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Different Scales of Randomness: Empirical Mixing Times of the Edge Switching and Curveball MCMC

Authors Deepak Ajwani , Melvin Kallmayer , Alexander Leonhardt , Ulrich Meyer , Ryan O'Connor , Manuel Penschuck

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Subject Classification

ACM Subject Classification
  • Theory of computation → Random network models
Keywords
  • Mixing Time
  • Graph Randomization
  • Machine Learning
  • Edge Switching

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Abstract

The Fixed Degree Sequence Model (FDSM) asks for a uniform sample from the set of all simple graphs that match a prescribed degree sequence. It is typically implemented using Markov-Chain Monte-Carlo (MCMC) processes, such as Edge Switching or Curveball (and their variants). Yet despite decades of research, rigorous bounds on the mixing times of such processes remain impractical.
Consequently, several experimental techniques have been used to derive "empirical lower bounds" on the mixing time. We address the following research questions: (1) Which commonly studied graph-theoretic properties serve as reliable empirical predictors for mixing of FDSM MCMC processes? (2) At what structural scales do these properties operate primarily (i. e., are they predominantly local or global in nature)? (3) How can these properties be characterised and quantified most effectively?
To this end, we propose Claim, a novel systematic method to establish empirical lower bounds using learnt classifiers, and compare it to existing methods. Apart from interesting insights into the usage of machine learning for this problem, we also derive robust graph properties with respect to different randomisation algorithms. Although experimental in nature, these results may influence both theorist’s and algorithm engineer’s work on improved bounds and better algorithm respectively.

Cite As Get BibTex

Deepak Ajwani, Melvin Kallmayer, Alexander Leonhardt, Ulrich Meyer, Ryan O'Connor, and Manuel Penschuck. Different Scales of Randomness: Empirical Mixing Times of the Edge Switching and Curveball MCMC. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SEA.2026.2

Author Details

Deepak Ajwani
  • University College Dublin, Ireland
Melvin Kallmayer
  • Goethe University Frankfurt, Germany
Alexander Leonhardt
  • Goethe University Frankfurt, Germany
Ulrich Meyer
  • Goethe University Frankfurt, Germany
Ryan O'Connor
  • University College Dublin, Ireland
Manuel Penschuck
  • University of Southern Denmark, Odense, Denmark

Funding

The research of the first and penultimate author is supported in part by a grant from Science Foundation Ireland (Grant number 18/CRT/6183). For the purpose of Open Access, the authors have applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission. This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG) – ME 2088/5-2, FOR 2975; and the Novo Nordisk Foundation grant NNF21OC0066551. The authors gratefully acknowledge the computing time provided to them at the NHR Center NHR@SW at Goethe University Frankfurt. This is funded by the Federal Ministry of Education and Research, and the state governments participating on the basis of the resolutions of the GWK for national high performance computing at universities (www.nhr-verein.de/unsere-partner).

Acknowledgements

We thank the anonymous reviewers for their valuable and insightful feedback.

Supplementary Materials

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