Work

Moser–Tardos Algorithm with small number of random bits

Year: 2026

Type: article

Abstract: 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 of 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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1815

Authors: Endre Csóka, Łukasz Grabowski, András Máthé, Oleg Pikhurko, Konstantinos Tyros

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Leipzig University, University of Warwick, National and Kapodistrian University of Athens

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Leverhulme Trust, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, National Research, Development and Innovation Office

Awards: G1046297303, G4053845998, G417675732, G4475798705