Document Open Access Logo

Brief Announcement: Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL

Authors Francesco d'Amore , Henrik Lievonen

PDF

File

Thumbnail PDF
PDF
LIPIcs.DISC.2026.59.pdf
  • Filesize: 0.58 MB
  • 7 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • Distributed graph algorithms
  • LOCAL model
  • quantum-LOCAL
  • finitely-dependent distributions
  • locally checkable labeling problems

Metrics

Abstract

We show that, on trees, any locally checkable labeling problem (LCL) Π that can be solved by an n^o(1)-dependent distribution can also be solved by an O(log n)-round deterministic LOCAL algorithm. The result is obtained through a rake-and-compress-style decomposition of the input tree, and local simulations of the bounded dependent distribution on the components of the decomposition. As a corollary to our result, any LCL problem on trees can either be solved by an O(log n) deterministic LOCAL algorithm, or requires n^Ω(1) rounds to solve by a quantum-LOCAL algorithm.

Cite As Get BibTex

Francesco d'Amore and Henrik Lievonen. Brief Announcement: Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 59:1-59:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.59

Author Details

Francesco d'Amore
  • Gran Sasso Science Institute, L'Aquila, Italy
Henrik Lievonen
  • Aalto University, Espoo, Finland
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

Funding

This work was supported in part by the Research Council of Finland, Grants 363558. Most of this work was done while Henrik Lievonen was affiliated with Aalto University. Francesco d’Amore was supported by Decreto MUR n. 47/2025, CUP D13C25000750001.

References

  1. Amirreza Akbari, Xavier Coiteux-Roy, Francesco D'Amore, François Le Gall, Henrik Lievonen, Darya Melnyk, Augusto Modanese, Shreyas Pai, Marc-Olivier Renou, Václav Rozhon, and Jukka Suomela. Online locality meets distributed quantum computing. In Michal Koucký and Nikhil Bansal, editors, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, STOC 2025, Prague, Czechia, June 23-27, 2025, pages 1295-1306. ACM, 2025. URL: https://doi.org/10.1145/3717823.3718211.
  2. Alkida Balliu, Sebastian Brandt, Xavier Coiteux-Roy, Francesco D'Amore, Massimo Equi, François Le Gall, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, Marc-Olivier Renou, Jukka Suomela, Lucas Tendick, and Isadora Veeren. Distributed quantum advantage for local problems. In Michal Koucký and Nikhil Bansal, editors, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, STOC 2025, Prague, Czechia, June 23-27, 2025, pages 451-462. ACM, 2025. URL: https://doi.org/10.1145/3717823.3718233.
  3. Alkida Balliu, Filippo Casagrande, Francesco d'Amore, Massimo Equi, Barbara Keller, Henrik Lievonen, Dennis Olivetti, Gustav Schmid, and Jukka Suomela. Distributed quantum advantage in locally checkable labeling problems. In Kasper Green Larsen and Barna Saha, editors, Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026, Vancouver, BC, Canada, January 11-14, 2026, pages 1268-1308. SIAM, 2026. URL: https://doi.org/10.1137/1.9781611978971.49.
  4. Alkida Balliu, Keren Censor-Hillel, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Locally checkable labelings with small messages. In Seth Gilbert, editor, 35th International Symposium on Distributed Computing, DISC 2021, October 4-8, 2021, Freiburg, Germany (Virtual Conference), volume 209 of LIPIcs, pages 8:1-8:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.DISC.2021.8.
  5. Alkida Balliu, Corinna Coupette, Antonio Cruciani, Francesco D'Amore, Massimo Equi, Henrik Lievonen, Augusto Modanese, Dennis Olivetti, and Jukka Suomela. New limits on distributed quantum advantage: Dequantizing linear programs. In Dariusz R. Kowalski, editor, 39th International Symposium on Distributed Computing, DISC 2025, October 27-31, 2025, Berlin, Germany, volume 356 of LIPIcs, pages 11:1-11:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. URL: https://doi.org/10.4230/LIPIcs.DISC.2025.11.
  6. Yi-Jun Chang. The complexity landscape of distributed locally checkable problems on trees. In Hagit Attiya, editor, 34th International Symposium on Distributed Computing, DISC 2020, October 12-16, 2020, Virtual Conference, volume 179 of LIPIcs, pages 18:1-18:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.DISC.2020.18.
  7. Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the LOCAL model. SIAM Journal on Computing, 48(1):122-143, 2019. URL: https://doi.org/10.1137/17M1117537.
  8. Yi-Jun Chang and Seth Pettie. A time hierarchy theorem for the LOCAL model. SIAM Journal on Computing, 48(1):33-69, 2019. URL: https://doi.org/10.1137/17M1157957.
  9. 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 Silvia Bonomi, Letterio Galletta, Etienne Rivière, and Valerio Schiavoni, editors, 28th International Conference on Principles of Distributed Systems, OPODIS 2024, December 11-13, 2024, Lucca, Italy, volume 324 of LIPIcs, pages 27:1-27:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2024.27.
  10. François Le Gall, Harumichi Nishimura, and Ansis Rosmanis. Quantum advantage for the LOCAL model in distributed computing. In Rolf Niedermeier and Christophe Paul, editors, 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019, March 13-16, 2019, Berlin, Germany, volume 126 of LIPIcs, pages 49:1-49:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.STACS.2019.49.
  11. Moni Naor and Larry J. Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995. URL: https://doi.org/10.1137/S0097539793254571.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact