Optimal Sequential Flows
Optimization and Control
2026-02-09 v2 Data Structures and Algorithms
Formal Languages and Automata Theory
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.
Cite
@article{arxiv.2511.13806,
title = {Optimal Sequential Flows},
author = {Hugo Gimbert and Corto Mascle and Patrick Totzke},
journal= {arXiv preprint arXiv:2511.13806},
year = {2026}
}