Related papers: Dynamic Construction of the Lov\'asz Local Lemma

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…

High order momentum-based parameter update algorithms have seen widespread applications in training machine learning models. Recently, connections with variational approaches have led to the derivation of new learning algorithms with…

The Lov\'{a}sz Local Lemma (LLL) is a probabilistic tool which shows that, if a collection of "bad" events $\mathcal B$ in a probability space are not too likely and not too interdependent, then there is a positive probability that no…

We study and further develop powerful general-purpose schemes to maintain random assignments under adversarial dynamic changes. The goal is to maintain assignments that are (approximately) distributed similarly as a completely fresh…

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…

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…

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…

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…

Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…

In the framework of the probabilistic method in combinatorics, we revisit the entropy compression method clarifying the setting in which it can be applied and providing a theorem yielding a general constructive criterion. We finally…

We present polynomial-time algorithms for approximate counting and sampling solutions to constraint satisfaction problems (CSPs) with atomic constraints within the local lemma regime: $$ pD^{2+o_q(1)}\lesssim 1. $$ When the domain size $q$…

We study distributed adaptive algorithms with local updates (intermittent communication). Despite the great empirical success of adaptive methods in distributed training of modern machine learning models, the theoretical benefits of local…

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…

While overparameterization in machine learning models offers great benefits in terms of optimization and generalization, it also leads to increased computational requirements as model sizes grow. In this work, we show that by leveraging the…

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any…

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…

This paper introduces a new step to the Direct Search Method (DSM) to strengthen its convergence analysis. By design, this so-called covering step may ensure that for all refined points of the sequence of incumbent solutions generated by…

Optimization methods that make use of derivatives of the objective function up to order $p > 2$ are called tensor methods. Among them, ones that minimize a regularized $p$th-order Taylor expansion at each step have been shown to possess…

Let $\Phi = (V, \mathcal{C})$ be a constraint satisfaction problem on variables $v_1,\dots, v_n$ such that each constraint depends on at most $k$ variables and such that each variable assumes values in an alphabet of size at most $[q]$.…

We reveal a connection between the incompressibility method and the Lovasz local lemma in the context of Ramsey theory. We obtain bounds by repeatedly encoding objects of interest and thereby compressing strings. The method is demonstrated…