Graph Matching in Random Geometric Graphs I: Efficient Algorithms

We study the recovery of the hidden vertex correspondence between two correlated dense random geometric graphs. Each graph is generated from $n$ latent unit vectors in $\mathbb R^d$; the vectors $u_i^A$ and $u_i^B$ of corresponding vertices satisfy $\langle u_i^A,u_i^B\rangle=ρ$, and the vertex labe