Partial Recovery in the Graph Alignment Problem

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