Local problems in trees across a wide range of distributed models

Anubhav Dhar; Eli Kujawa; Henrik Lievonen; Augusto Modanese; Mikail Müftüoglu; Jan Studený; Jukka Suomela

doi:10.4230/LIPIcs.OPODIS.2024.27

Local problems in trees across a wide range of distributed models

Anubhav Dhar, Eli Kujawa, Henrik Lievonen, Augusto Modanese, Mikail Müftüoglu, Jan Studený, Jukka Suomela

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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Abstract

The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models:
- the classical LOCAL model of distributed graph algorithms,
- the quantum version of the LOCAL model,
- finitely dependent distributions [e.g. Holroyd 2016],
- any model that does not violate physical causality [Gavoille, Kosowski, Markiewicz, DISC 2009],
- the SLOCAL model [Ghaffari, Kuhn, Maus, STOC 2017], and
- the dynamic-LOCAL and online-LOCAL models [Akbari et al., ICALP 2023].
In general, the online-LOCAL model can be much stronger than the LOCAL model. For example, there are locally checkable labeling problems (LCLs) that can be solved with logarithmic locality in the online-LOCAL model but that require polynomial locality in the LOCAL model.

However, in this work we show that in trees, many classes of LCL problems have the same locality in deterministic LOCAL and randomized online-LOCAL (and as a corollary across all the above-mentioned models). In particular, these classes of problems do not admit any distributed quantum advantage.

We present a near-complete classification for the case of rooted regular trees. We also fully classify the super-logarithmic region in unrooted regular trees. Finally, we show that in general trees (rooted or unrooted, possibly irregular, possibly with input labels) problems that are global in deterministic LOCAL remain global also in the randomized online-LOCAL model.

Original language	English
Title of host publication	28th International Conference on Principles of Distributed Systems (OPODIS 2024)
Editors	Silvia Bonomi, Letterio Galletta, Etienne Rivière, Valerio Schiavoni
Publisher	Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages	1-17
Number of pages	17
ISBN (Electronic)	978-3-95977-360-7
DOIs	https://doi.org/10.4230/LIPIcs.OPODIS.2024.27
Publication status	Published - 8 Jan 2025
MoE publication type	A4 Conference publication
Event	International Conference on Principles of Distributed Systems - IMT School for Advanced Studies Lucca, Lucca, Italy Duration: 11 Dec 2024 → 13 Dec 2024 https://opodis2024.imtlucca.it/

Publication series

Name	Leibniz International Proceedings in Informatics (LIPIcs)
Publisher	Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Volume	324
ISSN (Electronic)	1868-8969

Conference

Conference	International Conference on Principles of Distributed Systems
Abbreviated title	OPODIS
Country/Territory	Italy
City	Lucca
Period	11/12/2024 → 13/12/2024
Internet address	https://opodis2024.imtlucca.it/

Keywords

distributed algorithms
locally checkable labeling problems
quantum-LOCAL model
randomized online-LOCAL model
trees

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10.4230/LIPIcs.OPODIS.2024.27Licence: CC BY

Local Problems in Trees Across a Wide Range of Distributed ModelsFinal published version, 1.14 MBLicence: CC BY

Cite this

Dhar, A., Kujawa, E., Lievonen, H., Modanese, A., Müftüoglu, M., Studený, J., & Suomela, J. (2025). Local problems in trees across a wide range of distributed models. In S. Bonomi, L. Galletta, E. Rivière, & V. Schiavoni (Eds.), 28th International Conference on Principles of Distributed Systems (OPODIS 2024) (pp. 1-17). Article 27 (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 324). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.OPODIS.2024.27

Dhar, Anubhav ; Kujawa, Eli ; Lievonen, Henrik et al. / Local problems in trees across a wide range of distributed models. 28th International Conference on Principles of Distributed Systems (OPODIS 2024). editor / Silvia Bonomi ; Letterio Galletta ; Etienne Rivière ; Valerio Schiavoni. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. pp. 1-17 (Leibniz International Proceedings in Informatics (LIPIcs)).

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title = "Local problems in trees across a wide range of distributed models",

abstract = "The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models:- the classical LOCAL model of distributed graph algorithms,- the quantum version of the LOCAL model,- finitely dependent distributions [e.g. Holroyd 2016],- any model that does not violate physical causality [Gavoille, Kosowski, Markiewicz, DISC 2009],- the SLOCAL model [Ghaffari, Kuhn, Maus, STOC 2017], and- the dynamic-LOCAL and online-LOCAL models [Akbari et al., ICALP 2023].In general, the online-LOCAL model can be much stronger than the LOCAL model. For example, there are locally checkable labeling problems (LCLs) that can be solved with logarithmic locality in the online-LOCAL model but that require polynomial locality in the LOCAL model.However, in this work we show that in trees, many classes of LCL problems have the same locality in deterministic LOCAL and randomized online-LOCAL (and as a corollary across all the above-mentioned models). In particular, these classes of problems do not admit any distributed quantum advantage.We present a near-complete classification for the case of rooted regular trees. We also fully classify the super-logarithmic region in unrooted regular trees. Finally, we show that in general trees (rooted or unrooted, possibly irregular, possibly with input labels) problems that are global in deterministic LOCAL remain global also in the randomized online-LOCAL model.",

keywords = "distributed algorithms, locally checkable labeling problems, quantum-LOCAL model, randomized online-LOCAL model, trees",

author = "Anubhav Dhar and Eli Kujawa and Henrik Lievonen and Augusto Modanese and Mikail M{\"u}ft{\"u}oglu and Jan Studen{\'y} and Jukka Suomela",

