Shotgun assembly of labeled graphs

Elchanan Mossel, Nathan Ross

Published 2015-04-28Version 1

We consider the problem of reconstructing graphs or labeled graphs from neighborhoods of a given radius r. Special instances of this problem include DNA shotgun assembly, neural network reconstruction, and 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.