Capacitated p-median problem (CPMP) is a well-known facility-location problem, in which p capacitated facility points are selected to satisfy n demand points in such a way that the total assigned demand to each facility does not exceed its capacity. Minimizing the total sum of distances between each demand point and its nearest facility point is the objective of the problem. Developing an effic...

This paper studies nearest neighbor classification in a model where unlabeled data points arrive in a stream, and the learner decides, for each one, whether to ask for its label. Are there generic ways to augment or modify any selective sampling strategy so as to ensure the consistency of the resulting nearest neighbor classifier?

A fast nearest neighbor algorithm for pattern classiication is proposed and tested on real data. The patterns (points in d-dimensional Euclidean space) are sorted along a space-lling curve. This way the multidi-mensional problem is compressed to the simplest case of the nearest neighbor search in one dimension.

This paper presents kinetic data structures (KDS’s) for maintaining the Semi-Yao graph, all the nearest neighbors, and all the (1 + )-nearest neighbors of a set of moving points in R. Our technique provides the first KDS for the SemiYao graph in R. It generalizes and improves on the previous work on maintaining the Semi-Yao graph in R. Our KDS for all nearest neighbors is deterministic. The bes...

Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability that an arbitrary point is the mth nearest neighbor to its own nth nearest neighbor (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we p...

Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel graph and the k-Delaunay graph. For k = 0 (k = 1 in the case...

We introduce a novel algorithm for solving the nearest neighbour problem when the query points are known in advance, which is based on Fortune’s plane sweep algorithm. The crucial idea is to use the wavefront for solving the nearest neighbour queries as the Voronoi diagram is being computed, instead of storing it in an auxiliary data structure, as the algorithm presented by Lee and Yang does, a...

Algorithms that use point-cloud models make heavy use of the neighborhoods of the points. These neighborhoods are used to compute the surface normals for each point, mollification, and noise removal. All of these primitive operations require the seemingly repetitive process of finding the k nearest neighbors of each point. These algorithms are primarily designed to run in main memory. However, ...

When we have two data sets and want to find the nearest neighbour of each point in the first dataset among points in the second one, we need the all nearest neighbour operator. This is an operator in spatial databases that has many application in different fields such as GIS and VLSI circuit design. Existing algorithms for calculating this operator assume that there is no pre computation on the...

Finding point correspondences between two views is generally based on the matching of local photometric descriptors. A subsequent geometric constraint ensures that the set of matching points is consistent with a realistic camera motion. Starting from a paper by Moisan and Stival, we propose an a contrario model for matching interest points based on descriptor similarity and geometric constraint...