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arXiv · 2511.13806

Optimal Sequential Flows

Hugo Gimbert·Corto Mascle·Patrick Totzke
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Abstract

We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from a given finite set. Our method is based on a novel factorization theorem for finite semigroups that, applied to a suitable flow semigroup, allows to derive small witnesses. This generalises to multiple in/output vertices, as well as regular constraints.

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Hugo Gimbert, Corto Mascle, Patrick Totzke. 2025-11-17. Optimal Sequential Flows. https://arxiv.org/abs/2511.13806

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