Learning Heuristics to Reduce the Overestimation of Bipartite Graph Edit Distance Approximation

In data mining systems, which operate on complex data with structural relationships, graphs are often used to represent the basic objects under study. Yet, the high representational power of graphs is also accompanied by an increased complexity of the associated algorithms. Exact graph similarity or distance, for instance, can be computed in exponential time only. Recently, an algorithmic framework that allows graph dissimilarity computation in cubic time with respect to the number of nodes has been presented. This fast computation is at the expense, however, of generally overestimating the true distance. The present paper introduces six different post-processing algorithms that can be integrated in this suboptimal graph distance framework. These novel extensions aim at improving the overall distance quality while keeping the low computation time of the approximation. An experimental evaluation clearly shows that the proposed heuristics substantially reduce the overestimation in the existing approximation framework while the computation time remains remarkably low.