FRAM: Frobenius-Regularized Assignment Matching with Mixed-Precision Computing

Graph matching, usually cast as a discrete Quadratic Assignment Problem (QAP), aims to identify correspondences between nodes in two graphs. Since QAP is NP-hard, many methods its discrete constraints by projecting the discrete feasible set onto its convex hull and solving the resulting continuous problem. However, these relaxations inevitably enlarge the feasible set and introduce two errors: sensitivity to numerical scales and geometric misalignment between the relaxed and original feasible domains. To address these issues, we propose a novel relaxation framework to reformulate the projection step as a Frobenius-Regularized Linear Assignment (FRA) problem. This formulation incorporates a tunable regularization term to curb the inflation of the feasible region and ensure numerical scale invariance.