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Local Problems in Trees Across a Wide Range of Distributed Models

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

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Author Details

Anubhav Dhar
  • Aalto University, Espoo, Finland
  • Indian Institute of Technology Kharagpur, India
Eli Kujawa
  • Aalto University, Espoo, Finland
  • University of Illinois Urbana-Champaign, IL, USA
Henrik Lievonen
  • Aalto University, Espoo, Finland
Augusto Modanese
  • Aalto University, Espoo, Finland
Mikail Muftuoglu
  • Aalto University, Espoo, Finland
Jan Studený
  • Aalto University, Espoo, Finland
Jukka Suomela
  • Aalto University, Espoo, Finland

Funding

This work was supported in part by the Research Council of Finland, Grants 333837 and 359104, the Aalto Science Institute (AScI), and the Helsinki Institute for Information Technology (HIIT).

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Anubhav Dhar, Eli Kujawa, Henrik Lievonen, Augusto Modanese, Mikail Muftuoglu, Jan Studený, and Jukka Suomela. Local Problems in Trees Across a Wide Range of Distributed Models. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.27

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
Keywords
  • Distributed algorithms
  • quantum-LOCAL model
  • randomized online-LOCAL model
  • locally checkable labeling problems
  • trees

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References

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