Title: Exact Combinatorial Optimization for Synchronization of Partial Multi-Matching
Primary area: optimization
Keywords: combinatorial optimization, minorization-maximization scheme, partial multi-matching, permutation synchronization

Abstract: 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 superior cycle consistency and accuracy on real image‐matching benchmarks at competitive runtimes.