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.