Research on the Optimal Methods for Graph Edit Distance

Graph edit distance is an important way to measure the similarity of pairwise graphs and has been widely used to bioinformatics, chemistry, social networks, etc. However, the expensive computation of graph edit distance poses serious algorithmic challenges. One of recent methodologies to obtain graph edit distance is to search the vertex mapping. In existing methods, A-Star heuristic search and pruning are used to improve the performance, but they still suffer huge temporal-spatial consumption and loose lower bound. In this paper, based on the heuristic A-Star search methods, three optimal methods are proposed to improve the mapping search strategy. First, a pruning strategy based on Symmertry-Breaking is proposed which defines the concept of mapping-equivalence, and prunes before the equivalence mappings are extended. Second, a pruning strategy based on upper bound is proposed to filter invalid mappings in the priority queue to speed up the search time, which uses Hungarial algorithm to obtain the upper bound. Third, the dequeued order is specified for the mappings in the priority queue with the same lower bound of the edit cost. Experiments on real datasets show that our methods have significant temporal-spatial optimal results