Tensor product formulation for Hilbert space-filling curves

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings - 2003 International Conference on Parallel Processing, ICPP 2003
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages99-106
Number of pages8
Volume2003-January
ISBN (Electronic)0769520170
DOIs
Publication statusPublished - 2003
Event2003 International Conference on Parallel Processing, ICPP 2003 - Kaohsiung, Taiwan
Duration: Oct 6 2003Oct 9 2003

Conference

Conference2003 International Conference on Parallel Processing, ICPP 2003
CountryTaiwan
CityKaohsiung
Period10/6/0310/9/03

Fingerprint

Space-filling Curves
Hilbert spaces
Tensor Product
Tensors
Permutation
Hilbert space
Formulation
Product formula
Transposition
R-tree
Computer program listings
Image processing
Indexing
Hilbert
Image Processing

Keywords

  • Application software
  • Biomedical engineering
  • Biomedical imaging
  • Biomedical informatics
  • Computer science
  • Grid computing
  • Hilbert space
  • Image processing
  • Indexing
  • Tensile stress

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Hardware and Architecture

Cite this

Lin, S. Y., Chen, C. S., Liu, L., & Huang, C. H. (2003). Tensor product formulation for Hilbert space-filling curves. In Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003 (Vol. 2003-January, pp. 99-106). [1240570] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICPP.2003.1240570

Tensor product formulation for Hilbert space-filling curves. / Lin, Shen Yi; Chen, Chih Shen; Liu, Li; Huang, Chua Huang.

Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003. Vol. 2003-January Institute of Electrical and Electronics Engineers Inc., 2003. p. 99-106 1240570.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lin, SY, Chen, CS, Liu, L & Huang, CH 2003, Tensor product formulation for Hilbert space-filling curves. in Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003. vol. 2003-January, 1240570, Institute of Electrical and Electronics Engineers Inc., pp. 99-106, 2003 International Conference on Parallel Processing, ICPP 2003, Kaohsiung, Taiwan, 10/6/03. https://doi.org/10.1109/ICPP.2003.1240570
Lin SY, Chen CS, Liu L, Huang CH. Tensor product formulation for Hilbert space-filling curves. In Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003. Vol. 2003-January. Institute of Electrical and Electronics Engineers Inc. 2003. p. 99-106. 1240570 https://doi.org/10.1109/ICPP.2003.1240570
Lin, Shen Yi ; Chen, Chih Shen ; Liu, Li ; Huang, Chua Huang. / Tensor product formulation for Hilbert space-filling curves. Proceedings - 2003 International Conference on Parallel Processing, ICPP 2003. Vol. 2003-January Institute of Electrical and Electronics Engineers Inc., 2003. pp. 99-106
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