In this paper we define a new compact Hilbert index which, while maintaining all of the advantages of the standard Hilbert curve, permits spaces with unequal dimension cardinalities. The compact Hilbert index can be used in any application that would have previously relied on Hilbert curves but, in the case of unequal side lengths, provides a more memory efficient representation. This advantage...

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.

Numerical experiments in J. Maubach, Local bisection refinement and optimal order algebraic multilevel preconditioners, PRISM-97 conference Proceedings (eds. O. Axelsson et al), University of Nijmegen, the Netherlands, 1997, 121-136 indicated that the refinement with the use of local bisections presented in J. Maubach, Local bisection refinement for n-simplicial grids generated by reflections, ...

This paper proposes a new multi-start, stochastic global optimization algorithm that uses dimensional reduction techniques based upon approximations of space-filling curves and simulated annealing, aiming to find global minima of real-valued (possibly multimodal) functions that are not necessarily well behaved, that is, are not required to be differentiable, continuous, or even satisfying Lipsc...

Ever increasing computer performance, along with significant developments in CADI CAM technology and high precision digital motion controllers lead to rapid and significant developments in the field of rapid prototypingjfabrication. Together, these elements offer a wide range of possible approaches in the toolpath planning issue; two main sets have been analyzed and applied to Fused Deposition ...

This article describes sixteen different ways to traverse d-dimensional space recursively in a way that is well-defined for any number of dimensions. Each of these traversals has distinct properties that may be beneficial for certain applications. Some of the traversals are novel, some have been known in principle but had not been described adequately for any number of dimensions, some of the t...

The establishment of several large area monitoring networks over the past few decades has led to increased research into ways to spatially balance sample locations across the landscape. Many of these methods are well documented and have been used in the past with great success. In this paper, we present a method using geographic information systems (GIS) and fractals to create a sampling frame,...

The availability of a wide set of multidimensional information sources in different application fields (e.g., color cameras, multispectral remote sensing imagery devices, etc.) is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering. A new approach to multidimensional median filtering is presented. The ...

A database is populated with a set of points represented by n-tuples of real numbers. A query consists of a point q (not necessarily in the database) and an integer k, asking for the k "nearest" database points to the query point. The exact output for the query consists of the k nearest points, but if the database is large and a quick response is required, a good approximate output is sought. A...