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Fixed-radius near neighbor search is a fundamental data operation thatretrieves all data points within a user-specified distance to a query point.There are efficient algorithms that can provide fast approximate queryresponses, but they often have a very compute-intensive indexing phase andrequire careful parameter tuning. Therefore, exact brute force and tree-basedsearch methods are still widely used. Here we propose a new fixed-radius nearneighbor search method, called SNN, that significantly improves over bruteforce and tree-based methods in terms of index and query time, provably returnsexact results, and requires no parameter tuning. SNN exploits a sorting of thedata points by their first principal component to prune the query search space.Further speedup is gained from an efficient implementation using high-levelBasic Linear Algebra Subprograms (BLAS). We provide theoretical analysis of ourmethod and demonstrate its practical performance when used stand-alone and whenapplied within the DBSCAN clustering algorithm.

Fast and exact fixed-radius neighbor search based on sorting