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Journal of Information Science and Engineering, Vol. 24 No. 1, pp. 261-275 (January 2008)

Tensor Product Formulation for Hilbert Space-Filling Curves*

Shen-Yi Lin, Chih-Shen Chen, Li Liu+ and Chua-Huang Huang
Department of Information Engineering and Computer Science
Feng Chia University
Taichung, 407 Taiwan
+Graduate Institute of Medical Informatics
Taipei Medical University
Taipei, 110 Taiwan

We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed in the paper. 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 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 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 image processing, VLSI component layout, and R-tree indexing, etc.

Keywords: tensor product, block recursive algorithm, Hilbert space-filling curve, stride permutation, gray permutation, transposition, anti-diagonal transposition, data allocation

Full Text () Retrieve PDF document (200801_17.pdf)

Received October 27, 2005; revised April 25, June 21 & August 28, 2006; accepted September 7, 2006.
Communicated by Chin-Teng Lin.