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 …

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 …

We propose a novel mathematical framework to address the problem of automatically
solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal …

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 …

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 …

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 …

In a recent paper [6], J. Gaudio and E. Mossel studied the shotgun assembly of the Erd\H {o}
sR\'enyi graph $\mathcal G (n, p_n) $ with $ p_n= n^{-\alpha} $, and showed that the graph …

A random jigsaw puzzle is constructed by arranging $ n^ 2$ square pieces into an $ n\times
n $ grid and assigning to each edge of a piece one of $ q $ available colours uniformly at …

We consider a problem introduced by Mossel and Ross ('Shotgun assembly of labeled
graphs', arXiv: 1504.07682). Suppose a random n× n jigsaw puzzle is constructed by …

In this thesis we explore a novel combinatorial reconstruction problem. Starting with some
random binary matrix M, suppose we are presented with the collection of its rows and …