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A sampling Lovász Local Lemma — arXiv:2609.18712

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.18712
License (as archived): CC0-1.0
Archived: 2026-10-15T15:48:37.123Z
SHA-256 of the archived text: b35fd9aa571155167eca92d5ce54c5906c312cccb9792b2c13d077ff167072e9
Stable URL of this page: https://metraipolis.com/documento/dc_6871feeeeb82

How to cite

A sampling Lovász Local Lemma — arXiv:2609.18712 — arXiv (en), https://arxiv.org/abs/2609.18712 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6871feeeeb82 (Metraipolis archive dc_6871feeeeb82, sha256 b35fd9aa571155167eca92d5ce54c5906c312cccb9792b2c13d077ff167072e9)

BibTeX

@misc{dc6871feeeeb82,
  title = {A sampling Lovász Local Lemma — arXiv:2609.18712},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.18712},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6871feeeeb82; sha256 b35fd9aa571155167eca92d5ce54c5906c312cccb9792b2c13d077ff167072e9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.18712. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We give an approximately uniform sampler for satisfying assignments of constraint satisfaction problems that satisfy $4\mathrm e p(\Delta+1)^2\le1$, where $p$ is the largest constraint-violation probability under the uniform product distribution, and $\Delta$ 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 $(n+m/\varepsilon)^{O(k\Delta\log D)}$ 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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-17 in math.PR).
Categorie arXiv: Data Structures and Algorithms (cs.DS) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.18712 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T15:08:53.433Z dalla pagina https://arxiv.org/catchup/math.PR/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).