Graph Matching Problem

Graph matching aims to find the optimal correspondence between nodes in two or more graphs, a fundamental problem with applications across diverse fields like computer vision and bioinformatics. Current research focuses on developing efficient algorithms, including those based on integer programming, SAT solvers, convex relaxations (like simplex methods and optimal transport), and deep learning approaches that leverage graph neural networks. These advancements address the NP-hard nature of the problem, striving for improved accuracy and scalability, particularly for large graphs and those with complex structures like communities. The resulting improvements in graph matching algorithms have significant implications for various applications, enabling more accurate and efficient solutions in areas such as data association, object recognition, and network analysis.