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Local Recurrent Problems in the SUPPORTED Model

Authors Akanksha Agrawal , John Augustine , David Peleg , Srikkanth Ramachandran

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Author Details

Akanksha Agrawal
  • Indian Institute of Technology Madras, India
John Augustine
  • Indian Institute of Technology Madras, India
David Peleg
  • Weizmann Institute of Science, Rehovot, Israel
Srikkanth Ramachandran
  • Indian Institute of Technology Madras, India

Funding

John Augustine and Srikkanth Ramachandran are supported by the Centre of Excellence in Cryptography, Cybersecurity, and Distributed Trust (CCD) and by an IITM-Accenture project (SB/22-23/007/JOHN/ACC).

Acknowledgements

David Peleg holds the Venky Harinarayanan and Anand Rajaraman (VHAR) Visiting Chair Professorship at IIT Madras. This work was carried out in part during mutual visits that were supported by the VHAR Visiting Chair funds.

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Akanksha Agrawal, John Augustine, David Peleg, and Srikkanth Ramachandran. Local Recurrent Problems in the SUPPORTED Model. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.OPODIS.2023.22

Abstract

We study the SUPPORTED model of distributed computing introduced by Schmid and Suomela [Schmid and Suomela, 2013], which generalizes the LOCAL and CONGEST models. In this framework, multiple instances of the same problem, differing from each other by the subnetwork to which they apply. recur over time, and need to be solved efficiently online. To do that, one may rely on an initial preprocessing phase for computing some useful information. This preprocessing phase makes it possible, in some cases, to obtain improved distributed algorithms, overcoming locality-based time lower bounds. Our main contribution is to expand the class of problems to which the SUPPORTED model applies, by handling also multiple recurring instances of the same problem that differ from each other by some problem specific input, and not only the subnetwork to which they apply. We illustrate this by considering two extended problem classes. The first class, denoted PCS, concerns problems where client nodes of the network need to be served, and each recurring instance applies to some Partial Client Set. The second class, denoted PFO, concerns situations where each recurrent instance of the problem includes a partially fixed output, which needs to be completed to a full consistent solution. Specifically, we propose some natural recurrent variants of the dominating set problem and the coloring problem that are of interest particularly in the distributed setting. For these problems, we show that information about the topology can be used to overcome locality-based lower bounds. We also categorize the round complexity of Locally Checkable Labellings in the SUPPORTED model for the simple case of paths. Finally we present some interesting open problems and some partial results towards resolving them.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed Algorithms
  • LOCAL Model
  • SUPPORTED Model

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References

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