2026-07-23T08:46:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14724 2024-03-06T10:54:45Z ddc:004 open_access

A New Notion of Commutativity for the Algorithmic Lovász Local Lemma Harris, David G. Iliopoulos, Fotis Kolmogorov, Vladimir Lovász Local Lemma Resampling Moser-Tardos algorithm latin transversal commutativity The Lovász Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser & Tardos and follow-up works revealed that the LLL has intimate connections with a class of stochastic local search algorithms for finding such desirable objects. In particular, it can be seen as a sufficient condition for this type of algorithms to converge fast. Besides conditions for convergence, many other natural questions can be asked about algorithms; for instance, "are they parallelizable?", "how many solutions can they output?", "what is the expected "weight" of a solution?". These questions and more have been answered for a class of LLL-inspired algorithms called commutative. In this paper we introduce a new, very natural and more general notion of commutativity (essentially matrix commutativity) which allows us to show a number of new refined properties of LLL-inspired local search algorithms with significantly simpler proofs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David G. Harris and Fotis Iliopoulos and Vladimir Kolmogorov 2021 Is Part Of LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31 urn:nbn:de:0030-drops-147244 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.31 eng https://creativecommons.org/licenses/by/4.0/legalcode