Related papers: p-Adic scaled space filling curve indices for high…
Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…
In order to be able to process the increasing amount of spatial data, efficient methods for their handling need to be developed. One major challenge for big spatial data is access. This can be achieved through space-filling curves, as they…
Modern computer systems are characterized by deep memory hierarchies, composed of main memory, multiple layers of cache, and other specialized types of memory. In parallel and distributed systems, additional memory layers are added to this…
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that…
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to…
Homogeneous Hilbert curves (HHC) in two dimensions are generalized by introducing the construction of the space filling curves from the same affine transformations but using an arbitrary kernel, we call such curves HHCK. The new curves are…
It is demonstrated how linear computational time and storage efficient approaches can be adopted when analyzing very large data sets. More importantly, interpretation is aided and furthermore, basic processing is easily supported. Such…
Landscape analysis aims to characterise optimisation problems based on their objective (or fitness) function landscape properties. The problem search space is typically sampled, and various landscape features are estimated based on the…
The paper presents a systematic strategy for implementing Hilbert's space filling curve for use in online exploration tasks and addresses its application in scenarios wherein the space to be searched obstacles (or holes) whose locations are…
The goal of load balancing (grid partitioning) is to minimize overall computations and communications, and to make sure that all processors have a similar workload. Geometric methods divide a grid by using a location of a cell while…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
Hilbert's two-dimensional space-filling curve is appreciated for its good locality-preserving properties and easy implementation for many applications. However, Hilbert did not describe how to generalize his construction to higher…
We describe an algorithm to compute the local component at p of the Coleman-Gross p-adic height pairing on divisors on hyperelliptic curves. As the height pairing is given in terms of a Coleman integral, we also provide new techniques to…
Different space-filling curves (SFCs) are briefly reviewed in this paper, and a new one is proposed. A century has passed between the inception of this kind of curves, since then they have been found useful in computer science, particularly…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single…
High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…
Exemplar-based inpainting is the process of reconstructing missing parts of an image by searching the remaining data for patches that fit seamlessly. The image is completed to a plausible-looking solution by repeatedly inserting the patch…