Reverse nearest neighbor queries are defined as follows: Given an input point-set P , and a query point q, find all the points p in P whose nearest point in P ∪ {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).

Reverse nearest neighbor queries are defined as follows: Given an input point-set P , and a query point q, find all the points p in P whose nearest point in P ∪ {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).

Finding the nearest point on a given 2D or 3D object computation is a problem that arises in many computer graphics applications, such as interactive modeling, rendering of implicit surfaces or collision detection. Unfortunately, for objects with complex geometry such as curves or surfaces, the computation cost becomes prohibitive as a minimization process acting in multiple dimensions has to b...

We propose a new approach for outlier detection, based on a new ranking measure that focuses on the question of whether a point is “important” for its nearest neighbors; using our notations low cumulative rank implies the point is central. For instance, a point centrally located in a cluster has relatively low cumulative sum of ranks because it is among the nearest neighbors of its own nearest ...

A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., “find all my nearest gas stations during my route from point s to point e”). The result contains a set of tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitiv...

We consider the linear complementarity problem (q, M) in which M is a positive definite symmetric matrix of order n. This problem is equivalent to a nearest point problem [/'; b] in which F = {A4, ..., A~} is a basis for R", b is a given point in R ' ; and it is required to find the nearest point in the simplicial cone Pos(F) to b. We develop an algorithm for solving the linear complementarity ...

We present results on executing point location queries in well-shaped meshes in R and R using the Jumpand-Walk paradigm. If the jump step is performed on a nearest-neighbour search structure built on the vertices of the mesh, we demonstrate that the walk step can be performed in guaranteed constant time. Constant time for the walk step holds even if the jump step starts with an approximate near...