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Sudoku-based space-filling designs

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  • Xu Xu
  • BEN Haaland
  • Peter Z. G. Qian

Abstract

Sudoku is played by millions of people across the globe. It has simple rules and is very addictive. The game board is a nine-by-nine grid of numbers from one to nine. Several entries within the grid are provided and the remaining entries must be filled in subject to no row, column, or three-by-three subsquare containing duplicate numbers. By exploiting these three types of uniformity, we propose an approach to constructing a new type of design, called a Sudoku-based space-filling design. Such a design can be divided into groups of subdesigns so that the complete design and each subdesign achieve maximum uniformity in univariate and bivariate margins. Examples are given illustrating the proposed construction method. Applications of such designs include computer experiments with qualitative and quantitative factors, linking parameters in engineering and crossvalidation. Copyright 2011, Oxford University Press.

Suggested Citation

  • Xu Xu & BEN Haaland & Peter Z. G. Qian, 2011. "Sudoku-based space-filling designs," Biometrika, Biometrika Trust, vol. 98(3), pages 711-720.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:3:p:711-720
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    File URL: http://hdl.handle.net/10.1093/biomet/asr024
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    Cited by:

    1. Diane Donovan & Benjamin Haaland & David J. Nott, 2017. "A simple approach to constructing quasi-Sudoku-based sliced space-filling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 865-878, August.
    2. Xu Xu & Peter Z. G. Qian & Qing Liu, 2016. "Samurai Sudoku-Based Space-Filling Designs for Data Pooling," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 1-8, February.
    3. Li, Hongyi & Chatterjee, Kashinath & Li, Bo & Qin, Hong, 2016. "Construction of Sudoku-based uniform designs with mixed levels," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 111-118.

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