Shotgun assembly of labeled graphs

@article{Mossel2015ShotgunAO,
  title={Shotgun assembly of labeled graphs},
  author={Elchanan Mossel and Nathan Ross},
  journal={CoRR},
  year={2015},
  volume={abs/1504.07682}
}
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, Erdős-Rényi random graphs, and the random jigsaw puzzle model. Many open problems… CONTINUE READING