Geometric Graph Indexing for Similarity Search in Scientific Databases

Abstract

Searching a database for similar graphs is a critical task in many scientific applications, such as in drug discovery, geoinformatics, or pattern recognition. Typically, graph edit distance is used to estimate the similarity of non-identical graphs, which is a very hard task. Several indexing structures and lower bound distances have been proposed to prune the search space. Most of them utilize the number of edit operations and assume graphs with a discrete label alphabet that has a certain canonical order. Unfortunately, such assumptions cannot be guaranteed for geometric graphs where vertices have coordinates in some two dimensional space. In this paper, we study similarity range queries for geometric graphs with edit distance constraints. First, we propose an efficient index structure to discover similar vertices. For this, we embed the vertices of different graphs in a higher dimensional space, which are then indexed using the well-known R-tree. Second, we propose three lower bound distances to filter non-similar graphs with different pruning power and complexity. Using representative geometric graphs extracted from a variety of application domains, namely chemoinformatics, character recognition, and image analysis, our framework achieved on average a pruning performance of 94% with 77% reduction in the response time.