DeepAI AI Chat
Log In Sign Up

Local Computation Algorithms for the Lovász Local Lemma

by   Dimitris Achlioptas, et al.
berkeley college

We consider the task of designing Local Computation Algorithms (LCA) for applications of the Lovász Local Lemma (LLL). LCA is a class of sublinear algorithms proposed by Rubinfeld et al. that have received a lot of attention in recent years. The LLL is an existential, sufficient condition for a collection of sets to have non-empty intersection (in applications, often, each set comprises all objects having a certain property). The ground-breaking algorithm of Moser and Tardos made the LLL fully constructive, following earlier works by Beck and Alon giving algorithms under significantly stronger LLL-like conditions. LCAs under those stronger conditions were given in the paper of Rubinfeld et al. and later work by Alon et al., where it was asked if the Moser-Tardos algorithm can be used to design LCAs under the standard LLL condition. The main contribution of this paper is to answer this question affirmatively. In fact, our techniques yields LCAs for settings beyond the standard LLL condition.


page 1

page 2

page 3

page 4


Local planar domination revisited

We show how to compute a 20-approximation of a minimum dominating set in...

On a conjecture about a class of permutation quadrinomials

Very recently, Tu et al. presented a sufficient condition about (a_1,a_2...

A Stronger Impossibility for Fully Online Matching

We revisit the fully online matching model (Huang et al., J. ACM, 2020),...

Differentially-Private Sublinear-Time Clustering

Clustering is an essential primitive in unsupervised machine learning. W...

A Euclidean Distance Matrix Model for Convex Clustering

Clustering has been one of the most basic and essential problems in unsu...

Near-separable Non-negative Matrix Factorization with ℓ_1- and Bregman Loss Functions

Recently, a family of tractable NMF algorithms have been proposed under ...

Neural network identifiability for a family of sigmoidal nonlinearities

This paper addresses the following question of neural network identifiab...