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 $$(2+o(1))\varDelta $$ ( 2 + o ( 1 ) ) Δ -edge-coloring, improving on that of Ghaffari and Su.

中文翻译：

---

改进的分布式度分裂和边缘着色

度分裂问题需要将图的边着色为红色或蓝色，以便每个节点在每种颜色中具有几乎相同数量的边，直到有一个小的累加差异。该问题的有向变体需要对边进行定向，以便每个节点具有几乎相同数量的传入和传出边，再次达到小的附加差异。我们为这两种变体提供了确定性分布式算法，它们改进了 Ghaffari 和 Su (Proc SODA 2017:2505–2523, 2017) 提出的对应算法：我们的算法明显更简单、更快，并且差异小得多。这也导致了 $$(2+o(1))\varDelta $$ ( 2 + o ( 1 ) ) Δ -edge-coloring 的更快、更简单的确定性算法，改进了 Ghaffari 和 Su 的算法。