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 ...

The nearest neighbor problem is that of preprocessing a set P of n data points in Rd so that, given any query point q, the closest point in P to q can be determined efficiently. In the chromatic nearest neighbor problem, each point of P is assigned a color, and the problem is to determine the color of the nearest point to the query point. More generally, given k ≥ 1, the problem is to determine...

We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. The problem is to bound the communication complexity of the search for a nearest lattice point. Upper bounds have been developed in two recent works [3], [16]. Here we prove the optimality of a particular step in the derivation of th...

Nearest neighbor searching is a fundamental computational problem. A set of n data points is given in real d-dimensional space, and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported efficiently. Because data sets can be quite large, we are primarily interested in data structures that use only O...

Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an encoding which is essentially an ordinary 2’s complement representation with an appended round-bit. Not only is this rounding a constant time operation, so ...

We consider the problem of finding the nearest point (by Euclidean distance) in a simplicial cone to a given point, and develop an exterior penalty algorithm for it. Each iteration in the algorithm consists of a single Newton step following a reduction in the value of the penalty parameter. Proofs of convergence of the algorithm are given. Various other versions of exterior penalty algorithms f...

We present a parallel algorithm for k-nearest neighbor graph construction that uses Morton ordering. Experiments show that our approach has the following advantages over existing methods: (1) Faster construction of k-nearest neighbor graphs in practice on multi-core machines. (2) Less space usage. (3) Better cache efficiency. (4) Ability to handle large data sets. (5) Ease of parallelization an...

x Today I know that everything watches, that nothing goes unseen, and that even wallpaper has a better memory than ours. It isn't God in His heaven that sees all. A kitchen chair, a coat-hanger a half-filled ash tray, or the wood replica of a woman name Niobe, can perfectly well serve as an unforgetting witness to every one of our acts. – The tin drum, Gunter Grass 14.1 Hierarchical Representat...

In a spatial point set, clustering patterns (features) are difficult to locate due to the presence of noise. Previous methods, either using grid-based method or distance-based method to separate feature from noise, suffer from the parameter choice problem, which may produce different point patterns in terms of shape and area. This paper presents the Collective Nearest Neighbor method (CLNN) to ...

The computation of the minimum distance between a point and a surface is important for the applications such as CAD/CAM, NC verification, robotics and computer graphics. This paper presents a spherical clipping method to compute the minimum distance between a point and a clamped B-spline surface. The surface patches outside the clipping sphere which do not contain the nearest point are eliminat...