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booktitle = "28th International Conference on Principles of Distributed Systems (OPODIS 2024)",

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Dhar, A, Kujawa, E, Lievonen, H , Modanese, A, Müftüoglu, M, Studený, J & Suomela, J 2025, Local problems in trees across a wide range of distributed models. in S Bonomi, L Galletta, E Rivière & V Schiavoni (eds), 28th International Conference on Principles of Distributed Systems (OPODIS 2024)., 27, Leibniz International Proceedings in Informatics (LIPIcs), vol. 324, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, pp. 1-17, International Conference on Principles of Distributed Systems, Lucca, Italy, 11/12/2024. https://doi.org/10.4230/LIPIcs.OPODIS.2024.27

Local problems in trees across a wide range of distributed models. / Dhar, Anubhav; Kujawa, Eli; Lievonen, Henrik et al.
28th International Conference on Principles of Distributed Systems (OPODIS 2024). ed. / Silvia Bonomi; Letterio Galletta; Etienne Rivière; Valerio Schiavoni. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. p. 1-17 27 (Leibniz International Proceedings in Informatics (LIPIcs); Vol. 324).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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AU - Suomela, Jukka

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N2 - The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models:- the classical LOCAL model of distributed graph algorithms,- the quantum version of the LOCAL model,- finitely dependent distributions [e.g. Holroyd 2016],- any model that does not violate physical causality [Gavoille, Kosowski, Markiewicz, DISC 2009],- the SLOCAL model [Ghaffari, Kuhn, Maus, STOC 2017], and- the dynamic-LOCAL and online-LOCAL models [Akbari et al., ICALP 2023].In general, the online-LOCAL model can be much stronger than the LOCAL model. For example, there are locally checkable labeling problems (LCLs) that can be solved with logarithmic locality in the online-LOCAL model but that require polynomial locality in the LOCAL model.However, in this work we show that in trees, many classes of LCL problems have the same locality in deterministic LOCAL and randomized online-LOCAL (and as a corollary across all the above-mentioned models). In particular, these classes of problems do not admit any distributed quantum advantage.We present a near-complete classification for the case of rooted regular trees. We also fully classify the super-logarithmic region in unrooted regular trees. Finally, we show that in general trees (rooted or unrooted, possibly irregular, possibly with input labels) problems that are global in deterministic LOCAL remain global also in the randomized online-LOCAL model.

AB - The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models:- the classical LOCAL model of distributed graph algorithms,- the quantum version of the LOCAL model,- finitely dependent distributions [e.g. Holroyd 2016],- any model that does not violate physical causality [Gavoille, Kosowski, Markiewicz, DISC 2009],- the SLOCAL model [Ghaffari, Kuhn, Maus, STOC 2017], and- the dynamic-LOCAL and online-LOCAL models [Akbari et al., ICALP 2023].In general, the online-LOCAL model can be much stronger than the LOCAL model. For example, there are locally checkable labeling problems (LCLs) that can be solved with logarithmic locality in the online-LOCAL model but that require polynomial locality in the LOCAL model.However, in this work we show that in trees, many classes of LCL problems have the same locality in deterministic LOCAL and randomized online-LOCAL (and as a corollary across all the above-mentioned models). In particular, these classes of problems do not admit any distributed quantum advantage.We present a near-complete classification for the case of rooted regular trees. We also fully classify the super-logarithmic region in unrooted regular trees. Finally, we show that in general trees (rooted or unrooted, possibly irregular, possibly with input labels) problems that are global in deterministic LOCAL remain global also in the randomized online-LOCAL model.

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Dhar A, Kujawa E, Lievonen H , Modanese A, Müftüoglu M, Studený J et al. Local problems in trees across a wide range of distributed models. In Bonomi S, Galletta L, Rivière E, Schiavoni V, editors, 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. 2025. p. 1-17. 27. (Leibniz International Proceedings in Informatics (LIPIcs)). doi: 10.4230/LIPIcs.OPODIS.2024.27

Local problems in trees across a wide range of distributed models

Abstract

Publication series

Conference

Keywords

Access to Document

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Limits of Causal Comp/Suomela: Limits of Causal Computation

LocalMend /Suomela: Local Checking, Solving, and MendingNew Perspectives of Distributed Computing (LocalMend)

Cite this

Local problems in trees across a wide range of distributed models

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Limits of Causal Comp/Suomela: Limits of Causal Computation

LocalMend /Suomela: Local Checking, Solving, and MendingNew Perspectives of Distributed Computing (LocalMend)

Cite this

LocalMend /Suomela: Local Checking, Solving, and MendingNew Perspectives of Distributed Computing (LocalMend)