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A Perfect Sampler for Hypergraph Independent Sets

Authors Guoliang Qiu, Yanheng Wang, Chihao Zhang



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Author Details

Guoliang Qiu
  • Shanghai Jiao Tong University, China
Yanheng Wang
  • ETH Zürich, Switzerland
Chihao Zhang
  • Shanghai Jiao Tong University, China

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Guoliang Qiu, Yanheng Wang, and Chihao Zhang. A Perfect Sampler for Hypergraph Independent Sets. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 103:1-103:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICALP.2022.103

Abstract

The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a similar condition of the asymmetric Lovász local lemma. When specialized to d-regular k-uniform hypergraphs on n vertices, our sampler terminates in expected O(n log n) time provided d ≤ c⋅ 2^{k/2} where c > 0 is a constant, matching the rapid mixing condition for Glauber dynamics in Hermon, Sly and Zhang [Hermon et al., 2019]. The analysis of our algorithm is simple and clean.

Subject Classification

ACM Subject Classification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Coupling from the past
  • Markov chains
  • Hypergraph independent sets

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References

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