We describe the implementation of a fast, dynamic, approximate, nearest-neighbor search algorithm that works well in fixed dimensions (d ≤ 5), based on sorting points coordinates in Morton (or z-) ordering. Our code scales well on multi-core/cpu shared memory systems. Our implementation is competitive with the best approximate nearest neighbor searching codes available on the web, especially fo...

The Nearest Neighbor Search problem is deened as follows: given a set P of n points, preprocess the points so as to eeciently answer queries that require nding the closest point in P to a query point q. If we are willing to settle for a point that is almost as close as the nearest neighbor, then we can relax the problem to the approximate Nearest Neighbor Search. Nearest Neighbor Search (exact ...

Distance to the kth nearest facility is important when facilities are closed Emergency facilities !! Hospitals !! Fire stations !! Refuges Facilities are closed because of accidents and disasters Analytical expressions for the kth nearest distance have been obtained Grid Random Grid Random For finding the relationship between the distances, we need the joint distribution Distribution of the kth...

We show that a Poisson cluster point process is a nearest-neighbour Markov point process 2] if the clusters have uniformly bounded diameter. It is typically not a nite-range Markov point process in the sense of Ripley and Kelly 12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighb...

In this paper, we present a fast and versatile algorithm which can rapidly perform a variety of nearest neighbor searches. Efficiency improvement is achieved by utilizing the distance lower bound to avoid the calculation of the distance itself if the lower bound is already larger than the global minimum distance. At the preprocessing stage, the proposed algorithm constructs a lower bound tree (...

Motivated by applications in computer vision and databases, we introduce and study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of data points, the goal of SNN is to design a data structure that, given a collection of queries, finds a collection of close points that are “compatible” with each other. Formally, we are given k query points Q = q1, · · · , qk, and a compatibi...