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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.31
URN: urn:nbn:de:0030-drops-147244
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14724/
Harris, David G. ; Iliopoulos, Fotis ; Kolmogorov, Vladimir
A New Notion of Commutativity for the Algorithmic Lovász Local Lemma
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Abstract
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.
BibTeX - Entry
@InProceedings{harris_et_al:LIPIcs.APPROX/RANDOM.2021.31,
author = {Harris, David G. and Iliopoulos, Fotis and Kolmogorov, Vladimir},
title = {{A New Notion of Commutativity for the Algorithmic Lov\'{a}sz Local Lemma}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
pages = {31:1--31:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-207-5},
ISSN = {1868-8969},
year = {2021},
volume = {207},
editor = {Wootters, Mary and Sanit\`{a}, Laura},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14724},
URN = {urn:nbn:de:0030-drops-147244},
doi = {10.4230/LIPIcs.APPROX/RANDOM.2021.31},
annote = {Keywords: Lov\'{a}sz Local Lemma, Resampling, Moser-Tardos algorithm, latin transversal, commutativity}
}
| Keywords: | Lovász Local Lemma, Resampling, Moser-Tardos algorithm, latin transversal, commutativity | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 15.09.2021 |
