English
Related papers

Related papers: A constructive proof of the general Lovasz Local L…

200 papers

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

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 famous Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. Kratochvil et al. applied this technique to prove that a k-CNF in which…

Data Structures and Algorithms · Computer Science 2008-09-15 Robin A. Moser

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 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

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 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

A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required…

Discrete Mathematics · Computer Science 2013-10-29 Andrei Rumyantsev , Alexander Shen

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\'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

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 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\'asz 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.…

Combinatorics · Mathematics 2017-11-21 Nicholas J. A. Harvey , Jan Vondrák

This note is purely expository and is in Russian. We show how to prove interesting combinatorial results using the local Lovasz lemma. The note is accessible for students having basic knowledge of combinatorics; the notion of independence…

History and Overview · Mathematics 2015-01-26 D. Ilyinskiy , A. Raigorodskiy , A. Skopenkov

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

We develop tools for analyzing focused stochastic local search algorithms. These are algorithms which search a state space probabilistically by repeatedly selecting a constraint that is violated in the current state and moving to a random…

Discrete Mathematics · Computer Science 2015-08-18 Dimitris Achlioptas , Fotis Iliopoulos

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

Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…

Logic in Computer Science · Computer Science 2024-01-18 Chelsea Edmonds , Lawrence C. Paulson

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

In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a…

Combinatorics · Mathematics 2019-08-29 Anton Bernshteyn
‹ Prev 1 2 3 10 Next ›