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Poster
Theory and Approximate Solvers for Branched Optimal Transport with Multiple Sources
Peter Lippmann · Enrique Fita Sanmartín · Fred Hamprecht

Tue Nov 29 02:00 PM -- 04:00 PM (PST) @ Hall J #741
in Poster Session 2 »
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. Third, we show that the results obtained for the Euclidean plane generalize directly to optimal transportation networks on two-dimensional Riemannian manifolds. Finally, we present a simple but effective approximate BOT solver combining geometric optimization with a combinatorial optimization of the network topology.
Keywords: Combinatorial Optimization · Structured Prediction · optimal transport · Irrigation Networks · Branched Optimal Transport · Steiner Tree Problem · Transportation Networks

Author Information

Peter Lippmann (University Heidelberg, HCI)
Enrique Fita Sanmartín (Heidelberg University)
Fred Hamprecht (Heidelberg University)

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