Title: 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 [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.