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Computer Science > Data Structures and Algorithms

arXiv:2205.02050 (cs)
[Submitted on 4 May 2022 (v1), last revised 13 Sep 2022 (this version, v2)]

Title:A Perfect Sampler for Hypergraph Independent Sets

Authors:Guoliang Qiu, Yanheng Wang, Chihao Zhang
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Abstract:The problem of uniformly sampling hypergraph independent sets is revisited. We design an efficient perfect sampler for the problem under a condition similar to that of the asymmetric Lovász Local Lemma. When applied to $d$-regular $k$-uniform hypergraphs on $n$ vertices, our sampler terminates in expected $O(n\log n)$ time provided $d\le c\cdot 2^{k/2}/k$ for some constant $c>0$. If in addition the hypergraph is linear, the condition can be weaken to $d\le c\cdot 2^{k}/k^2$ for some constant $c>0$, matching the rapid mixing condition for Glauber dynamics in Hermon, Sly and Zhang [HSZ19].
Comments: fixed an error in the definition of the witness graphs; added analysis for linear hypergraphs; the bound in Theorem 2 is affected by a 1/k factor
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM)
Cite as: arXiv:2205.02050 [cs.DS]
  (or arXiv:2205.02050v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2205.02050

Submission history

From: Guoliang Qiu [view email]
[v1] Wed, 4 May 2022 13:16:58 UTC (70 KB)
[v2] Tue, 13 Sep 2022 14:20:42 UTC (70 KB)
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