Moser-Tardos Algorithm with small number of random bits

Fuente: arXiv
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Main Authors: Csóka, Endre, Grabowski, Łukasz, Máthé, András, Pikhurko, Oleg, Tyros, Konstantinos
Format: Preprint
Published: 2022
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author Csóka, Endre
Grabowski, Łukasz
Máthé, András
Pikhurko, Oleg
Tyros, Konstantinos
author_facet Csóka, Endre
Grabowski, Łukasz
Máthé, András
Pikhurko, Oleg
Tyros, Konstantinos
contents 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 is constant; in particular, it is independent from the number of variables. This is achieved by using the same random bits to resample variables which are far enough in the dependency graph. There are two corollaries. First, we obtain a deterministic algorithm for finding a satisfying assignment, which for any class of problems as in the previous paragraph runs in time O(n), where n is the number of variables. Second, we present a Borel version of the Lovász Local Lemma.
format Preprint
id arxiv_https___arxiv_org_abs_2203_05888
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Moser-Tardos Algorithm with small number of random bits
Csóka, Endre
Grabowski, Łukasz
Máthé, András
Pikhurko, Oleg
Tyros, Konstantinos
Combinatorics
Distributed, Parallel, and Cluster Computing
Data Structures and Algorithms
Logic
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 is constant; in particular, it is independent from the number of variables. This is achieved by using the same random bits to resample variables which are far enough in the dependency graph. There are two corollaries. First, we obtain a deterministic algorithm for finding a satisfying assignment, which for any class of problems as in the previous paragraph runs in time O(n), where n is the number of variables. Second, we present a Borel version of the Lovász Local Lemma.
title Moser-Tardos Algorithm with small number of random bits
topic Combinatorics
Distributed, Parallel, and Cluster Computing
Data Structures and Algorithms
Logic
url https://arxiv.org/abs/2203.05888