Document Open Access Logo

Locally Checkable Labelings with Small Messages

Authors Alkida Balliu , Keren Censor-Hillel, Yannic Maus , Dennis Olivetti , Jukka Suomela

PDF
Thumbnail PDF

File

LIPIcs.DISC.2021.8.pdf
  • Filesize: 0.75 MB
  • 18 pages

Document Identifiers

Author Details

Alkida Balliu
  • Universität Freiburg, Germany
Keren Censor-Hillel
  • Technion, Haifa, Israel
Yannic Maus
  • Technion, Haifa, Israel
Dennis Olivetti
  • Universität Freiburg, Germany
Jukka Suomela
  • Aalto University, Finland

Funding

This project was partially supported by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 755839 (Keren Censor-Hillel, Yannic Maus).

Cite As Get BibTex

Alkida Balliu, Keren Censor-Hillel, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Locally Checkable Labelings with Small Messages. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.DISC.2021.8

Abstract

A rich line of work has been addressing the computational complexity of locally checkable labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study the landscape of LCL complexities under bandwidth restrictions. Our main results are twofold. First, we show that on trees, the CONGEST complexity of an LCL problem is asymptotically equal to its complexity in the LOCAL model. An analog statement for non-LCL problems is known to be false. Second, we show that for general graphs this equivalence does not hold, by providing an LCL problem for which we show that it can be solved in O(log n) rounds in the LOCAL model, but requires Ω̃(n^{1/2}) rounds in the CONGEST model.

Subject Classification

ACM Subject Classification
  • Networks → Network algorithms
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithms
  • CONGEST
  • locally checkable labelings

