We address the problem of replicating a Voronoi diagram V (S) of a planar point set S by making proximity queries: 1. the exact location of the nearest site(s) in S 2. the distance to and label(s) of the nearest site(s) in S 3. a unique label for every nearest site in S. In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural al...

Given n data points in d-dimensional space, nearest neighbor searching involves determining the nearest of these data points to a given query point. Most average-case analyses of nearest neighbor searching algorithms are made under the simplifying assumption that d is xed and that n is so large relative to d that boundary eeects can be ignored. This means that for any query point the statistica...

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 (...

Given a set of sites in a simple polygon, a geodesic Voronoi diagram partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones form ≤ n/polylogn. Moreover, the algorithms for the ne...

We consider the Approximate Nearest Line Search (NLS) problem. Given a set L of N lines in the high dimensional Euclidean space R, the goal is to build a data structure that, given a query point q ∈ R, reports a line ` ∈ L such that its distance to the query is within (1+ ) factor of the distance of the closest line to the query point q. The problem is a natural generalization of the well-studi...

Given a closed set C in a Banach space (X, ‖ · ‖), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ‖x − z‖, where dC is the distance of x from C. We shortly survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta-convex functions and indicate how it is related to finding neare...

In the Nearest Neighbor problem (NN), the objects in the database that are nearer to a given query object than any other objects in the database have to be found. In the conceptually inverse problem, Reverse Nearest Neighbor problem (RNN), objects that have the query object as their nearest neighbor have to be found. Reverse Nearest Neighbors queries have emerged as an important class of querie...

This paper describes an enhanced clustering method for 3D point cloud data which is acquired from a laser range scanning system. The proposed method overcomes the instinctive problems of the vertical or horizontal scanning system. The acquired 3D laser range data for an autonomous vehicle has a disadvantage in that the point cloud data from the system is not equally distributed based on distanc...