Efficient algorithms computing distances between Radon measures on R

In this paper numerical methods of computing distances between two Radon measures on R are discussed. Efficient algorithms for Wasserstein-type metrics are provided. In particular, we propose a novel algorithm to compute the flat metric (bounded Lipschitz distance) with a computational cost O(nlogn). The flat distance has recently proven to be adequate for the Escalator Boxcar Train (EBT) method for solving transport equations with growth terms. Therefore, finding efficient numerical algorithms to compute the flat distance between two measures is important for finding the residual error and validating empirical convergence of different methods.