An Efficient Algorithm for Reverse Furthest Neighbors Query with Metric Index

The variants of similarity queries have been widely studied in recent decade, such as k-nearest neighbors (k-NN), range query, reverse nearest neighbors (RNN), an so on. Nowadays, the reverse furthest neighbor (RFN) query is attracting more attention because of its applicability. Given an object set O and a query object q, the RFN query retrieves the objects of O, which take q as their furthest neighbor. Yao et al. proposed R-tree based algorithms to handle the RFN query using Voronoi diagrams and the convex hull property of dataset. However, computing the convex hull and executing range query on R-tree are very expensive on the fly. In this paper, we propose an efficient algorithm for RFN query with metric index. We also adapt the convex hull property to enhance the efficiency, but its computation is not on the fly. We select external pivots to construct metric indexes, and employ the triangle inequality to do efficient pruning by using the metric indexes. Experimental evaluations on both synthetic and real datasets are performed to confirm the efficiency and scalability.