# Fusion Moves for Graph Matching

arXiv: https://arxiv.org/abs/2101.12085 · HTML: https://mlsanity.com/paper/2101.12085/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 59 references that are in the map.
- First posted on arXiv 28 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [Deep Graph Matching Consensus](https://mlsanity.com/paper/2001.09621/) (2020)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching](https://mlsanity.com/paper/1612.05476/) (2016)
- [DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems](https://mlsanity.com/paper/1711.10733/) (2017)
- [A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems](https://mlsanity.com/paper/1404.0533/) (2014)
- [MPLP++: Fast, Parallel Dual Block-Coordinate Ascent for Dense Graphical Models](https://mlsanity.com/paper/2004.08227/) (2020)
- [GLMNet: Graph Learning-Matching Networks for Feature Matching](https://mlsanity.com/paper/1911.07681/) (2019)
- [Discrete graphical models -- an optimization perspective](https://mlsanity.com/paper/2001.09017/) (2020)
- [Taxonomy of Dual Block-Coordinate Ascent Methods for Discrete Energy Minimization](https://mlsanity.com/paper/2004.07715/) (2020)
- [A Dual Ascent Framework for Lagrangean Decomposition of Combinatorial Problems](https://mlsanity.com/paper/1612.05460/) (2016)
- [Exact MAP-Inference by Confining Combinatorial Search with LP Relaxation](https://mlsanity.com/paper/2004.06370/) (2020)

## Built on by (most cited first, 16 of 16)

- [A Comparative Study of Graph Matching Algorithms in Computer Vision](https://mlsanity.com/paper/2207.00291/) (2022)
- [It's a (Blind) Match! Towards Vision-Language Correspondence without Parallel Data](https://mlsanity.com/paper/2503.24129/) (2025)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [FastDOG: Fast Discrete Optimization on GPU](https://mlsanity.com/paper/2111.10270/) (2021)
- [DOGE-Train: Discrete Optimization on GPU with End-to-end Training](https://mlsanity.com/paper/2205.11638/) (2022)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Structured Prediction Problem Archive](https://mlsanity.com/paper/2202.03574/) (2022)
- [Review of Serial and Parallel Min-Cut/Max-Flow Algorithms for Computer Vision](https://mlsanity.com/paper/2202.00418/) (2022)
- [Unsupervised Deep Graph Matching Based on Cycle Consistency](https://mlsanity.com/paper/2307.08930/) (2023)
- [Optimizing Incomplete, Large-Scale and Sparse Multi-Graph Matching in Bioimaging](https://mlsanity.com/paper/2406.18215/) (2024)
- [Relative-Interior Solution for the (Incomplete) Linear Assignment Problem with Applications to the Quadratic Assignment Problem](https://mlsanity.com/paper/2301.11201/) (2023)
- [Normalized Matching Transformer](https://mlsanity.com/paper/2503.17715/) (2025)
- [Correlation Clustering of Organoid Images](https://mlsanity.com/paper/2403.13376/) (2024)
- [Cycle-Consistent Multi-Graph Matching for Self-Supervised Annotation of C.Elegans](https://mlsanity.com/paper/2503.07348/) (2025)
- [Graph Alignment via Dual-Pass Spectral Encoding and Latent Space Communication](https://mlsanity.com/paper/2509.09597/) (2025)
- [Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm](https://mlsanity.com/paper/2605.13402/) (2026)

## Abstract (arXiv)

We contribute to approximate algorithms for the quadratic assignment problem also known as graph matching. Inspired by the success of the fusion moves technique developed for multilabel discrete Markov random fields, we investigate its applicability to graph matching. In particular, we show how fusion moves can be efficiently combined with the dedicated state-of-the-art dual methods that have recently shown superior results in computer vision and bio-imaging applications. As our empirical evaluation on a wide variety of graph matching datasets suggests, fusion moves significantly improve performance of these methods in terms of speed and quality of the obtained solutions. Our method sets a new state-of-the-art with a notable margin with respect to its competitors.