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Brief Announcement: Decreasing Verification Radius in Local Certification

Authors Jan Matyáš Křišťan , Josef Erik Sedláček

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Local certification
  • locally checkable proofs
  • proof-labeling schemes
  • graphs
  • distributed computing

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Abstract

This paper deals with local certification, specifically locally checkable proofs: given a graph property, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done locally without the knowledge of the whole graph.
We examine the trade-off between the visibility radius and the size of certificates. We describe a procedure that decreases the radius by encoding the neighbourhood of each vertex into its certificate. We also provide a corresponding lower bound on the required certificate size increase, showing that such an approach is close to optimal.

Cite As Get BibTex

Jan Matyáš Křišťan and Josef Erik Sedláček. Brief Announcement: Decreasing Verification Radius in Local Certification. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 49:1-49:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.49

Author Details

Jan Matyáš Křišťan
  • Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Josef Erik Sedláček
  • Faculty of Information Technology, Czech Technical University in Prague, Czech Republic

Funding

This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS23/205/OHK3/3T/18 and by the Czech Science Foundation Grant no. 24-12046S.

Acknowledgements

We would like to thank Laurent Feuilloley for his helpful discussions and suggestions.

References

  1. Laurent Feuilloley. Introduction to local certification. Discrete Mathematics & Theoretical Computer Science, 23(Distributed Computing and Networking), 2021. URL: https://doi.org/10.46298/dmtcs.6280.
  2. Laurent Feuilloley, Pierre Fraigniaud, Juho Hirvonen, Ami Paz, and Mor Perry. Redundancy in distributed proofs. Distributed Comput., 34(2):113-132, 2021. URL: https://doi.org/10.1007/S00446-020-00386-Z.
  3. Orr Fischer, Rotem Oshman, and Dana Shamir. Explicit space-time tradeoffs for proof labeling schemes in graphs with small separators. In Quentin Bramas, Vincent Gramoli, and Alessia Milani, editors, 25th International Conference on Principles of Distributed Systems (OPODIS 2021), volume 217 of LIPIcs, pages 21:1-21:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2021.21.
  4. Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12(1):1-33, 2016. URL: https://doi.org/10.4086/toc.2016.v012a019.
  5. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Comput., 22(4):215-233, 2010. URL: https://doi.org/10.1007/S00446-010-0095-3.
  6. David Peleg. Distributed computing: a locality-sensitive approach. SIAM, 2000. URL: https://doi.org/10.1137/1.9780898719772.
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