in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

We explore the eeect of dimensionality on the \nearest neigh-bor" problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as di-mensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective , we present empirical results on both real and s...

w0-Nearest Points and w0-Farthest Point in Normed Linear Spaces

DEFINITION Given a set of n points and a query point, q, the nearest-neighbor problem is concerned with finding the point closest to the query point. Figure 1 shows an example of the nearest neighbor problem. On the left side is a set of n = 10 points in a two-dimensional space with a query point, q. The right shows the problem solution, s. Figure 1: An example of a nearest-neighbor problem dom...

Given a query point q and a set D of data points, a nearest neighbor (NN) query returns the data point p in D that minimizes the distance DIST(q,p), where the distance function DIST(,) is the L2 norm. One important variant of this query type is kNN query, which returns k data points with the minimum distances. When taking the temporal dimension into account, the kNN query result may change over...