CONSTRUCTION AND ANALYSIS OF BALANCED INCOMPLETE SUDOKU SQUARE DESIGN
Abstract
Sudoku squares have been widely used to design an experiment where each treatment occurs exactly once in each row, column or sub-block. For some experiments, the size of row (or column or sub-block) may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Sudoku squares design (BISSD) is proposed. A general method for constructing BISSD is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Sudoku designs. The relative efficiencies of a delete-one-transversal balance incomplete Latin Square (BILS) design with respect to Sudoku design are derived. In addition, linear model, numerical examples and procedure for the analysis of data for BISSD are proposed
References
Bejar R., Fernandez C. Mateu C. Megda Valls M. (2012). The Sudoku Completion Problem With Rectangular Hole
Pattern Is NP-Complete. Discrete Mathematics 312, 3306-3315.
Bose R.C., Shrikhande, S.S., Parker, E.T., (1960). Further results on the construction of mutually orthogonal Latin
squares and the falsify of Euler’s conjecture. Canadian Journal of Mathematics 12, 189-203.
Colbourn C., The complexity of completing partial latin squares, Discrete Appl. Math. 8 (1984), 151–158.
Danbaba, A., Odeyale. A.B., Musa. Y., (2018). Joint Analysis of Several Experiments Conducted via Orthogonal
Sudoku Design of Odd Order, International Journal of Statistics and Applications, 8(6), 323-331
Das, A., Dey, A. (1990). A note on construction of Graeco Latin square of order 2n+1,Journal of India Soc Agric Statist 42, 247-249.D.,
Donovan, D., Haaland B. and Nott D.J (2015). A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs. arxiv.1502.05522v1
Hui-Dong M. and Ru-Gen, X. (2008). Sudoku Square- a New Design in field Experiment, Acta Agron Sin, 34(9), 1489–1493.
Kanaana, I. and Ravikumar B. (2010). Row-filled completion problem for Sudoku. Util. Math., 81, 65–84
Kumar, A., Varghese C. Varghese, E. and Jaggi S. (2015). On the construction of designs with three-way blocking. Model;Assisted Statistics and Applications 10, 43–52 43
Mahdian, M., E.S. Mahmoodian (2015) , Sudoku Rectangle Completion, Electronic Notes in Discrete Mathematics 49, 747–755
Mingyao, Ai., Kang, Li., Sanmao, Liu., Dennis, and KJ Lin., (2013). Balanced Incomplete Latin Square Designs. Journal of Statistical and Inference 143 (2013) 1575-1582.
Subramani, J. and K.N. Ponnuswamy (2009). Construction and Analysis of Sudoku designs. Model Assisted Statistics and Applications, 4(4), 287-301.
Subramani, J. (2013). Construction of Graeco Sudoku square Designs of Odd Orders, Bonfring International Journal of Data Mining, 2 (2), 37-41.
Wu C.F.J, and Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York.
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