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Amir Abboud, Keren Censor-Hillel, and Seri Khoury. Near-linear lower bounds for distributed distance computations, even in sparse networks. In Proc. 30th International Symposium on Distributed Computing (DISC 2016), volume 9888 of Lecture Notes in Computer Science, pages 29-42. Springer, 2016. URL: https://doi.org/10.1007/978-3-662-53426-7_3.
  2. Nir Bachrach, Keren Censor-Hillel, Michal Dory, Yuval Efron, Dean Leitersdorf, and Ami Paz. Hardness of distributed optimization. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019), pages 238-247, 2019. URL: https://doi.org/10.1145/3293611.3331597.
  3. Alkida Balliu, Sebastian Brandt, Yi-Jun Chang, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. The distributed complexity of locally checkable problems on paths is decidable. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019), pages 262-271. ACM Press, 2019. URL: https://doi.org/10.1145/3293611.3331606.
  4. Alkida Balliu, Sebastian Brandt, Yuval Efron, Juho Hirvonen, Yannic Maus, Dennis Olivetti, and Jukka Suomela. Classification of distributed binary labeling problems. In Proc. 34th International Symposium on Distributed Computing (DISC 2020), volume 179 of LIPIcs, pages 17:1-17:17. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.DISC.2020.17.
  5. Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. Lower bounds for maximal matchings and maximal independent sets. In Proc. 60th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2019), pages 481-497. IEEE, 2019. URL: https://doi.org/10.1109/FOCS.2019.00037.
  6. Alkida Balliu, Sebastian Brandt, Fabian Kuhn, and Dennis Olivetti. Improved distributed lower bounds for MIS and bounded (out-)degree dominating sets in trees. In Proc. 40th ACM Symposium on Principles of Distributed Computing (PODC 2021). ACM Press, 2021. URL: https://doi.org/10.1145/3465084.3467901.
  7. Alkida Balliu, Sebastian Brandt, and Dennis Olivetti. Distributed lower bounds for ruling sets. In 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 365-376. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00042.
  8. Alkida Balliu, Sebastian Brandt, Dennis Olivetti, Jan Studený, Jukka Suomela, and Aleksandr Tereshchenko. Locally checkable problems in rooted trees. In Proc. 40th ACM Symposium on Principles of Distributed Computing (PODC 2021). ACM Press, 2021. URL: https://doi.org/10.1145/3465084.3467934.
  9. Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela. Almost global problems in the LOCAL model. Distributed Computing, 2020. URL: https://doi.org/10.1007/s00446-020-00375-2.
  10. Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela. How much does randomness help with locally checkable problems? In Proc. 39th ACM Symposium on Principles of Distributed Computing (PODC 2020), pages 299-308. ACM Press, 2020. URL: https://doi.org/10.1145/3382734.3405715.
  11. Alkida Balliu, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Dennis Olivetti, and Jukka Suomela. New classes of distributed time complexity. In Proc. 50th ACM Symposium on Theory of Computing (STOC 2018), pages 1307-1318. ACM Press, 2018. URL: https://doi.org/10.1145/3188745.3188860.
  12. Alkida Balliu, Juho Hirvonen, Dennis Olivetti, and Jukka Suomela. Hardness of minimal symmetry breaking in distributed computing. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019), pages 369-378. ACM Press, 2019. URL: https://doi.org/10.1145/3293611.3331605.
  13. Leonid Barenboim, Michael Elkin, and Cyril Gavoille. A fast network-decomposition algorithm and its applications to constant-time distributed computation. Theor. Comput. Sci., 751:2-23, 2018. URL: https://doi.org/10.1016/j.tcs.2016.07.005.
  14. Sebastian Brandt. An automatic speedup theorem for distributed problems. In Proc. 38th ACM Symposium on Principles of Distributed Computing (PODC 2019), pages 379-388. ACM, 2019. URL: https://doi.org/10.1145/3293611.3331611.
  15. Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela, and Jara Uitto. A lower bound for the distributed Lovász local lemma. In Proc. 48th ACM Symposium on Theory of Computing (STOC 2016), pages 479-488. ACM Press, 2016. URL: https://doi.org/10.1145/2897518.2897570.
  16. Sebastian Brandt, Jan Grebík, Christoph Grunau, and Václav Rozhoň. The landscape of distributed complexities on trees, 2021. Unpublished manuscript. Google Scholar
  17. Sebastian Brandt, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Patric R. J. Östergård, Christopher Purcell, Joel Rybicki, Jukka Suomela, and Przemysław Uznański. LCL problems on grids. In Proc. 36th ACM Symposium on Principles of Distributed Computing (PODC 2017), pages 101-110. ACM Press, 2017. URL: https://doi.org/10.1145/3087801.3087833.
  18. Keren Censor-Hillel and Michal Dory. Distributed spanner approximation. In Calvin Newport and Idit Keidar, editors, Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, July 23-27, 2018, pages 139-148. ACM, 2018. URL: https://doi.org/10.1145/3212734.3212758.
  19. Keren Censor-Hillel, Seri Khoury, and Ami Paz. Quadratic and near-quadratic lower bounds for the CONGEST model. In Proc. 31st International Symposium on Distributed Computing (DISC 2017), volume 91 of LIPIcs, pages 10:1-10:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.10.
  20. Y.-J. Chang, Q. He, W. Li, S. Pettie, and J. Uitto. The complexity of distributed edge coloring with small palettes. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 2018. URL: https://doi.org/10.1137/1.9781611975031.168.
  21. Yi-Jun Chang. The complexity landscape of distributed locally checkable problems on trees. In Proc. 34th International Symposium on Distributed Computing (DISC 2020), 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.
  22. Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the LOCAL model. SIAM J. Comput., 48(1):122-143, 2019. URL: https://doi.org/10.1137/17M1117537.
  23. Yi-Jun Chang and Seth Pettie. A time hierarchy theorem for the LOCAL model. SIAM J. Comput., 48(1):33-69, 2019. URL: https://doi.org/10.1137/17M1157957.
  24. Yi-Jun Chang, Jan Studený, and Jukka Suomela. Distributed graph problems through an automata-theoretic lens. In Proc. 28th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2021), LNCS. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-79527-6_3.
  25. Kai-Min Chung, Seth Pettie, and Hsin-Hao Su. Distributed algorithms for the Lovász local lemma and graph coloring. Distributed Comput., 30(4):261-280, 2017. URL: https://doi.org/10.1007/s00446-016-0287-6.
  26. Michael Elkin. An unconditional lower bound on the time-approximation trade-off for the distributed minimum spanning tree problem. SIAM Journal on Computing, 36(2):433-456, 2006. URL: https://doi.org/10.1137/s0097539704441058.
  27. P. Erdős and L. Lovász. Problems and results on 3-chromatic hypergraphs and some related questions, 1973. Google Scholar
  28. M. Fischer and M. Ghaffari. Sublogarithmic distributed algorithms for Lovász local lemma, and the complexity hierarchy. In Proceedings of the International Symposium on Distributed Computing (DISC), volume 91 of LIPIcs, pages 18:1-18:16. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.18.
  29. Orr Fischer, Tzlil Gonen, Fabian Kuhn, and Rotem Oshman. Possibilities and impossibilities for distributed subgraph detection. In Christian Scheideler and Jeremy T. Fineman, editors, Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, SPAA 2018, Vienna, Austria, July 16-18, 2018, pages 153-162. ACM, 2018. URL: https://doi.org/10.1145/3210377.3210401.
  30. Silvio Frischknecht, Stephan Holzer, and Roger Wattenhofer. Networks cannot compute their diameter in sublinear time. In Proc. 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012), pages 1150-1162. SIAM, 2012. URL: https://doi.org/10.1137/1.9781611973099.91.
  31. Nathan Linial. Distributive graph algorithms - global solutions from local data. In Proc. Symp. on Foundations of Computer Science (FOCS 1987), pages 331-335, 1987. URL: https://doi.org/10.1109/SFCS.1987.20.
  32. Nathan Linial. Locality in distributed graph algorithms. SIAM J. Comput., 21(1):193-201, 1992. URL: https://doi.org/10.1137/0221015.
  33. Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 565-573, 2014. URL: https://doi.org/10.1145/2591796.2591850.
  34. Moni Naor and Larry Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259-1277, 1995. URL: https://doi.org/10.1137/S0097539793254571.
  35. Dennis Olivetti. Round Eliminator: a tool for automatic speedup simulation, 2020. URL: https://github.com/olidennis/round-eliminator.
  36. David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, 2000. Google Scholar
  37. David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM Journal on Computing, 30(5):1427-1442, 2000. URL: https://doi.org/10.1137/s0097539700369740.
  38. Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM Journal on Computing, 41(5):1235-1265, 2012. URL: https://doi.org/10.1137/11085178x.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact