Improved distributed degree splitting and edge coloring

Abstract

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.

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Correspondence to Fabian Kuhn.

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Juho Hirvonen was supported by Ulla Tuominen Foundation. Fabian Kuhn, Yannic Maus and Jara Uitto were partly supported by ERC Grant No. 336495 (ACDC). A preliminary version of this paper appeared in the 31st International Symposium on Distributed Computing (DISC 2017) [12].

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Ghaffari, M., Hirvonen, J., Kuhn, F. et al. Improved distributed degree splitting and edge coloring. Distrib. Comput. 33, 293–310 (2020). https://doi.org/10.1007/s00446-018-00346-8

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Keywords

  • Distributed graph algorithms
  • Degree splitting
  • Edge coloring
  • Discrepancy