Heuristic Optimal Transport in Branching Networks

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.