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Optimal Sequential Flows

Authors Hugo Gimbert , Corto Mascle , Patrick Totzke

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LIPIcs.ICALP.2026.98.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
  • Computing methodologies → Symbolic and algebraic algorithms
  • Computing methodologies → Algebraic algorithms
  • Theory of computation → Algebraic language theory
Keywords
  • Network Flow
  • Sequential Flow
  • Semigroup Factorization

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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.

Cite As Get BibTex

Hugo Gimbert, Corto Mascle, and Patrick Totzke. Optimal Sequential Flows. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.98

Author Details

Hugo Gimbert
  • CNRS, LaBRI, Université de Bordeaux, Talence, France
Corto Mascle
  • Max Planck Institute for Software Systems, Kaiserslautern, Germany
Patrick Totzke
  • University of Liverpool, UK

Funding

  • Totzke, Patrick: EPSRC, grant no.: EP/X042596/1.

References

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