Compact Similarity Joins

Similarity joins have attracted significant interest, with applications in geographical information systems, astronomy, marketing analyzes, and anomaly detection. However, all the past algorithms, although highly fine-tuned, suffer an output explosion if the query range is even moderately large relative to the local data density. Under such circumstances, the response time and the search effort are both almost quadratic in the database size, which is often prohibitive. We solve this problem by providing two algorithms that find a compact representation of the similarity join result, while retaining all the information in the standard join. Our algorithms have the following characteristics: (a) they are at least as fast as the standard similarity join algorithm, and typically much faster, (b) they generate significantly smaller output, (c) they provably lose no information, (d) they scale well to large data sets, and (e) they can be applied to any of the standard tree data structures. Experiments on real and realistic point-sets show that our algorithms are up to several orders of magnitude faster.