Tensor product formulation for Hilbert space-filling curves

Shen Yi Lin; Chih Shen Chen; Li Liu; Chua Huang Huang

doi:10.1109/ICPP.2003.1240570

Tensor product formulation for Hilbert space-filling curves

Shen Yi Lin, Chih Shen Chen, Li Liu, Chua Huang Huang

醫學資訊研究所

研究成果: 書貢獻/報告類型 › 會議貢獻

15 引文斯高帕斯（Scopus）

摘要

We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2n×2n 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 antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc.

原文	英語
主出版物標題	Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003
發行者	Institute of Electrical and Electronics Engineers Inc.
頁面	99-106
頁數	8
卷	2003-January
ISBN（電子）	0769520170
DOIs	https://doi.org/10.1109/ICPP.2003.1240570
出版狀態	已發佈 - 2003
事件	2003 International Conference on Parallel Processing, ICPP 2003 - Kaohsiung, 臺灣持續時間: 10月 6 2003 → 10月 9 2003

會議

會議	2003 International Conference on Parallel Processing, ICPP 2003
國家/地區	臺灣
城市	Kaohsiung
期間	10/6/03 → 10/9/03

ASJC Scopus subject areas

軟體
數學(全部)
硬體和架構

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10.1109/ICPP.2003.1240570

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Lin, SY, Chen, CS, Liu, L & Huang, CH 2003, Tensor product formulation for Hilbert space-filling curves. 於 Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003. 卷 2003-January, 1240570, Institute of Electrical and Electronics Engineers Inc., 頁 99-106, 2003 International Conference on Parallel Processing, ICPP 2003, Kaohsiung, 臺灣, 10/6/03. https://doi.org/10.1109/ICPP.2003.1240570

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abstract = "We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2n×2n 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 antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc.",

keywords = "Application software, Biomedical engineering, Biomedical imaging, Biomedical informatics, Computer science, Grid computing, Hilbert space, Image processing, Indexing, Tensile stress",

author = "Lin, {Shen Yi} and Chen, {Chih Shen} and Li Liu and Huang, {Chua Huang}",

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pages = "99--106",

booktitle = "Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003",

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note = "2003 International Conference on Parallel Processing, ICPP 2003 ; Conference date: 06-10-2003 Through 09-10-2003",

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AU - Lin, Shen Yi

AU - Chen, Chih Shen

AU - Liu, Li

AU - Huang, Chua Huang

PY - 2003

Y1 - 2003

N2 - We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2n×2n 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 antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc.

AB - We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed. We view a Hilbert space-filling curve as a permutation which maps two-dimensional 2n×2n 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 antidiagonal transposition. The iterative tensor product formula can be manipulated to obtain the inverse Hilbert permutation. Also, the formulas are directly translated into computer programs which can be used in various applications including R-tree indexing, image processing, and process allocation, etc.

KW - Application software

KW - Biomedical engineering

KW - Biomedical imaging

KW - Biomedical informatics

KW - Computer science

KW - Grid computing

KW - Hilbert space

KW - Image processing

KW - Indexing

KW - Tensile stress

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BT - Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2003 International Conference on Parallel Processing, ICPP 2003

Y2 - 6 October 2003 through 9 October 2003

ER -

Tensor product formulation for Hilbert space-filling curves

摘要

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ASJC Scopus subject areas

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