Related papers: Deterministic Algorithms for the Lovasz Local Lemm…

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…

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…

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…

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…

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…

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…

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…

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)…

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…

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.…

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…

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…

The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems known where it provides an asymptotically tight answer. The main theme of our paper is to…

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…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by…

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~$n$…

Load balancing is among the basic primitives in distributed computing. In this paper, we consider this problem when executed locally on a network with nodes prone to failures. We show that there exist lightweight network topologies that are…

We illustrate the use of probability theory in existential proofs, focusing on the Lov\'asz Local Lemma. This result gives a lower bound for the probability of avoiding a suitable finite collection of events. We describe some applications…

We give new algorithms based on Markov chains to sample and approximately count satisfying assignments to $k$-uniform CNF formulas where each variable appears at most $d$ times. For any $k$ and $d$ satisfying $kd<n^{o(1)}$ and $k\ge 20\log…