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arXiv · 1504.07682

Shotgun assembly of labeled graphs

Elchanan Mossel·Nathan Ross
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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.

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Elchanan Mossel, Nathan Ross. 2015-04-28. Shotgun assembly of labeled graphs. https://doi.org/10.1109/tnse.2017.2776913

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