Relaxed reverse nearest neighbors queries

Given a set of users U, a set of facilities F, and a query facility q, a reverse nearest neighbors (RNN) query retrieves every user u for which q is its closest facility. Since q is the closest facility of 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 relaxed reverse nearest neighbors (RRNN) queries. Formally, given a value of x > 1, an RRNN query q returns every user u for which dist(u, q) ≤ x × NNDist(u) where NNDist(u) denotes the distance between a user u and its nearest facility. Based on effective pruning techniques and several non-trivial observations, we propose an efficient RRNN query processing algorithm. Our extensive experimental study conducted on several real and synthetic data sets demonstrates that our algorithm is several orders of magnitude better than a naïve algorithm as well as a significantly improved version of the naïve algorithm.