Nearest neighborhood search in spatial databases

Abstract

This paper proposes a group version of the nearest neighbor (NN) query, called the nearest neighborhood (NNH) query, which aims to find the nearest group of points, instead of one nearest point. Given a set O of points, a query point q, and a ρ-radius circle C, the NNH query returns the nearest placement of C to q such that there are at least k points enclosed by C. We present a fast algorithm for processing the NNH query based on the incremental retrieval of nearest neighbors using the Rtree structure on O. Our solution includes several techniques, to efficiently maintain sets of retrieved nearest points and identify their validities in terms of the closeness constraint of their points. These techniques are devised from the unique characteristics of the NNH search problem. As a side product, we solve a new geometric problem, called the nearest enclosing circle (NEC) problem, which is of independent interest. We present a linear expected-time algorithm solving the NEC problem using the properties of the NEC similar to those of the smallest enclosing circle. We provide extensive experimental results, which show that our techniques can significantly improve the query performance.

Neighborhood Query Processing and Surrounding Objects Retrieval in Spatial Databases: Applications and Algorithms

“…Definition 1. Neighborhood [3]. Given a set of users U , a distance parameter ρ and a positive integer k, a neighborhood w.r.t.…”

“…ρ and k denoted by NH(ρ, k), is a ρ-radius circle enclosing at least k users in U . [3]. Given a set of users U , a distance parameter ρ, a query location q and a positive integer k, a nearest neighborhood query finds the center of the nearest neighborhood NH(ρ, k) to q.…”

“…Both nearest neighborhoods (NNHs) and reverse nearest neighborhoods (RNHs) are modeled by nearest enclosing circles (NECs) [3,5] -a circle which is pulled towards the query. The motivation for this is that a neighborhood is always pulled towards the query facility (service center) by it its special deals.…”

“…NHQ Query Applications. There are many potential applications of NHQ queries in spatial databases [3] as discussed below.…”

“…Choi et al [3] have developed an efficient incremental algorithm to evaluate NHQ queries in spatial databases. The algorithm has two main steps:…”