Improved Distributed Degree Splitting and Edge Coloring

Authors Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus, Jukka Suomela, Jara Uitto

Thumbnail PDF


  • Filesize: 0.84 MB
  • 15 pages

Document Identifiers

Author Details

Mohsen Ghaffari
Juho Hirvonen
Fabian Kuhn
Yannic Maus
Jukka Suomela
Jara Uitto

Cite AsGet BibTex

Mohsen Ghaffari, Juho Hirvonen, Fabian Kuhn, Yannic Maus, Jukka Suomela, and Jara Uitto. Improved Distributed Degree Splitting and Edge Coloring. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires orienting the edges such that each node has almost the same number of incoming and outgoing edges, again up to a small additive discrepancy. We present deterministic distributed algorithms for both variants, which improve on their counterparts presented by Ghaffari and Su [SODA'17]: our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for (2+o(1))Delta-edge-coloring, improving on that of Ghaffari and Su.
  • Distributed Graph Algorithms
  • Degree Splitting
  • Edge Coloring
  • Discrepancy


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


  1. Leonid Barenboim and Michael Elkin. Distributed deterministic edge coloring using bounded neighborhood independence. In Proc. PODC 2011, pages 129-138, 2011. URL:
  2. József Beck and Tibor Fiala. "Integer-making" theorems. Discrete Applied Mathematics, 3(1):1-8, 1981. URL:
  3. Debe Bednarchak and Martin Helm. A note on the beck-fiala theorem. Combinatorica, 17(1):147-149, 1997. Google Scholar
  4. 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. STOC 2016, pages 479-488, 2016. URL:
  5. Boris Bukh. An improvement of the Beck-Fiala theorem. Combinatorics, Probability & Computing, 25(03):380-398, 2016. URL:
  6. Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the local model. In Proc. FOCS 2016, pages 615-624, 2016. URL:
  7. Bernard Chazelle. The Discrepancy Method: Randomness and Complexity. Cambridge University Press, 2000. Google Scholar
  8. Andrzej Czygrinow, Michał Hańćkowiak, and Michał Karoński. Distributed O(Δlog n)-edge-coloring algorithm. In Proc. ESA 2001, pages 345-355, 2001. URL:
  9. Yefim Dinitz. Dinitz' algorithm: The original version and Even’s version. In Theoretical Computer Science, Essays in Memory of Shimon Even, pages 218-240. Springer, 2006. URL:
  10. M. Ghaffari, J. Hirvonen, F. Kuhn, Y. Maus, J. Suomela, and J. Uitto. Improved Distributed Degree Splitting and Edge Coloring. ArXiv e-prints, June 2017. URL:
  11. Mohsen Ghaffari and Hsin-Hao Su. Distributed degree splitting, edge coloring, and orientations. In Proc. SODA 2017, pages 2505-2523, 2017. Google Scholar
  12. Michał Hańćkowiak, Michał Karoński, and Alessandro Panconesi. On the distributed complexity of computing maximal matchings. SIAM J. Discrete Math., 15(1):41-57, 2001. URL:
  13. Amos Israeli and Yossi Shiloach. An improved parallel algorithm for maximal matching. Inf. Process. Lett., 22(2):57-60, 1986. URL:
  14. Howard J. Karloff and David B. Shmoys. Efficient parallel algorithms for edge coloring problems. J. Algorithms, 8(1):39-52, 1987. URL:
  15. Nathan Linial. Distributive graph algorithms - global solutions from local data. In Proc. FOCS 1987, pages 331-335, 1987. URL:
  16. Moni Naor and Larry Stockmeyer. What can be computed locally? In Proc. STOC 1993, pages 184-193, 1993. URL:
  17. David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, 2000. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail