Shotgun assembly of labeled graphs
Probability
2022-08-19 v3 Information Theory
math.IT
Abstract
We consider the problem of reconstructing graphs or labeled graphs from neighborhoods of a given radius r. Special instances of this problem include the well known: DNA shotgun assembly; the lesser-known: neural network reconstruction; and a new problem: assembling random jigsaw puzzles. We provide some necessary and some sufficient conditions for correct recovery both in combinatorial terms and for some generative models including random labelings of lattices, Erdos-Renyi random graphs, and the random jigsaw puzzle model. Many open problems and conjectures are provided.
Keywords
Cite
@article{arxiv.1504.07682,
title = {Shotgun assembly of labeled graphs},
author = {Elchanan Mossel and Nathan Ross},
journal= {arXiv preprint arXiv:1504.07682},
year = {2022}
}
Comments
Ver3: 23 pages, matches published version but with a corrected proof of Theorem 4.5 (result unchanged); Ver2: 22 pages; Ver1: 21 pages