Variations of Nearest Neighbor Queries in Euclidean Space

Synonyms

Aggregate nearest neighbor queries; Constrained nearest neighbor queries; Reverse nearest neighbor queries

Definition

There are several variations of nearest neighbor (NN) queries. Some of the variations are based on constraining the search space, some change the distance function, and some of them reverse the objective by searching for the objects having a given object as their NN. In this entry, we present in detail a specific query from each category.

Constrained nearest neighbor query. Given a set P of points in a d-dimensional space $\mathbb{R}^{d}$, a query point q, and a subset R of $\mathbb{R}^{d}$, called the constrained region, the constrained nearest neighbor query finds the nearest point in P, which belongs to region R. Formally, $CNN(q)\ =\ \{p\vert p \in P \cap R,\forall p' \in P \cap \ R,dist(q,p) \leq dist(q,p')\}$, where dist() is the Euclidean distance function.

Reverse nearest neighbor query. Given a set P of points in a d-dimensional space \(\mathbb{R}^{d}\)...