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

Abstract

The reverse k nearest neighbors (RkNN) 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 RkNN 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 RkNN set. With CSD, only a small fraction of candidates require costly k nearest neighbors (kNN) 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 RkNN algorithm named CSD-RkNN. A comprehensive set of experiments is conducted to compare CSD-RkNN with Slice as the state-of-the-art RkNN algorithm, and VR-RkNN as the original RkNN algorithm on VoR-tree. The results indicate that CSD-RkNN consistently outperforms the other two algorithms, especially when k is relatively large.