We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al. for graphs with excluded topological minors to very general classes of uniformly sparse graphs. We demonstrate how our general algorithm can be modified and fine-tuned to compute an ($11+\epsilon$)-approximation (for any $\epsilon>0)$ of a minimum dominating set on planar graphs. This improves on the previously best known approximation factor of 52 on planar graphs, which was achieved by an elegant and simple algorithm of Lenzen et al.

翻译：我们显示,占支配地位的设定问题在LOCAL模型中,在分布式计算图类的分布式计算模型中,在固定的几轮中都承认一个恒定的系数近似值。这概括了Czygrinow等人的结果,用于将具有排他性的表层未成年人的图表改成非常普通的稀有图类。我们展示了如何修改和微调我们的一般算法,以计算平面图上最起码占支配地位的美元($\epsilon>0)的11 ⁇ epsilon-approcimation($@0)。这改善了平面图上原先最已知的52的近似系数,这是通过Lenzen等人的优雅而简单的算法实现的。