High Dimensional Reverse Nearest Neighbor Queries

Abstract

Reverse Nearest Neighbor (RNN) queries are of particular interest in a wide range of applications such as decision support systems, profile based marketing, data streaming, document databases, and bioinformatics. The earlier approaches to solve this problem mostly deal with two dimensional data. However most of the above applications inherently involve high dimensions and high dimensional RNN problem is still unexplored. In this paper, we propose an approximate solution to answer RNN queries in high dimensions. Our approach is based on the strong correlation in practice between <i>k</i>-NN and RNN. It works in two phases. In the first phase the <i>k</i>-NN of a query point is found and in the next phase they are further analyzed using a novel type of query <i>Boolean Range Query (BRQ)</i>. Experimental results show that <i>BRQ</i> is much more efficient than both NN and range queries, and can be effectively used to answer RNN queries. Performance is further improved by running multiple <i>BRQ</i> simultaneously. The proposed approach can also be used to answer other variants of RNN queries such as RNN of order <i>k</i>, bichromatic RNN, and <i>Matching Query</i> which has many applications of its own. Our technique can efficiently answer NN, RNN, and its variants with approximately same number of I/O as running a NN query.