Nearest Neighbor Query

Given a set P of n points in a d-dimensional space ℜ d and a query point q ∈ ℜ d , a nearest neighbor (NN) query is to find the set of nearest points to the query point q. Formally, NNq = p | p ∈ P, ∀ o ∈ P, (o ≠ p), | qp | < qo. In most cases, ℜ d refers to a d-dimensional Euclidean space.