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The papers describes an easy approach, based on a classical construction byDacorogna and Moser, to prove that optimal vector fields in some minimal flowproblem linked to optimal transport models (congested traffic, branchedtransport, Beckmann's problem...) are induced by a probability measure on thespace of paths. This gives a new, easier, proof of a classical result bySmirnov, and allows handling optimal flows without taking care of the presenceof cycles.

A Dacorogna-Moser approach to flow decomposition and minimal flow problems