On Tighter Inequalities for Efficient Similarity Search in Metric Spaces

Similarity search consists of the efficient retrieval of relevant information satisfying user formulated query conditions from a database with prebuilt indexing structures. Since the evaluation of the distance functions between queries and indexed objects is often computationally expensive, there have been many attempts to build indexing structures that use as few distance computations as possible to answer queries. Among these methods, for 20 years the Approximating and Eliminating Search Algorithm (AESA) has been the baseline in terms of the required distance computations. By storing a pre-computed inter-object distance matrix, AESA is able to extensively apply the triangle-inequality based pruning rules to avoid unnecessary distance computations. In this paper, to further improve the performance of AESA, we introduce a novel group of pruning rules that are proven to be tighter than the triangleinequality based rules and hence can further reduce the number of distance computations during the search. The new pruning rules require the assumption of positive semi-definite metric space models and can be used in most modern applications. With some slight modification, they can be easily extended to search algorithms in general metric spaces. In the simulations, when incorporated with the proposed pruning rules, AESA showed a significant improvement in distance-computation reduction. For low dimensional problems, applying the new pruning rules cut the distance computations in half, and for high dimensional problems, the reduction was sometimes more than 90%. The pruning rules were also applied to LAESA, a variant of AESA which imposes a linear storage requirement. For this algorithm, they not only helped to save more distance computations, but considerably reduced the storage requirement as well.