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Sink-Free Orientations: A Local Sampler with Applications

Authors Konrad Anand , Graham Freifeld , Heng Guo , Chunyang Wang , Jiaheng Wang

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ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Sink-free orientations
  • local sampling
  • deterministic counting

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Abstract

For sink-free orientations in graphs of minimum degree at least 3, we show that there is a deterministic approximate counting algorithm that runs in time O((n^33/ε^32)log(n/ε)), a near-linear time sampling algorithm, and a randomised approximate counting algorithm that runs in time O((n/ε)²log(n/ε)), where n denotes the number of vertices of the input graph and 0 < ε < 1 is the desired accuracy. All three algorithms are based on a local implementation of the sink popping method (Cohn, Pemantle, and Propp, 2002) under the partial rejection sampling framework (Guo, Jerrum, and Liu, 2019).

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Konrad Anand, Graham Freifeld, Heng Guo, Chunyang Wang, and Jiaheng Wang. Sink-Free Orientations: A Local Sampler with Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.60

Author Details

Konrad Anand
  • University of Edinburgh, UK
Graham Freifeld
  • University of Edinburgh, UK
Heng Guo
  • University of Edinburgh, UK
Chunyang Wang
  • Nanjing University, China
Jiaheng Wang
  • 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). Jiaheng Wang also acknowledges support from the ERC (grant agreement No. 101077083, CountHom).

Acknowledgements

We thank Guus Regts for helpful comments on an earlier version of this paper.

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