Random graph matching refers to recovering the underlying vertex correspondence
between two random graphs with correlated edges; a prominent example is when the two …

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 …

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 …

We study the problem of recovering a planted matching in randomly weighted complete
bipartite graphs K n, n. For some unknown perfect matching M∗, the weight of an edge is …

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 …

We consider the problem of reconstructing a graph G in two natural sampling models: 1)
each sample corresponds to a random induced subgraph and 2) for a fixed adjacency matrix …

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 …

We study the problem of learning a node-labeled tree given independent traces from an
appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes …

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 …