Locally Checkable Labelings with Small Messages

Alkida Balliu; Keren Censor-Hillel; Yannic Maus; Dennis Olivetti; Jukka Suomela

doi:10.4230/LIPICS.DISC.2021.8

Locally Checkable Labelings with Small Messages

Alkida Balliu, Keren Censor-Hillel, Yannic Maus, Dennis Olivetti, Jukka Suomela

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

Abstract

A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω( n ¹/ ²) rounds in the CONGEST model.

Original language	English
Pages	8:1-8:18
DOIs	https://doi.org/10.4230/LIPICS.DISC.2021.8
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

ASJC Scopus subject areas

Software

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10.4230/LIPICS.DISC.2021.8Licence: CC BY 4.0

https://dblp.org/rec/conf/wdag/BalliuCMOS21

Cite this

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title = "Locally Checkable Labelings with Small Messages",

abstract = "A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω( n 1/ 2) rounds in the CONGEST model. ",

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author = "Alkida Balliu and Keren Censor-Hillel and Yannic Maus and Dennis Olivetti and Jukka Suomela",

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doi = "10.4230/LIPICS.DISC.2021.8",

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

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TY - CONF

T1 - Locally Checkable Labelings with Small Messages

AU - Balliu, Alkida

AU - Censor-Hillel, Keren

AU - Maus, Yannic

AU - Olivetti, Dennis

AU - Suomela, Jukka

PY - 2021/10/1

Y1 - 2021/10/1

N2 - A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω( n 1/ 2) rounds in the CONGEST model.

AB - A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω( n 1/ 2) rounds in the CONGEST model.

KW - CONGEST

KW - Distributed graph algorithms

KW - Locally checkable labelings

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U2 - 10.4230/LIPICS.DISC.2021.8

DO - 10.4230/LIPICS.DISC.2021.8

M3 - Paper

SP - 8:1-8:18

T2 - 35th International Symposium on Distributed Computing

Y2 - 4 October 2021 through 8 October 2021

ER -

Locally Checkable Labelings with Small Messages

Abstract

Conference

Keywords

ASJC Scopus subject areas

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