Partial Recovery in the Graph Alignment Problem

Abstract

Partially Recovering a Graph Alignment in the Correlated Erdös–Renyi Model Given two graphs, how can we partially recover a one-to-one mapping between nodes that maximizes edge overlap? This problem, known as the graph alignment problem, appears in settings such as social network deanonymization and cellular biology. In “Partial Recovery in the Graph Alignment Problem,” G. Hall and L. Massoulié consider a stylized mathematical model of problems of this type: they assume that the input graphs are generated via a probabilistic model, namely, the correlated Erdös–Renyi model with parameters (n, q, s). They provide both necessary and sufficient conditions on (n, q, s) under which partial recovery can be achieved. In particular, they show that partial recovery can be achieved in the nqs = Ɵ(1) regime under certain additional assumptions.