Partial Recovery in the Graph Alignment Problem

07/01/2020
by   Georgina Hall, et al.
0

In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on partial recovery, i.e., we look for a one-to-one mapping which is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated Erdös-Rényi graphs of parameters (n,q,s). Our main contribution is then to give necessary and sufficient conditions on (n,q,s) under which partial recovery is possible with high probability as the number of nodes n goes to infinity. In particular, we show that it is possible to achieve partial recovery in the nqs=Θ(1) regime under certain additional assumptions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/04/2021

Impossibility of Partial Recovery in the Graph Alignment Problem

Random graph alignment refers to recovering the underlying vertex corres...
research
09/10/2018

Partial Recovery of Erdős-Rényi Graph Alignment via k-Core Alignment

We determine information theoretic conditions under which it is possible...
research
04/05/2019

Learning Erdős-Rényi Graphs under Partial Observations: Concentration or Sparsity?

This work examines the problem of graph learning over a diffusion networ...
research
10/16/2020

Joint Inference of Multiple Graphs from Matrix Polynomials

Inferring graph structure from observations on the nodes is an important...
research
07/22/2021

Recovering lost and absent information in temporal networks

The full range of activity in a temporal network is captured in its edge...
research
11/05/2021

Strong Recovery In Group Synchronization

The group synchronization problem is to estimate unknown group elements ...
research
09/25/2015

Information Limits for Recovering a Hidden Community

We study the problem of recovering a hidden community of cardinality K f...

Please sign up or login with your details

Forgot password? Click here to reset