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

TL;DR

FRAM introduces a Frobenius-regularized relaxation framework for graph matching that reduces errors and accelerates computation through mixed-precision architecture, significantly outperforming baseline methods.

Contribution

The paper proposes a novel Frobenius-regularized relaxation framework and a mixed-precision architecture for efficient and accurate graph matching.

Findings

FRAM outperforms baseline methods in CPU benchmarks.

Mixed-precision architecture achieves up to 370X speedup.

Negligible accuracy loss with mixed-precision implementation.

Abstract

Graph matching, typically formulated as a Quadratic Assignment Problem (QAP), seeks to establish node correspondences between two graphs. To address the NP-hardness of QAP, some existing methods adopt projection-based relaxations that embed the problem into the convex hull of the discrete domain. However, these relaxations inevitably enlarge the feasible set, introducing two sources of error: numerical scale sensitivity and geometric misalignment between the relaxed and original domains. To alleviate these errors, we propose a novel relaxation framework by reformulating the projection step as a Frobenius-regularized Linear Assignment (FRA) problem, where a tunable regularization term mitigates feasible region inflation. This formulation enables normalization-based operations to preserve numerical scale invariance without compromising accuracy. To efficiently solve FRA, we propose the Scaling Doubly Stochastic Normalization (SDSN) algorithm. Building on its favorable computational properties, we develop a theoretically grounded mixed-precision architecture to achieve substantial acceleration. Comprehensive CPU-based benchmarks demonstrate that FRAM consistently outperforms all baseline methods under identical precision settings. When combined with a GPU-based mixed-precision architecture, FRAM achieves up to 370X speedup over its CPU-FP64 counterpart, with negligible loss in solution accuracy.