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Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees

Authors Konrad Anand , Weiming Feng , Graham Freifeld , Heng Guo , Mark Jerrum , Jiaheng Wang

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ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
  • Theory of computation → Computational geometry
Keywords
  • non-crossing spanning trees
  • Markov chain
  • mixing time

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Abstract

We show that the flip chain for non-crossing spanning trees of n+1 points in convex position mixes in time O(n⁸log n). We use connections between Fuss-Catalan structures to construct a comparison argument with a chain similar to Wilson’s lattice path chain (Wilson 2004).

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Konrad Anand, Weiming Feng, Graham Freifeld, Heng Guo, Mark Jerrum, and Jiaheng Wang. Rapid Mixing of the Flip Chain over Non-Crossing Spanning Trees. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.8

Author Details

Konrad Anand
  • School of Informatics, Informatics Forum, University of Edinburgh, UK
Weiming Feng
  • School of Computing and Data Science, The University of Hong Kong, China
Graham Freifeld
  • School of Informatics, Informatics Forum, University of Edinburgh, UK
Heng Guo
  • School of Informatics, Informatics Forum, University of Edinburgh, UK
Mark Jerrum
  • School of Mathematical Sciences, Queen Mary University of London, UK
Jiaheng Wang
  • Faculty of Informatics and Data Science, University of Regensburg, Germany

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947778). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
  • Feng, Weiming: Weiming Feng acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation during his affiliation at ETH Zürich.
  • Wang, Jiaheng: Jiaheng Wang also acknowledges support from ERC (grant agreement No. 101077083, CountHom).

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