Fast Coloring Despite Congested Relays

Authors Maxime Flin , Magnús M. Halldórsson , Alexandre Nolin

Thumbnail PDF


  • Filesize: 0.93 MB
  • 24 pages

Document Identifiers

Author Details

Maxime Flin
  • Reykjavik University, Iceland
Magnús M. Halldórsson
  • Reykjavik University, Iceland
Alexandre Nolin
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

Cite AsGet BibTex

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Fast Coloring Despite Congested Relays. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We provide a O(log⁶ log n)-round randomized algorithm for distance-2 coloring in CONGEST with Δ²+1 colors. For Δ≫polylog n, this improves exponentially on the O(logΔ+polylog log n) algorithm of [Halldórsson, Kuhn, Maus, Nolin, DISC'20].

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Graph coloring
  • CONGEST model
  • distributed graph coloring
  • power graphs


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


  1. Noga Alon and Sepehr Assadi. Palette sparsification beyond (Δ+1) vertex coloring. In APPROX/RANDOM, volume 176 of LIPIcs, pages 6:1-6:22. LZI, 2020. URL:
  2. Noga Alon, László Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms, 7(4):567-583, 1986. URL:
  3. Sepehr Assadi, Yu Chen, and Sanjeev Khanna. Sublinear algorithms for (Δ + 1) vertex coloring. In SODA, pages 767-786. SIAM, 2019. URL:
  4. Leonid Barenboim and Michael Elkin. Distributed Graph Coloring: Fundamentals and Recent Developments. Morgan & Claypool Publishers, 2013. URL:
  5. Leonid Barenboim, Michael Elkin, and Uri Goldenberg. Locally-iterative distributed (Δ + 1)-coloring and applications. J. ACM, 69(1):5:1-5:26, 2022. URL:
  6. Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. The locality of distributed symmetry breaking. Journal of the ACM, 63(3):20:1-20:45, 2016. URL:
  7. Leonid Barenboim and Uri Goldenberg. Speedup of distributed algorithms for power graphs in the CONGEST model. Technical Report 2305.04358, arXiv, 2023. URL:
  8. Yi-Jun Chang, Qizheng He, Wenzheng Li, Seth Pettie, and Jara Uitto. The complexity of distributed edge coloring with small palettes. In SODA, pages 2633-2652. SIAM, 2018. URL:
  9. Yi-Jun Chang, Wenzheng Li, and Seth Pettie. Distributed (Δ+1)-coloring via ultrafast graph shattering. SIAM J. Computing, 49(3):497-539, 2020. URL:
  10. 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:
  11. Michael Elkin and Shaked Matar. Near-additive spanners in low polynomial deterministic CONGEST time. In PODC, pages 531-540. ACM, 2019. URL:
  12. Michael Elkin, Seth Pettie, and Hsin-Hao Su. (2Δ-1)-edge-coloring is much easier than maximal matching in the distributed setting. In SODA, pages 355-370. SIAM, 2015. URL:
  13. Salwa Faour, Mohsen Ghaffari, Christoph Grunau, Fabian Kuhn, and Václav Rozhoň. Local distributed rounding: Generalized to MIS, matching, set cover, and beyond. In SODA, pages 4409-4447. SIAM, 2023. URL:
  14. Manuela Fischer, Magnús M. Halldórsson, and Yannic Maus. Fast distributed Brooks' theorem. In SODA, pages 2567-2588. SIAM, 2023. URL:
  15. Maxime Flin, Mohsen Ghaffari, Magnús M. Halldórsson, Fabian Kuhn, and Alexandre Nolin. Coloring fast with broadcasts. In SPAA, pages 455-465. ACM, 2023. URL:
  16. Maxime Flin, Mohsen Ghaffari, Magnús M. Halldórsson, Fabian Kuhn, and Alexandre Nolin. A distributed palette sparsification theorem. Technical Report 2301.06457, arXiv, 2023. URL:
  17. Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Fast coloring despite congested relays. Technical Report 2308.01359, arXiv, 2023. Full version of this paper. URL:
  18. Pierre Fraigniaud, Magnús M. Halldórsson, and Alexandre Nolin. Distributed testing of distance-k colorings. In SIROCCO, volume 12156 of LNCS, pages 275-290. Springer, 2020. URL:
