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 …

The science of networks represented a substantial change in the way we see natural and
technological phenomena. Now we have a better understanding that networks are, in most …

In the graph shotgun assembly problem, we are given the balls of radius $ r $ around each
vertex of a graph and asked to reconstruct the graph. We study the shotgun assembly of the …

In the shotgun assembly problem for a graph, we are given the empirical profile for rooted
neighborhoods of depth (up to isomorphism) for some and we wish to recover the underlying …

Given a positive integer n, an unlabeled graph G on n vertices, and a vertex v of G, let\(N_G
(v)\) be the subgraph of G induced by vertices of G of distance at most one from v. We show …

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 Erdős–Rényi random …

Given a random binary picture P n P _n of size nn, that is, an n× nn * n grid filled with zeros
and ones uniformly at random, when is it possible to reconstruct P n P _n from its kk‐deck …

We consider the shotgun assembly problem for a random jigsaw puzzle, introduced by
Mossel and Ross (2015). Their model consists of a puzzle—an n× n grid, where each vertex …

Mossel and Ross raised the question of when a random coloring of a graph can be
reconstructed from local information, namely, the colorings (with multiplicity) of balls of given …

Given some binary matrix, suppose we are presented with the collection of its rows and
columns in independent arbitrary orderings. From this information, can we recover the …