Shotgun assembly threshold for lattice labeling model
成果类型：
Article; Early Access
署名作者：
Ding, Jian; Liu, Haoyu
署名单位：
Peking University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-023-01199-4
发表日期：
2023
关键词：
摘要：
We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a d-dimensional box of side length n. We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length r. 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 (IEEE Trans Netw Sci Eng 6(2):145-157, 2019) and thus solves a question therein.