Kernel-based Similarity Search in Massive Graph Databases with Wavelet Trees

Similarity search in databases of labeled graphs is a fundamental task in managing graph data such as XML, chemical compounds and social networks. Typically, a graph is decomposed to a set of substructures (e.g., paths, trees and subgraphs) and a similarity measure is defined via the number of common substructures. Using the representation, graphs can be stored in a document database by regarding graphs as documents and substructures as words. A graph similarity query then translates to a semi-conjunctive query that retrieves graphs sharing at least k substructures in common with the query graph. We argue that this kind of query cannot be solved efficiently by conventional inverted indexes, and develop a novel recursive search algorithm on wavelet trees (Grossi et al., SODA’03). Unlike gIndex, it does not require frequent subgraph mining for indexing. In experiments, our method was successfully applied to 25 million chemical compounds.