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.

给定一个图\（G =（V，E）\），假设我们感兴趣的是选择一个顶点序列\（（x_j）_ {j = 1} ^ n \）使得\（\ left \ {x_1， \ dots，x_k \ right \} \）在 k中均匀分布。我们描述了一种由潜能理论和持续发展中的相应发展所激发的贪婪算法。该算法在图形上表现良好，可用于采样问题。我们可以将算法解释为试图贪婪地最小化负Sobolev范数。我们通过在反映连续设置中R. Peyre估计的图表上的Wasserstein距离上建立纯谱界限，来解释为什么这与Wasserstein距离有关。我们将通过许多示例来说明这一点，并讨论几个未解决的问题。