The authors of the present paper previously introduced a fast approximation framework for the graph edit distance problem. The basic idea of this approximation is to build a square cost matrix C = (C_(ij)), where each entry C_(ij) 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 is established in polynomial time. Yet, this procedure considers the graph structure only in a local way, and thus, an overestimation of the true graph edit distance has to be accepted. The present paper aims at reducing this overestimation by means of an additional greedy search strategy that builds upon the initial assignment. In an experimental evaluation on three real world data sets we empirically verify a substantial gain of distance accuracy while run time is nearly not affected.
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