Abstract—This paper develops an algorithm for NMR backbone resonance assignment given a 3D structure and a set of relatively sparse 15 N-edited NMR data, with the through-space 15 N-edited NOESY as the primary source of information. Our approach supports high-throughput solution studies of dynamics and interactions (e.g., ligand binding), when the structure has previously been determined by crystallography or modeled computationally. We employ a graph matching approach, identifying correspondence between a given contact graph and a corrupted version representing the NMR data. Our hierarchical grow-andmatch algorithm decomposes the contact graph into sequential fragments with relatively dense interactions, and then combines possible assignments for the fragments, searching over the combinations with effective but conservative pruning. Our algorithm is complete, guaranteed to identify all solutions consistent with the data within a likelihood threshold of the optimal solution. It also ...