Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to targets, and it does not exhibit branching. These optimal solutions are in stark contrast with both natural, and man-made transportation networks, where branching structures are prevalent. Here we discuss a fast heuristic branching method for optimal transport in networks. We also provide several numerical applications to synthetic examples, a simplified cardiovascular network, and the "Santa Claus" distribution network which includes 141,182 cities around the world, with known location and population.

翻译：最优输运旨在通过最小化代价（通常定义为距离的函数）来学习源点到目标点的映射。该问题的解由最优连接源点与目标点的直线段构成，且不呈现分支结构。这些最优解与自然界及人造运输网络中普遍存在的分支结构形成鲜明对比。本文讨论了一种用于网络最优输运的快速启发式分支方法，并提供了多个数值应用示例，包括合成案例、简化心血管网络，以及包含全球141,182个已知位置与人口数据的“圣诞老人”配送网络。