Approximating the Graph Edit Distance with Compact Neighborhood Representations

Franka Bause, Christian Permann, Nils M. Kriege

Abstract: The graph edit distance, used for comparing graphs in various domains, is often approximated due to its high computational complexity. Widely used heuristics search for an optimal assignment of vertices based on the distance between local substructures. However, some sacrifice accuracy by only considering direct neighbors, while others demand intensive distance calculations. Our method abstracts local substructures to neighborhood trees, efficiently comparing them using tree matching techniques. This yields a ground distance for vertex mapping, delivering high quality approximations of the graph edit distance. By limiting the maximum tree height, our method offers to balance accuracy and computation speed. We analyze the running time of the tree matching method and propose techniques to accelerate computation in practice, including compressed tree representations, tree canonization to identify redundancies, and caching. Experimental results demonstrate significant improvements in the trade-off between running time and approximation quality compared to existing state-of-the-art approaches.