Nearest-Neighbor Searching Under Uncertainty I.

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor ( $$\mathop {\mathrm {ENN}}$$ ). We present methods for computing an exact $$\mathop {\mathrm {ENN}}$$ or an $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ , for a given error parameter $$0<\varepsilon < 1$$ , under different distance functions. These methods build a data structure of near-linear size and answer $$\mathop {\mathrm {ENN}}$$ queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or $$\varepsilon $$ -approximate $$\mathop {\mathrm {ENN}}$$ queries with provable performance guarantees. Moreover, we extend our results to answer exact or $$\varepsilon $$ -approximate k- $$\mathop {\mathrm {ENN}}$$ queries. [ABSTRACT FROM AUTHOR]