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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

We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…

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

While there has been significant progress on algorithmic aspects of the Lov\'{a}sz Local Lemma (LLL) in recent years, a noteworthy exception is when the LLL is used in the context of random permutations. The breakthrough algorithm of Moser…

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

Assume we are given (finitely many) mutually independent variables and (finitely many) "undesirable" events, each depending on a subset of the variables of at most $k$ elements, called the scope of the event. Assume that the probability of…

Discrete Mathematics · Computer Science 2018-08-08 Lefteris Kirousis , John Livieratos , Kostas I. Psaromiligkos

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

The Local Computation Algorithm (LCA) model is a popular model in the field of sublinear-time algorithms that measures the complexity of an algorithm by the number of probes the algorithm makes in the neighborhood of one node to determine…

Data Structures and Algorithms · Computer Science 2021-12-06 Sebastian Brandt , Christoph Grunau , Václav Rozhoň

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 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

Let $\mathcal{L}$ be a language that can be decided in linear space and let $\epsilon >0$ be any constant. Let $\mathcal{A}$ be the exponential hardness assumption that for every $n$, membership in $\mathcal{L}$ for inputs of length~$n$…

Computational Complexity · Computer Science 2023-03-30 Edward Pyne , Ran Raz , Wei Zhan

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

We show that any randomised Monte Carlo distributed algorithm for the Lov\'asz local lemma requires $\Omega(\log \log n)$ communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-11-04 Sebastian Brandt , Orr Fischer , Juho Hirvonen , Barbara Keller , Tuomo Lempiäinen , Joel Rybicki , Jukka Suomela , Jara Uitto

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

In this work, we study the Lov\'asz local lemma (LLL) problem in the area of distributed quantum computing, which has been the focus of attention of recent advances in quantum computing [STOC'24, STOC'25, STOC'25]. We prove a lower bound of…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-20 Sebastian Brandt , Tim Göttlicher

Suppose a language $L$ can be decided by a bounded-error randomized algorithm that runs in space $S$ and time $n \cdot \text{poly}(S)$. We give a randomized algorithm for $L$ that still runs in space $O(S)$ and time $n \cdot \text{poly}(S)$…

Computational Complexity · Computer Science 2019-05-17 William M. Hoza

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

In this paper, we apply the Clique Lov\'asz Local Lemma to provide sufficient conditions on memory and lifting degree for removing certain harmful combinatorial structures in spatially-coupled (SC) codes that negatively impact decoding…

Information Theory · Computer Science 2025-09-23 Lei Huang

One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-16 Sameep Dahal , Francesco d'Amore , Henrik Lievonen , Timothé Picavet , Jukka Suomela

Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…

Computational Complexity · Computer Science 2024-07-11 Venkatesan Guruswami , Jonathan Mosheiff

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

Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…

Statistics Theory · Mathematics 2025-08-05 Qin Lu , Yaakov Bar-Shalom , Peter Willett