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Near-Linear Time Samplers for Matroid Independent Sets with Applications

Authors Xiaoyu Chen, Heng Guo, Xinyuan Zhang, Zongrui Zou

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Author Details

Xiaoyu Chen
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, 163 Xianlin Avenue, Nanjing, Jiangsu Province, China
Heng Guo
  • School of Informatics, University of Edinburgh, Informatics Forum, 10 Crichton Street, Edinburgh, EH8 9AB, UK
Xinyuan Zhang
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, 163 Xianlin Avenue, Nanjing, Jiangsu Province, China
Zongrui Zou
  • State Key Laboratory for Novel Software Technology, New Cornerstone Science Laboratory, Nanjing University, 163 Xianlin Avenue, Nanjing, Jiangsu Province, China

Funding

  • Guo, Heng: 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).

Acknowledgements

We would like to thank the hospitality of NII Shonan meeting No. 186, where some of the discussion took place.

Cite AsGet BibTex

Xiaoyu Chen, Heng Guo, Xinyuan Zhang, and Zongrui Zou. Near-Linear Time Samplers for Matroid Independent Sets with Applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 32:1-32:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.32

Abstract

We give a Õ(n) time almost uniform sampler for independent sets of a matroid, whose ground set has n elements and is given by an independence oracle. As a consequence, one can sample connected spanning subgraphs of a given graph G = (V,E) in Õ(|E|) time, whereas the previous best algorithm takes O(|E||V|) time. This improvement, in turn, leads to a faster running time on estimating all-terminal network reliability. Furthermore, we generalise this near-linear time sampler to the random cluster model with q ≤ 1.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Network reliability
  • Random cluster modek
  • Matroid
  • Bases-exchange walk

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References

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