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, and we provide several applications.

翻译：最优传输旨在通过最小化代价（通常定义为距离的函数）来学习从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传输的快速启发式分支方法，并给出了若干应用实例。