We show that graphs excluding $K_{2,t}$ as a minor admit a $f(t)$-round $50$-approximation deterministic distributed algorithm for \minDS. The result extends to \minVC. Though fast and approximate distributed algorithms for such problems were already known for $H$-minor-free graphs, all of them have an approximation ratio depending on the size of $H$. To the best of our knowledge, this is the first example of a large non-trivial excluded minor leading to fast and constant-approximation distributed algorithms, where the ratio is independent of the size of $H$. A new key ingredient in the analysis of these distributed algorithms is the use of \textit{asymptotic dimension}.

翻译：我们证明了排除$K_{2,t}$作为子式的图对于\minDS问题允许一个$f(t)$轮$50$倍逼近的确定性分布式算法。该结果可推广至\minVC问题。尽管针对此类问题在$H$子式自由图上已有快速逼近分布式算法，但所有现有算法的逼近比均依赖于$H$的规模。据我们所知，这是首个非平凡的大规模排除子式类能导出快速且具有常数逼近比的分布式算法的实例，其中逼近比与$H$的规模无关。分析这些分布式算法时引入的新关键工具是\textit{渐近维数}的运用。