Is either $W_1$ or $W_2$ (the Wasserstein distances) available in closed form when comparing two collections of point masses?
To be specific, let $p = \sum_{i=1}^n \delta_{x_i}$ and $q = \sum_{j=1}^m \delta_{y_j}$ for two arbitrary sets of points $\{x_i\}_{i=1}^n, \{y_j\}_{j=1}^m\subseteq \mathbb{R}^d$. For $d = 1$ or $2$, could one compute either $W_1(p, q)$ or $W_2(p, q)$ efficiently?