Shotgun assembly threshold for lattice labeling model
Probability
2022-05-04 v1
Abstract
We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a -dimensional box of side length . We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length . We determine the threshold around which there is a sharp transition from impossible to recover with probability tending to 1, to possible to recover with an efficient algorithm with probability tending to 1. Our result sharpens a constant factor in a previous work of Mossel and Ross (2019) and thus solves a question therein.
Cite
@article{arxiv.2205.01327,
title = {Shotgun assembly threshold for lattice labeling model},
author = {Jian Ding and Haoyu Liu},
journal= {arXiv preprint arXiv:2205.01327},
year = {2022}
}
Comments
16 pages