Faster subgraph isomorphism detection by well-founded total order indexing

In this paper an extension to index-based subgraph matching is proposed. This extension significantly speeds up the indexing time for graphs where the nodes are labeled with a rather small amount of different classes. Furthermore, the needed storage amount is significantly reduced. In order to reduce the complexity, we introduce a weight function for labeled graphs. Using this weight function, a well-founded total order is defined on the weights of the labels. Inversions which violate the order are not allowed. A computational complexity analysis of the new preprocessing is given and its completeness is proven. Furthermore, in a number of practical experiments with randomly generated graphs the improvement of the new approach is shown. In experiments performed on random sample graphs, and on real-world datasets. The number of permutations for the real-world datasets have been decreased to a fraction of 10−5 and 10−8 in average compared to the original approach by Messmer. The novel indexing strategy makes indexing of larger graphs feasible, allowing for fast detection of subgraphs.

► We propose an extension to Messmer’s index-based exact subgraph matching.
► The average number of permutations has been decreased to a fraction of up to 10−18.
► The novel indexing strategy makes indexing of larger graphs feasible >19 vertices).