{
  "abstract": "We give an approximately uniform sampler for satisfying assignments of constraint satisfaction problems that satisfy $4\\mathrm e p(Δ+1)^2\\le1$, where $p$ is the largest constraint-violation probability under the uniform product distribution, and $Δ$ is the maximum degree of the dependency graph. The algorithm invokes the recent efficient approximate counting algorithm of Liu, Wang, Yin, Zhang, and Zhou~\\cite{CountingLLL} as a subroutine and returns a satisfying assignment sampled within total-variation distance $\\varepsilon$ of the uniform distribution in $(n+m/\\varepsilon)^{O(kΔ\\log D)}$ time, where $n$ and $m$ are the numbers of variables and constraints, $D$ is the common domain size, and $k$ bounds the constraint arity. We also give an asymmetric product-form condition under which both counting and sampling are efficient. To supply the counts needed in the additional regime, we extend the marginal-expansion proof of Liu et al.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18712",
  "author_total": 1,
  "authors": [
    {
      "name": "Dimitris Achlioptas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/159tkt3p503gy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18712",
  "fulltext_url": null,
  "id": "159tkt3p503gy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18712",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Constraint Satisfaction and Optimization"
    ]
  ],
  "openalex": "W7213529163",
  "pdf_url": "https://arxiv.org/pdf/2609.18712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/159tkt3p503gy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.18712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A sampling Lovász Local Lemma",
  "title_text": "A sampling Lovász Local Lemma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/159tkt3p503gy",
  "venue": "arXiv",
  "versions": []
}