Approximating Maximum Integral Multiflows on Bounded Genus Graphs

Authors Chien-Chung Huang, Mathieu Mari, Claire Mathieu, Jens Vygen

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Chien-Chung Huang
  • CNRS, ENS, PSL, Paris, France
Mathieu Mari
  • University of Warsaw, Poland
Claire Mathieu
  • CNRS, IRIF, Université de Paris, France
Jens Vygen
  • Research Institute for Discrete Mathematics & Hausdorff Center for Mathematics, University of Bonn, Germany


The authors would like to thank Arnaud de Mesmay for useful suggestions. This work was partially funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).

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Chien-Chung Huang, Mathieu Mari, Claire Mathieu, and Jens Vygen. Approximating Maximum Integral Multiflows on Bounded Genus Graphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 80:1-80:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We devise the first constant-factor approximation algorithm for finding an integral multi-commodity flow of maximum total value for instances where the supply graph together with the demand edges can be embedded on an orientable surface of bounded genus. This extends recent results for planar instances. Our techniques include an uncrossing algorithm, which is significantly more difficult than in the planar case, a partition of the cycles in the support of an LP solution into free homotopy classes, and a new rounding procedure for freely homotopic non-separating cycles.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Multi-commodity flows
  • approximation algorithms
  • bounded genus graphs


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