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Computation of Toroidal Schnyder Woods Made Simple and Fast: From Theory to Practice

Authors Luca Castelli Aleardi , Eric Fusy , Jyh-Chwen Ko , Razvan-Stefan Puscasu

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LIPIcs.SoCG.2025.30.pdf
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ACM Subject Classification
  • Mathematics of computing → Combinatoric problems
  • Theory of computation → Computational geometry
Keywords
  • Schnyder woods
  • toroidal triangulations
  • canonical ordering

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Abstract

We consider the problem of computing Schnyder woods for graphs embedded on the torus. We design simple linear-time algorithms based on canonical orderings that compute toroidal Schnyder woods for simple toroidal triangulations. The Schnyder woods computed by one of our algorithm are crossing and satisfy an additional structural property: at least two of the mono-chromatic components of the Schnyder wood are connected. We also exhibit experimental results empirically confirming three conjectures involving the structure of toroidal and higher genus Schnyder woods.

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Luca Castelli Aleardi, Eric Fusy, Jyh-Chwen Ko, and Razvan-Stefan Puscasu. Computation of Toroidal Schnyder Woods Made Simple and Fast: From Theory to Practice. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.30

Author Details

Luca Castelli Aleardi
  • LIX, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
Eric Fusy
  • LIGM, Université Gustave Eiffel, Champs-sur-Marne, France
Jyh-Chwen Ko
  • LIX, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
Razvan-Stefan Puscasu
  • École polytechnique fédérale de Lausanne (EPFL), Switzerland

Funding

  • Castelli Aleardi, Luca: this work is supported by ANR grant “3DMaps” ANR-20-CE48-0018.
  • Fusy, Eric: this work is supported by ANR grant “3DMaps” ANR-20-CE48-0018.

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References

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