Theory and Approximate Solvers for Branched Optimal Transport with Multiple Sources

Branched optimal transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route, favoring branched transportation networks. We here study the NP-hard optimization of BOT networks connecting a finite number of sources and sinks in \mathbb{R} 2 . First, we show how to efficiently find the best geometry of a BOT network for many sources and sinks, given a topology. Second, we argue that a topology with more than three edges meeting at a branching point is never optimal.