Greedy Graph Edit Distance

In pattern recognition and data mining applications, where the underlying data is characterized by complex structural relationships, graphs are often used as a formalism for object representation. Yet, the high representational power and flexibility of graphs is accompanied by a significant increase of the complexity of many algorithms. For instance, exact computation of pairwise graph dissimilarity, i.e. distance, can be accomplished in exponential time complexity only. A previously introduced approximation framework reduces the problem of graph comparison to an instance of a linear sum assignment problem which allows graph dissimilarity computation in cubic time. The present paper introduces an extension of this approximation framework that runs in quadratic time. We empirically confirm the scalability of our extension with respect to the run time, and moreover show that the quadratic approximation leads to graph dissimilarities which are sufficiently accurate for graph based pattern classification.