Generic uniqueness of optimal transportation networks

TL;DR

This paper proves that for most boundary conditions, there is a unique optimal transportation network minimizing cost, establishing a generic uniqueness result in branched transportation problems.

Contribution

It establishes the generic uniqueness of solutions in optimal branched transportation networks for a broad class of boundary conditions.

Findings

Unique minimizer exists for generic boundary conditions.

The result applies to a wide class of boundary configurations.

Provides theoretical foundation for the stability of optimal networks.

Abstract

We prove that for the generic boundary, in the sense of Baire categories, there exists a unique minimizer of the associated optimal branched transportation problem.