We introduce a new clustering method for DNA microarray data that is based on space filling curves and wavelet denoising. The proposed method is much faster than the established fuzzy c-means clustering because clustering occurs in one dimension and it clusters cells that contain data, instead of data themselves. Moreover, preliminary evaluation results on data sets from Small Round Blue-Cell t...

For the incremental construction of a Delaunay triangulation, we prove that inserting points in rounds and walking along a space-filling curve in each round yields an algorithm running in linear expected time for uniformly distributed points. We complement this result by a simpler incremental construction running in linear expected time in any dimension.

Conventional encryption techniques are usually applicable for text data and often unsuited for encrypting multimedia objects for two reasons. Firstly, the huge sizes associated with multimedia objects make conventional encryption computationally costly. Secondly, multimedia objects come with massive redundancies which are useful in avoiding encryption of the objects in their entirety. Hence a c...

Space-filling curves (SFCs) provide a continuous mapping from a one-dimensional to a d-dimensional space and have been used to linearize spatially distributed data for partitioning, memory management and image processing. This paper gives a short introduction to the concept of SFCs and highlights some of the applications found in computer science. The main focus will be on dynamic distribution ...

Nearest neighbor-finding is one of the most important spatial operations in the field of spatial data structures concerned with proximity. Because the goal of the space-filling curves is to preserve the spatial proximity, the nearest neighbor queries can be handled by these space-filling curves. When data is ordered by the Peano curve, we can directly compute the sequence numbers of the neighbo...

This paper introduces a new way of generalizing Hilbert’s two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d′ < d, the d-dimensional curve is compatible with the d′-dimensional curve with respect to the order in which the curves visit the points of any d′-dimensional axis-parallel space that cont...

Linear orderings defined through space-filling curves are often applied to quickly partition graphs arising in finite element simulations. In applications with constant meshes but a rapidly changing load per element, an ordering has to be determined only once and all subsequent partitionings can be computed very quickly through a simple interval splitting. However, partitionings based on space-...

We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers—heuristic algorithms that find models CNF boolean formulas. Our was implemented and applied to the surjective $$\gamma :[0,1]\rightarrow [0,1]^d$$ with minimal dilation $$\begin{aligned} \sup _{t_1<t_2}\frac{\Vert \gamma (t_2)-\gamma (t_1)\Vert ^d}{t_2-t_1}. \end{aligned}$$ repo...