A k-nearest neighbor (kNN) query, which retrieves nearest k points from a database is one of the fundamental query types in spatial databases. An all k-nearest neighbor query (AkNN query), a variation of a kNN query, determines the k-nearest neighbors for each point in the dataset in a query process. In this paper, we propose a method for processing AkNN queries in Hadoop. We decompose the give...

This paper examines the relationship between road directions and the rectilinear distance in regular point patterns. We derive the distributions of the rectilinear distances to the nearest and the second nearest points in rotated regular point patterns. These distributions demonstrate that road directions significantly affect the rectilinear distances. As an application of the nearest and the s...

In modern database applications the similarity of complex objects is examined by performing distance-based queries (e.g. nearest neighbour search) on data of high dimensionality. Most multidimensional indexing methods have failed to efficiently support these queries in arbitrary high-dimensional datasets (due to the dimensionality curse). Similarity join queries and K closest pairs queries are ...

Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point mi ∈ M with an independent probability pi. How difficult is it to compute elementary statistics about the closest pair of points in such a subset? For instance, what is the probability that the distance between the closest pair of points in the random subset is no more ...

In this paper, we present our research on data analysis and nearest neighbor search problems. A nearest neighbor search problem is normally described as finding data point or data points from a data set that are closest to a given query point. It is used in many research and industrial fields. In our paper, we propose an approach that explores the meaning of K nearest neighbors from a new persp...

If we pick n random points uniformly in [0, 1]d and connect each point to its k−nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in [0, 1]d it suffices to connect every point to cd,1 log logn points chosen randomly among its cd,2 logn−nearest neighbors to ensure a giant component of size n− o(n) with high probability. Th...

The prediction of ship location has become an increasingly popular research hotspot in the field maritime transportation engineering, which benefits safety supervision and security. Existing methods based on motion characteristics have a large uncertainty cannot guarantee trajectory accuracy target ship. An improved method using k-nearest neighbor (KNN) is proposed this paper. expanded circle a...

The Reverse Nearest Neighbor (RNN) problem is to find all points in a given data set whose nearest neighbor is a given query point. Given a set of blue points and a set of red points, the bichromatic version of the RNN problem, for a query blue point, is to find all the red points whose blue nearest neighbour is the given query point. In this paper, we introduce and investigate new optimization...