Shotgun assembly of labeled graphs
arXiv:1504.07682 · doi:10.1109/TNSE.2017.2776913
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.
Ver3: 23 pages, matches published version but with a corrected proof of Theorem 4.5 (result unchanged); Ver2: 22 pages; Ver1: 21 pages