Improved distributed degree splitting and edge coloring

  • Mohsen Ghaffari
  • Juho Hirvonen
  • Fabian KuhnEmail author
  • Yannic Maus
  • Jukka Suomela
  • Jara Uitto


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 (Proc SODA 2017:2505–2523, 2017): our algorithms are significantly simpler and faster, and have a much smaller discrepancy. This also leads to a faster and simpler deterministic algorithm for \((2+o(1))\varDelta \)-edge-coloring, improving on that of Ghaffari and Su.


Distributed graph algorithms Degree splitting Edge coloring Discrepancy 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ETH ZurichZurichSwitzerland
  2. 2.Aalto UniversityHelsinkiFinland
  3. 3.University of FreiburgFreiburgGermany

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