  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.
