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Tensor product formulation for Hilbert space-filling curves

Shen-Yi Lin, Chih-Shen Chen, Li Liu, Chua-Huang Huang
2003 2003 International Conference on Parallel Processing, 2003. Proceedings.  
We view a Hilbert space-filling curve as a permutation which maps two-dimensional data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve.  ...  The tensor product formula of Hilbert space-filling curves uses several permutation operations: stride permutation, radix-2 Gray permutation, transposition, and anti-diagonal transposition.  ...  The program rearranges data elements of a two-dimensional matrix from the row (or column) major order to the Hilbert space-filling curve order.  ... 
doi:10.1109/icpp.2003.1240570 dblp:conf/icpp/LinCLH03 fatcat:nglpylaqcnaczkeezhjceuohba

A Matrix Iterative Approach to Systematically Generate Hilbert-type Space-filling Curves

Ruisong Ye, Li Liu
In this paper, we construct the complete six Hilbert-type space-filling curves form amatrix point of view.  ...  The merit of the matrix approach is that the iterative algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.  ...  ACKNOWLEDGMENTS This research is supported by National Natural Science Foundation of China (No. 11271238).  ... 
doi:10.24297/ijct.v14i12.1741 fatcat:646vyrsah5fb5anavkhtnptdam

A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves

Chih-Sheng CHEN, Shen-Yi LIN, Min-Hsuan FAN, Chua-Huang HUANG
2010 IEICE transactions on information and systems  
The process of program generation is explained in the paper. key words: block recursive algorithm, tensor product, n-dimensional Hilbert space-filling curve, Gray permutation 2.  ...  major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve.  ...  In this paper, we present program generation of the iterative formula for the Hilbert space-filling curve.  ... 
doi:10.1587/transinf.e93.d.1807 fatcat:2jw2eunnynfmlml4mhyileumty

Convergence with Hilbert's space filling curve

Arthur R. Butz
1969 Journal of computer and system sciences (Print)  
The following topics are discussed: convergence to solutions of systems of equalities or inequalities, convergence to minima, the advantages of the present space filling curve over other known space filling  ...  The space filling curve is shown to provide a tool for doing this.  ...  INTRODUCTION The notion of using "space filling curves" to solve certain problems in mathematical programming was previously diseussed [1] .  ... 
doi:10.1016/s0022-0000(69)80010-3 fatcat:pyfd47htirei3ds7rvhchlm6ba

On the Parallelization of a Cache-Optimal Iterative Solver for PDEs Based on Hierarchical Data Structures and Space-Filling Curves [chapter]

Frank Günther, Andreas Krahnke, Markus Langlotz, Miriam Mehl, Markus Pögl, Christoph Zenger
2004 Lecture Notes in Computer Science  
and cheaply by cutting the queue of data linearized along the space-filling curve into equal pieces.  ...  The key to this success was to integrate space-filling curves consequently not only in the programs flow control but also in the construction of data structures which are processed linearly even for hierarchical  ...  The basic idea is to deeply integrate the concept of space-filling curves [10] in the flow control of a recursive cell-oriented iterative program for solving PDEs.  ... 
doi:10.1007/978-3-540-30218-6_58 fatcat:mq5ycibh5bcenfzcka7alte2qu

Page 79 of American Society of Civil Engineers. Collected Journals Vol. 7, Issue 2 [page]

2003 American Society of Civil Engineers. Collected Journals  
The space-filling curve is used in order to provide one-to-one mapping of two-dimensional space on a unit interval (from 0 to |) and preserve the “nearness” of points with in the space.  ...  as well as the capacity of the vehicles that collect; and (2) set up a sequence of institutions by using a space-filling curve (SFC) (Bartholdi and Platzman 1982).  ... 

Methods for optimizing routes in digital logistics

Lubov Ivanova, Andrey Kurkin, Sergei Ivanov, V. Kankhva
2021 E3S Web of Conferences  
"remove crossings", "space filling curve", "simulated annealing", "two-opt".  ...  Application of the "integer-linear-programming" method in logistics is the most accurate at the optimal time for calculating efficient routes of freight traffic.  ...  A space-filling curve is constructed as the limit of a sequence of piecewise-linear continuous curves.  ... 
doi:10.1051/e3sconf/202125802015 fatcat:apivuxvzjbbitc6dbfjzyeygcm

FDL: Mission Support Challenge [article]

