Speeding up Graph Matching by Means of Systematic Graph Reductions Using Centrality Measures

Comparing large graphs using graph edit distance is a time-consuming or even intractable problem. This is mainly due to the exponential time complexity of graph edit distance w.r.t. to the size of the underlying graphs. Nevertheless, considering its great adaptability, graph edit distance is a popular metric in structural pattern recognition and has found widespread applications. Main contribution of the present paper is to substantially speed up the computation of graph edit distance by initially reducing the graphs to the most important substructures. The graph downsizing is based on centrality measures - e.g. Page Rank -. That is, we systematically delete nodes including their edges from our graphs that offer the least level of influence to the overall graph structure. We empirically validate the benefit of our reduction method by classifying reduced graphs from a broad range of applications with a distance-based classifier. The main finding is that we can reduce the computation time by a wide margin while maintaining satisfying classification accuracy.