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Shotgun Assembly of the Non-Uniform Labeled Lattice Model — arXiv:2611.05532

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.05532
License (as archived): CC0-1.0
Archived: 2026-11-05T18:27:39.885Z
SHA-256 of the archived text: 1a8da5321d26b016a816760cc3d9cdccfcba536fab60cfde078c3219f6ad4812
Stable URL of this page: https://metraipolis.com/documento/dc_2bcd2ebb2530

How to cite

Shotgun Assembly of the Non-Uniform Labeled Lattice Model — arXiv:2611.05532 — arXiv (en), https://arxiv.org/abs/2611.05532 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2bcd2ebb2530 (Metraipolis archive dc_2bcd2ebb2530, sha256 1a8da5321d26b016a816760cc3d9cdccfcba536fab60cfde078c3219f6ad4812)

BibTeX

@misc{dc2bcd2ebb2530,
  title = {Shotgun Assembly of the Non-Uniform Labeled Lattice Model — arXiv:2611.05532},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.05532},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2bcd2ebb2530; sha256 1a8da5321d26b016a816760cc3d9cdccfcba536fab60cfde078c3219f6ad4812},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.05532. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we study the graph shotgun assembly problem in the labeled lattice model, as introduced by Mossel and Ross (2019). We start with a $d$-dimensional lattice of length $n$, where the color of each vertex is sampled i.i.d. from a distribution $\pi$. Then, we ask whether it is possible to reconstruct the coloring of the lattice given the coloring of each subgrid of length $k$. While previous work by Ding and Liu (2023) and Demidovich, Panichkin, and Zhukovskii (2023) identified the reconstruction threshold when $\pi$ is uniform, we examine the non-uniform case. This paper establishes a sufficient condition for the impossibility of reconstruction for $d \geq 2$ using information-theoretic arguments. Our negative result matches the known threshold in the uniform case.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.05532 — 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 2026-11-05T18:18:04.064Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).