Reverse nearest neighbor queries in fixed dimension

Reverse nearest neighbor queries are defined as follows: Given an input point-set P, and a query point q, find all the points p in P whose nearest point in P U {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).