Exact alignment recovery for correlated Erdős-Rényi graphs
This addresses a fundamental graph alignment problem for theoretical computer science and network analysis, with incremental contributions to threshold characterization.
The paper tackles the problem of perfectly recovering vertex correspondence between two correlated Erdős-Rényi graphs, determining the information-theoretic threshold for exact recovery under conditions with unbounded computational resources.
We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdős-Rényi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. We determine the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources.