Improving Reverse k Nearest Neighbors Queries

TL;DR

This paper introduces a new efficient algorithm for reverse k nearest neighbor queries using conic-based verification on VoR-tree, significantly outperforming existing methods in computational efficiency.

Contribution

The paper presents a novel conic-based verification method for RkNN queries and implements an efficient algorithm on VoR-tree with improved complexity.

Findings

Our algorithm achieves higher efficiency than state-of-the-art methods.

Experimental results confirm significant performance improvements.

Complexity is reduced to O(k^{1.5} log k) for RkNN verification.

Abstract

The reverse $k$ nearest neighbor query finds all points that have the query point as one of their $k$ nearest neighbors, where the $k$NN query finds the $k$ closest points to its query point. Based on conics, we propose an efficent R$k$NN verification method. By using the proposed verification method, we implement an efficient R$k$NN algorithm on VoR-tree, which has a computational complexity of $O(k^{1.5}\cdot log\,k)$. The comparative experiments are conducted between our algorithm and other two state-of-the-art R$k$NN algorithms. The experimental results indicate that the efficiency of our algorithm is significantly higher than its competitors.