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Emerging location-based systems and data analysis frameworks requiresefficient management of spatial data for approximate and exact search. Exactsimilarity search can be done using space partitioning data structures, such asKd-tree, R*-tree, and Ball-tree. In this paper, we focus on Ball-tree, anefficient search tree that is specific for spatial queries which use euclideandistance. Each node of a Ball-tree defines a ball, i.e. a hypersphere thatcontains a subset of the points to be searched.  In this paper, we propose Ball*-tree, an improved Ball-tree that is moreefficient for spatial queries. Ball*-tree enjoys a modified space partitioningalgorithm that considers the distribution of the data points in order to findan efficient splitting hyperplane. Also, we propose a new algorithm for KNNqueries with restricted range using Ball*-tree, which performs better than bothKNN and range search for such queries. Results show that Ball*-tree performs39%-57% faster than the original Ball-tree algorithm.

Ball*-tree: Efficient spatial indexing for constrained nearest-neighbor search in metric spaces