Speeding Up Graph Edit Distance Computation with a Bipartite Heuristic

Graph edit distance is a dissimilarity measure for arbitrarily structured and arbitrarily labeled graphs. In contrast with other approaches, it does not suffer from any restrictions and can be applied to any type of graph, including hypergraphs [1]. Graph edit distance can be used to address various graph classification problems with different methods, for instance, k-nearest-neighbor classifier (k-NN), graph embedding classifier [2], or classification with graph kernel machines [3]. The main drawback of graph edit distance is its computational complexity which is exponential in the number of nodes of the involved graphs. Consequently, computation of graph edit distance is feasible for graphs of rather small size only. In order to overcome this restriction, a number of fast but suboptimal methods have been proposed in the literature (e.g. [4]). In the present paper we aim at speeding up the computation of exact graph edit distance. We propose to combine the standard tree search approach to graph edit distance computation with the suboptimal procedure described in [4]. The idea is to use a fast but suboptimal bipartite graph matching algorithm as a heuristic function that estimates the future costs. The overhead for computing this heuristic function is small, and easily compensated by the speed-up achieved in tree traversal. Since the heuristic function provides us with a lower bound of the future costs, it is guaranteed to return the exact graph edit distance of two given graphs.