Given a graph $G=(V,E)$, suppose we are interested in selecting a sequence of vertices $(x_j)_{j=1}^n$ such that $\left\{x_1, \dots, x_k\right\}$ is `well-distributed' uniformly in $k$. We describe a greedy algorithm motivated by potential theory and corresponding developments in the continuous setting. The algorithm performs nicely on graphs and may be of use for sampling problems. We can interpret the algorithm as trying to greedily minimize a negative Sobolev norm; we explain why this is related to Wasserstein distance by establishing a purely spectral bound on the Wasserstein distance on graphs that mirrors R. Peyre's estimate in the continuous setting. We illustrate this with many examples and discuss several open problems.

翻译：以 $G = (V, E) 表示, 假设我们有兴趣选择 $( x_ j) ⁇ j = 1 ⁇ n 的顺序, 这样, $\ left\\ x_ 1,\ dots, x_ k\right\ $ 均以 $ 美元 表示“ 正常分配 ” 。 我们描述一种贪婪的算法, 其动机是潜在的理论和连续设置中的相应发展。 算法在图表上表现良好, 并可用于取样问题。 我们可以将算法解释为试图贪婪地尽量减少一个负的 Sobolev 规范; 我们解释为什么这与瓦瑟斯坦 距离有关, 在连续设置中反映 R. Peyre 估计数的图表上设置一个纯粹的光谱。 我们用许多例子来说明这一点, 并讨论几个尚未解决的问题 。