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Optimal transport aims to learn a mapping of sources to targets by minimizingthe cost, which is typically defined as a function of distance. The solution tothis problem consists of straight line segments optimally connecting sources totargets, and it does not exhibit branching. These optimal solutions are instark contrast with both natural, and man-made transportation networks, wherebranching structures are prevalent. Here we discuss a fast heuristic branchingmethod for optimal transport in networks, and we provide several applications.

Heuristic Optimal Transport in Branching Networks