---
_id: '10072'
abstract:
- lang: eng
text: 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 and 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
existence of and fast convergence to desirable objects, one may naturally ask
further questions regarding properties of these algorithms. For instance, "are
they parallelizable?", "how many solutions can they output?", "what is the expected
"weight" of a solution?", etc. 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.
acknowledgement: "Fotis Iliopoulos: This material is based upon work directly supported
by the IAS Fund for Math and indirectly supported by the National Science Foundation
Grant No. CCF-1900460. Any opinions, findings and conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily reflect
the views of the National Science Foundation. This work is also supported by the
National Science Foundation Grant No. CCF-1815328.\r\nVladimir Kolmogorov: Supported
by the European Research Council under the European Unions Seventh Framework Programme
(FP7/2007-2013)/ERC grant agreement no 616160."
alternative_title:
- LIPIcs
article_number: '31'
article_processing_charge: Yes
arxiv: 1
author:
- first_name: David G.
full_name: Harris, David G.
last_name: Harris
- first_name: Fotis
full_name: Iliopoulos, Fotis
last_name: Iliopoulos
- first_name: Vladimir
full_name: Kolmogorov, Vladimir
id: 3D50B0BA-F248-11E8-B48F-1D18A9856A87
last_name: Kolmogorov
citation:
ama: 'Harris DG, Iliopoulos F, Kolmogorov V. A new notion of commutativity for the
algorithmic Lovász Local Lemma. In: Approximation, Randomization, and Combinatorial
Optimization. Algorithms and Techniques. Vol 207. Schloss Dagstuhl - Leibniz
Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31'
apa: 'Harris, D. G., Iliopoulos, F., & Kolmogorov, V. (2021). A new notion of
commutativity for the algorithmic Lovász Local Lemma. In Approximation, Randomization,
and Combinatorial Optimization. Algorithms and Techniques (Vol. 207). Virtual:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31'
chicago: Harris, David G., Fotis Iliopoulos, and Vladimir Kolmogorov. “A New Notion
of Commutativity for the Algorithmic Lovász Local Lemma.” In Approximation,
Randomization, and Combinatorial Optimization. Algorithms and Techniques,
Vol. 207. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.31.
ieee: D. G. Harris, F. Iliopoulos, and V. Kolmogorov, “A new notion of commutativity
for the algorithmic Lovász Local Lemma,” in Approximation, Randomization, and
Combinatorial Optimization. Algorithms and Techniques, Virtual, 2021, vol.
207.
ista: 'Harris DG, Iliopoulos F, Kolmogorov V. 2021. A new notion of commutativity
for the algorithmic Lovász Local Lemma. Approximation, Randomization, and Combinatorial
Optimization. Algorithms and Techniques. APPROX/RANDOM: Approximation Algorithms
for Combinatorial Optimization Problems/ Randomization and Computation, LIPIcs,
vol. 207, 31.'
mla: Harris, David G., et al. “A New Notion of Commutativity for the Algorithmic
Lovász Local Lemma.” Approximation, Randomization, and Combinatorial Optimization.
Algorithms and Techniques, vol. 207, 31, Schloss Dagstuhl - Leibniz Zentrum
für Informatik, 2021, doi:10.4230/LIPIcs.APPROX/RANDOM.2021.31.
short: D.G. Harris, F. Iliopoulos, V. Kolmogorov, in:, Approximation, Randomization,
and Combinatorial Optimization. Algorithms and Techniques, Schloss Dagstuhl -
Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-08-18
location: Virtual
name: 'APPROX/RANDOM: Approximation Algorithms for Combinatorial Optimization Problems/
Randomization and Computation'
start_date: 2021-08-16
date_created: 2021-10-03T22:01:22Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2022-03-18T10:08:25Z
day: '15'
ddc:
- '000'
department:
- _id: VlKo
doi: 10.4230/LIPIcs.APPROX/RANDOM.2021.31
ec_funded: 1
external_id:
arxiv:
- '2008.05569'
file:
- access_level: open_access
checksum: 9d2544d53aa5b01565c6891d97a4d765
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-06T13:51:54Z
date_updated: 2021-10-06T13:51:54Z
file_id: '10098'
file_name: 2021_LIPIcs_Harris.pdf
file_size: 804472
relation: main_file
success: 1
file_date_updated: 2021-10-06T13:51:54Z
has_accepted_license: '1'
intvolume: ' 207'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 25FBA906-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '616160'
name: 'Discrete Optimization in Computer Vision: Theory and Practice'
publication: Approximation, Randomization, and Combinatorial Optimization. Algorithms
and Techniques
publication_identifier:
isbn:
- 978-3-9597-7207-5
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A new notion of commutativity for the algorithmic Lovász Local Lemma
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 207
year: '2021'
...