Improving Graph Edit Distance Approximation by Centrality Measures

Abstract

In recent years the authors of the present paper introduced a powerful approximation fra or the graph edit distance problem. The basic idea of this approximation is to build a square cost matrix C = (cj), where each entry reflects the cost of a node substitution, deletion or insertion plus the matching cost arising from the local edge structure. Based on C an optimal assignment of the nodes and their local structure can be established in polynomial time (using, for instance, the Hungarian algorithm). Since this approach considers the local -- rather than the global -- structural properties of the graphs only, the obtained graph edit distance value is suboptimal in the sense of overestimating the true edit distance in general. The present paper pursues the idea of including topological information in the node labels in order to increase the amount of structural information available during the initial assignment process. In an experimental evaluation on three real world data sets a reduction of the overestimation can be observed while the run time is only moderately increased compared to our original framework.