Reverse Approximate Nearest Neighbor Queries

Given a set of facilities and a set of users, a reverse nearest neighbors (RNN) query retrieves every user u for which the query facility q is its closest facility. Since q is the closest facility to u, the user u is said to be influenced by q. In this paper, we propose a relaxed definition of influence where a user u is said to be influenced by not only its closest facility but also every other facility that is almost as close to u as its closest facility is. Based on this definition of influence, we propose reverse approximate nearest neighbors (RANN) queries. Formally, given a value x > 1, an RANN query q returns every user u for which dist (u,q) <= x x NNDist(u) where NNDis(u) denotes the distance between a user u and its nearest facility, i.e., q is an approximate nearest neighbor of u. In this paper, we study both snapshot and continuous versions of RANN queries. In a snapshot RANN query, the underlying data sets do not change and the results of a query are to be computed only once. In the continuous version, the users continuously change their locations and the results of RANN queries are to be continuously monitored. Based on effective pruning techniques and several non-trivial observations, we propose efficient RANN query processing algorithms for both the snapshot and continuous RANN queries. We conduct extensive experiments on both real and synthetic data sets and demonstrate that our algorithm for both snapshot and continuous queries are significantly better than the competitors.