Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs

In pattern recognition applications, it is useful to represent objects by attributed graphs considering their structural properties. Besides, some graph matching problems need a Common Labelling between vertices of a set of graphs. Computing this Common Labelling is an NP-complete problem. State of the-art algorithms are composed by two steps: in the first, they compute all pairwise labellings among the graphs and in the second, they combine this information to obtain a Common Labelling. The drawback of these methods is that global information is only considered in the second step. To solve this problem, by reducing the Common Labelling problem to the quadratic assignment one, all graphs nodes are labelled to a virtual structure whereby the Common Labeling is generated using global information. We tested the algorithm on both real-world and synthetic data. We show that the algorithm offers better performance than a reference method with same computational cost.