Luís F. Simões, Ben Day, Vinutha M. Shreenath, Callum Wilson, Chris Bridges, Sylvester Kaczmarek, Yarin Gal
2019 arXiv   pre-print
The Frontier Development Lab (FDL) is a National Aeronautics and Space Administration (NASA) machine learning program with the stated aim of conducting artificial intelligence research for space exploration  ...  and all humankind with support in the European program from the European Space Agency (ESA).  ...  We would also like to thank the sponsors of the FDL program, in particular the Google Cloud Platform.  ... 
arXiv:1912.09279v1 fatcat:r3aqg2scwnckvnusqp66kxczlu

A Multi-Dimensional Data Storage Using Quad-Tree and Z-Ordering

Fang Hou, Cheng Hui Huang, Ji Yuan Lu
2013 Applied Mechanics and Materials  
Multi-dimensional applications use tree structure to store data and space filling curves to traverse data. Most frequently used Quad-tree and Z-ordering curve are analyzed.  ...  Figure 2 An example of Quad-tree B. Z-ordering Space filling curves To map multi-dimensional data objects to 1-D objects, several space filling curves have been designed.  ...  For example, a 3-D data set is created by sampling program or simulation program, and then was compressed by an In-Situ process.  ... 
doi:10.4028/ fatcat:kwtbnzmz2zgf3mkqqxsoodzub4

Space filling curves and mathematical programming

Arthur R. Butz
1968 Information and Control  
E~ X The problem of finding 2 in n dimensional Euclidean space such that f~(2) -< 0, i = 1, 2, -.. , N, is considered.  ...  It is anticipated that the future use of space filling curves based on binary representations (i.e., generalizations of Hi]bert's curve) will reduce the number of iterations required in these examples,  ...  The implicitly exhaustive feature is made possible by adapting "space filling curves" to discrete spaces of general dimensionality.  ... 
doi:10.1016/s0019-9958(68)90367-7 fatcat:2andvz37fres7knfjh552bsdlu

Hilbert space filling curve using scilab

Sushma T.V, Roopa M
2018 International Journal of Engineering & Technology  
Space filling curve is used widely for linear mapping of multi-dimensional space.  ...  The paper highlights the locality preserving property of Hilbert Space filling curve which is essential in numerous applications such asin image compression, numerical analysis of a large aray of data,  ...  Fig. 1 : 1 First Three Stages in the Generation of Hilbert's Space Filling Curve.  ... 
doi:10.14419/ijet.v7i1.9.9748 fatcat:ztif4bomx5ftrpjvm2iunez2ru

A New Mathematical Approach for Pattern Generation

Navdeep Kumar, Pankaj Garg
2011 International Journal of Computer Applications  
Accordingly, to the requirement of customer , the whole system regenerate the designs using the power of macro programming.  ...  This whole system will use the power of Web technology and macro programming to generalize the designs.  ...  The Peano Fractal Curve The Peano Curve (also known as the Hilbert plane-filling curve) is a subset of the family known as space-filling curves. These curves just so happen to also be fractals.  ... 
doi:10.5120/2920-3853 fatcat:zqnh7vkuxfhafhgtsq6cw3nmy4

DXSoil, a library for 3D image analysis in soil science

Jean-François Delerue, Edith Perrier
2002 Computers & Geosciences  
Beyond the application example, the successive algorithms presented in the paper allow, from any 3D object image, the extraction of the object skeleton, the measurement of the distribution of local apertures  ...  and the partition of the object into a set of interconnected subobjects according to different size classes.  ...  Acknowledgements This work was partly supported by a grant from the French Programme National Sol et Erosion program. We warmly thank Anthony Timmerman who let us use his sets of tomographic data.  ... 
doi:10.1016/s0098-3004(02)00020-1 fatcat:4z3rvbjxefd3bhpe2q6vtrclym

An Iterated Function System based Method to Generate Hilbert-type Space-filling Curves

Ruisong Ye, Li Liu
2015 International Journal of Information Technology and Computer Science  
space-filling curves at any resolution n.  ...  In this paper, we will explore the generation of Hilbert-type space-filling curves via iterated function system based approach systematically.  ...  This research is partly supported by National Natural Science Foundation of China (No. 11271238).  ... 
doi:10.5815/ijitcs.2015.12.02 fatcat:tpxq76eihzf6pkmw7kdiznu5f4

Exhaustive geographic search with mobile robots along space-filling curves [chapter]

Shannon V. Spires, Steven Y. Goldsmith
1998 Lecture Notes in Computer Science  
Many of the "obvious" approaches are inefficient or lack robustness. One efficient approach is to have the robots traverse a space-filling curve.  ...  This report presents some preliminary results from applying the Hilbert space-filling curve to geographic search by mobile robots.  ...  Conclusions We have begun to explore how space-filling curves can enhance the efficiency and robustness of geographic search by robot collectives.  ... 
doi:10.1007/bfb0033369 fatcat:ffabi73zlredvc4tx44im4uosi
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