Ranked reverse nearest neighbor search

Abstract—Given a set of data points P and a query point q in a multidimensional space, Reverse Nearest Neighbor (RNN) query finds data points in P whose nearest neighbors (NNs) are q. Reverse k-NN ðRkNNÞ query (where k 1) generalizes RNN query to find data points whose kNNs include q. For RkNN query semantics, q is said to have an influence on all those answer data points. The degree of q’s influence on a data point p ð2 PÞ is denoted by p, where q is the pth NN of p. We introduce a new variant of RNN query, namely, Ranked RNN (RRNN) query, that retrieves t data points most influenced by q, i.e., the t data points having the smallest s with respect to q. To answer this RRNN query efficiently, we propose two novel algorithms,-Counting and-Browsing that are applicable to both monochromatic and bichromatic scenarios and are able to deliver results progressively. Through an extensive performance evaluation, we validate that the two proposed RRNN algorithms are superior to solutions derived from algorithms designed for RkNN query. Index Terms—Reverse Nearest Neighbor query, ranking, search algorithm.