng Liu

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 recently proven Quantum Lovasz Local Lemma generalises the well-known Lovasz Local Lemma. It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints. It…

Quantum Physics · Physics 2013-11-28 Toby S. Cubitt , Martin Schwarz

Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role…

Artificial Intelligence · Computer Science 2015-12-07 Sixue Liu

In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave…

Machine Learning · Computer Science 2025-11-03 Junfan Li , Shizhong Liao , Zenglin Xu , Liqiang Nie