Shotgun assembly of Erdős-Rényi random graphs
Name
22-ECP445.pdf
Description
Published version
Size
295.9 KB
Format
Adobe PDF
Checksum (MD5)
022ccd892f5e388ae6e581a088cd9043
Author(s)
Gaudio, Julia
Mossel, Elchanan
Date Issued
2022
Journal
Electronic Communications in Probability
Publisher
Institute of Mathematical Statistics
Citation
Gaudio, Julia and Mossel, Elchanan. 2022. "Shotgun assembly of Erdős-Rényi random graphs." Electronic Communications in Probability, 27 (none).
Version
Final published version
Abstract
Graph shotgun assembly refers to the problem of reconstructing a graph from a
collection of local neighborhoods. In this paper, we consider shotgun assembly
of \ER random graphs $G(n, p_n)$, where $p_n = n^{-\alpha}$ for $0 < \alpha <
1$. We consider both reconstruction up to isomorphism as well as exact
reconstruction (recovering the vertex labels as well as the structure). We show
that given the collection of distance-$1$ neighborhoods, $G$ is exactly
reconstructable for $0 < \alpha < \frac{1}{3}$, but not reconstructable for
$\frac{1}{2} < \alpha < 1$. Given the collection of distance-$2$ neighborhoods,
$G$ is exactly reconstructable for $\alpha \in \left(0, \frac{1}{2}\right) \cup
\left(\frac{1}{2}, \frac{3}{5}\right)$, but not reconstructable for
$\frac{3}{4} < \alpha < 1$.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/22-ECP445
