The analysis of a probabilistic approach to nearest neighbor searching

Given a set S of n data points in some metric space. Given a query point q in this space, a nearest neighbor query asks for the nearest point of S to q. Throughout we will assume that the space is real d-dimensional space Rd, and the metric is Euclidean distance. The goal is to preprocess S into a data structure so that such queries can be answered efficiently. Nearest neighbor searching has applications in many areas, including data mining [7], pattern classification [5], data compression [10].