Exact Combinatorial Optimization for Partial Permutation Synchronization

In permutation synchronization, the goal is to find globally cycle‐consistent correspondences from noisy pairwise matchings. In this work, unlike spectral relaxations that embed permutations into an orthogonal space and often result in inaccuracies, we maintain the problem in its original combinatorial form. By shifting the affinity spectrum to ensure positive semidefiniteness, we cast the trace‐maximization over partial permutations as a convex‐in‐P formulation. Our minorization-maximization scheme then replaces this with a sequence of exact linear‐assignment subproblems, the row-/column-sum constraints of which are totally unimodular, guaranteeing integral solutions with no rounding. This direct, combinatorial approach delivers a monotonic objective ascent, convergence to a KKT point, and achieves superior accuracy, cycle consistency, and runtime on image-matching benchmarks.