We present a general space-filling curve algorithm for partitioning an arbitrary 3D mesh. We discuss communication patterns in Adaptive Mesh Refinement (AMR) applications and how we can reduce communication and improve the quality of partitions using a better space-filling curve. We compare the our partitions with those generated using Morton order, which is currently used by majority of AMR so...

The analysis of spatial data occurs in many disciplines and covers a wide variety activities. Available techniques for such analysis include spatial interpolation which is useful for tasks such as visualization and imputation. This paper proposes a novel approach to interpolation using space-filling curves. Two simple interpolation methods are described and their ability to interpolate is compa...

Kolmogorov superpositions and Hecht-Nielsen's neural network based on them are dimension reducing. This dimension reduction can be understood in terms of space-filling curves that characterize Kolmogorov's functions, and the subject of this paper is the construction of such a curve. We construct a space-filling curve with Lebesgue measure 1 in the unit square, [0,1]2, with approximating curves ...

The Zoltan dynamic load balancing library provides applications with a reusable object oriented interface to several load balancing techniques, including coordinate bisection, octree/space filling curve methods, and multilevel graph partitioners. We describe enhancements to Zoltan’s octree load balancing procedure and its distributed structures that improve performance of the space filling curv...

Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The linearization is often achieved by constructing a space filling curve inside the domain. But existing methods cannot handle networks distributed on surfaces of complex topology. This paper presents a novel method for generati...

We present a simple and efficient algorithm to compute cache-friendly layouts of unstructured geometric data. Coherent mesh layouts minimize cache misses and page faults by laying out vertices, triangles or tetrahedra in a spatially structured manner. Recently, Yoon et al. have shown that it is possible to construct an optimal cache-oblivious mesh layout (COML) for surface and volume data. Howe...

A Hilbert space-filling curve is a curve traversing the 2(n) x 2(n)two-dimensional space and it visits neighboring points consecutively without crossing itself. The application of Hilbert space-filling curves in image processing is to rearrange image pixels in order to enhance pixel locality. A computer program of the Hilbert space-filling curve ordering generated from a tensor product formula ...

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We present a new approach for approximate nearest neighbor queries for sets of high dimensional points under any L t-metric, t = 1; : : : ; 1. The proposed algorithm is eecient and simple to implement. The algorithm uses multiple shifted copies of the data points and stores them in up to (d + 1) B-trees where d is the dimensionality of the data, sorted according to their position along a space ...