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The reverse  k  nearest neighbors (R k NN) query is a prominent yet time-consuming spatial query used in facility siting, influential domain analysis, potential customer analysis, etc. Its aim is to identify all points that consider the query point as one of their  k  closest points. However, when  k  is relatively large (e.g.  k  = 1000), existing R k NN techniques often struggle to provide acceptable response times (within a few seconds). To address this issue, we propose a verification approach called conic section discriminance (CSD). This method serves to determine whether points belong to the R k NN set. With CSD, only a small fraction of candidates require costly  k  nearest neighbors ( k NN) queries for verification, while the rest can be rapidly verified with  O (1) complexity. Furthermore, we propose a Voronoi-based candidate generation approach to curtail the candidate set size. By leveraging the VoR-tree structure, we integrate these two approaches to form a novel R k NN algorithm named CSD-R k NN. A comprehensive set of experiments is conducted to compare CSD-R k NN with  Slice  as the state-of-the-art R k NN algorithm, and VR-R k NN as the original R k NN algorithm on VoR-tree. The results indicate that CSD-R k NN consistently outperforms the other two algorithms, especially when  k  is relatively large.

CSD-R k NN: reverse k nearest neighbors queries with conic section discriminances