Efficient CONGEST Algorithms for the Lovász Local Lemma.

Yannic Maus; Jara Uitto

doi:10.4230/LIPICS.DISC.2021.31

Efficient CONGEST Algorithms for the Lovász Local Lemma.

Research output: Contribution to conference › Paper › peer-review

Abstract

We present a poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhoň and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhoň [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.

Original language	English
Pages	31:1-31:19
DOIs	https://doi.org/10.4230/LIPICS.DISC.2021.31
Publication status	Published - 1 Oct 2021
Externally published	Yes
Event	35th International Symposium on Distributed Computing: DISC 2021 - Virtual, Freiburg, Germany Duration: 4 Oct 2021 → 8 Oct 2021

Conference

Conference	35th International Symposium on Distributed Computing
Country/Territory	Germany
City	Virtual, Freiburg
Period	4/10/21 → 8/10/21

Keywords

CONGEST
Distributed graph algorithms
Locally checkable labelings
Lovász Local Lemma

ASJC Scopus subject areas

Software

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10.4230/LIPICS.DISC.2021.31Licence: CC BY 4.0

https://dblp.org/rec/conf/wdag/MausU21

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title = "Efficient CONGEST Algorithms for the Lov{\'a}sz Local Lemma.",

abstract = "We present a poly log log n time randomized CONGEST algorithm for a natural class of Lov{\'a}sz Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozho{\v n} and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozho{\v n} [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.",

keywords = "CONGEST, Distributed graph algorithms, Locally checkable labelings, Lov{\'a}sz Local Lemma",

author = "Yannic Maus and Jara Uitto",

year = "2021",

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doi = "10.4230/LIPICS.DISC.2021.31",

language = "English",

pages = "31:1--31:19",

note = "35th International Symposium on Distributed Computing : DISC 2021 ; Conference date: 04-10-2021 Through 08-10-2021",

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AU - Maus, Yannic

AU - Uitto, Jara

PY - 2021/10/1

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N2 - We present a poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhoň and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhoň [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.

AB - We present a poly log log n time randomized CONGEST algorithm for a natural class of Lovász Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized complexity between Ω(log n) and poly log log n. Furthermore, we provide extensions to the network decomposition algorithms given in the recent breakthrough by Rozhoň and Ghaffari [STOC2020] and the follow up by Ghaffari, Grunau, and Rozhoň [SODA2021]. In particular, we show how to obtain a large distance separated weak network decomposition with a negligible dependency on the range of unique identifiers.

KW - CONGEST

KW - Distributed graph algorithms

KW - Locally checkable labelings

KW - Lovász Local Lemma

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DO - 10.4230/LIPICS.DISC.2021.31

M3 - Paper

SP - 31:1-31:19

T2 - 35th International Symposium on Distributed Computing

Y2 - 4 October 2021 through 8 October 2021

ER -

Efficient CONGEST Algorithms for the Lovász Local Lemma.

Abstract

Conference

Keywords

ASJC Scopus subject areas

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