  19. Pierre Fraigniaud, Marc Heinrich, and Adrian Kosowski. Local conflict coloring. In FOCS, 2016. URL:
  20. Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In SODA, pages 270-277. SIAM, 2016. URL:
  21. Mohsen Ghaffari. Distributed maximal independent set using small messages. In SODA, pages 805-820. SIAM, 2019. URL:
  22. Mohsen Ghaffari and Christoph Grunau. Faster deterministic distributed MIS and approximate matching. STOC, abs/2303.16043, 2023. URL:
  23. Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, and Václav Rozhoň. Improved distributed network decomposition, hitting sets, and spanners, via derandomization. In SODA, pages 2532-2566. SIAM, 2023. URL:
  24. Mohsen Ghaffari, Christoph Grunau, and Václav Rozhoň. Improved deterministic network decomposition. In SODA, 2021. URL:
  25. Mohsen Ghaffari and Fabian Kuhn. Deterministic distributed vertex coloring: Simpler, faster, and without network decomposition. In FOCS, pages 1009-1020. IEEE Computer Society, 2021. URL:
  26. Mohsen Ghaffari and Julian Portmann. Improved network decompositions using small messages with applications on MIS, neighborhood covers, and beyond. In DISC, volume 146 of LIPIcs, pages 18:1-18:16. LZI, 2019. URL:
  27. Magnús M. Halldórsson, Fabian Kuhn, and Yannic Maus. Distance-2 coloring in the CONGEST model. In PODC, pages 233-242. ACM, 2020. URL:
  28. Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin. Coloring fast without learning your neighbors' colors. In DISC, pages 39:1-39:17. LZI, 2020. URL:
  29. Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Tigran Tonoyan. Efficient randomized distributed coloring in CONGEST. In STOC, pages 1180-1193. ACM, 2021. URL:
  30. Magnús M. Halldórsson and Alexandre Nolin. Superfast coloring in CONGEST via efficient color sampling. Theor. Comput. Sci., 948:113711, 2023. URL:
  31. Magnús M. Halldórsson, Fabian Kuhn, Alexandre Nolin, and Tigran Tonoyan. Near-optimal distributed degree+1 coloring. In STOC, pages 450-463. ACM, 2022. URL:
  32. Magnús M. Halldórsson, Alexandre Nolin, and Tigran Tonoyan. Overcoming congestion in distributed coloring. In PODC, pages 26-36. ACM, 2022. URL:
  33. David G. Harris, Johannes Schneider, and Hsin-Hao Su. Distributed (Δ + 1)-coloring in sublogarithmic rounds. Journal of the ACM, 65:19:1-19:21, 2018. URL:
  34. Öjvind Johansson. Simple distributed Δ+1-coloring of graphs. Inf. Process. Lett., 70(5):229-232, 1999. URL:
  35. Sven Oliver Krumke, Madhav V. Marathe, and S. S. Ravi. Models and approximation algorithms for channel assignment in radio networks. Wirel. Networks, 7(6):575-584, 2001. URL:
  36. Nathan Linial. Locality in distributed graph algorithms. SIAM J. Computing, 21(1):193-201, 1992. URL:
  37. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Computing, 15:1036-1053, 1986. URL:
  38. Yannic Maus, Saku Peltonen, and Jara Uitto. Distributed symmetry breaking on power graphs via sparsification. In PODC, pages 157-167. ACM, 2023. full version available at URL:
  39. Yannic Maus and Tigran Tonoyan. Linial for lists. Distributed Comput., 35(6):533-546, 2022. URL:
  40. Yannic Maus and Jara Uitto. Efficient CONGEST algorithms for the Lovász local lemma. In DISC, volume 209 of LIPIcs, pages 31:1-31:19. LZI, 2021. URL:
  41. Seth Pettie and Hsin-Hao Su. Distributed coloring algorithms for triangle-free graphs. Inf. Comput., 243:263-280, 2015. URL:
  42. Bruce A. Reed. ω, Δ, and χ. J. Graph Theory, 27(4):177-212, 1998. URL:<177::AID-JGT1>3.0.CO;2-K.
  43. Václav Rozhon and Mohsen Ghaffari. Polylogarithmic-time deterministic network decomposition and distributed derandomization. In STOC, pages 350-363. ACM, 2020. URL:
  44. Johannes Schneider and Roger Wattenhofer. A new technique for distributed symmetry breaking. In PODC, pages 257-266. ACM, 2010. URL: