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Shotgun Assembly of Labeled Graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2019Embargo end date: 01 Jan 2015Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Network Science and Engineering, volume 6, pages 145-157 (eissn: 2334-329X, Copyright policy )Funded by:NSF | Combinatorial Statistics ..., ARC | Discovery Projects - Gran..., NSF | AF: Small: Boolean Functi...
Authors: Mossel, E; Ross, N;

doi: 10.1109/tnse.2017.2776913 , 10.48550/arxiv.1504.07682

arXiv: http://arxiv.org/abs/1504.07682

handle: 11343/290541

Shotgun Assembly of Labeled Graphs

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

Related Organizations
Keywords

FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), Probability (math.PR), FOS: Mathematics, Mathematics - Probability

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
11
Top 10%
Top 10%
Top 10%
Green
hybrid