Reordering Variables using ‘Contribution Number’ Strategy to Neutralize Sudoku Sets

Saajid Abuluaih, Azlinah Hj. Mohamed, Annamalai Muthukkaruppan, Hiroyuki Iida

Abstract

Humans tend to form decisions intuitively, often based on experience, and without considering optimality; sometimes, search algorithms and their strategies apply the same approach. For example, the minimum remaining values (MRV) strategy selects Sudoku squares based on their remaining values; squares with less number of values are selected first, and the search algorithm continues solving squares until the Sudoku rule is violated. Then, the algorithm reverses the steps and attempts different values. The MRV strategy reduces the backtracking rate; however, when there are two or more blank squares with the same number of minimum values, such strategy selects any of these blank squares randomly. In addition, MRV continues to target squares with minimum values, ignoring that some of those squares could be considered ‘solved’ when they have no influence on other squares. Hence, we aim to introduce a new strategy called Contribution Number (CtN) with the ability to evaluate squares based on their influence on others candidates to reduce squares explorations and the backtracking rate. The results show that the CtN strategy behaves in a more disciplined manner and outperforms MRV in most cases.

References

  1. Aaronson, L. 2006. Sudoku Science. Spectrum, IEEE, 43(2), 16-17. doi:10.1111/birt.12116.
  2. Crook, J. F. 2007. A Pencil-and-Paper Algorithm for Solving Sudoku Puzzles, 56(4), 460-468.
  3. Edelkamp, S., & Schrodl, S. 2012. Heuristic Search: Theory and Applications, (pp. 574-631). Waltham: Elsevier Inc.
  4. Eppstein, D. 2012. Solving Single-digit Sudoku Subproblems. In Kranakis, E., Krizanc, D., & Luccio, F. Eds., Fun with Algorithms, 7288, 142-153. Springer Berlin Heidelberg..
  5. Ercsey-Ravasz, M., & Toroczkai, Z. 2012. The Chaos within Sudoku. Scientific Reports, 2, 725. doi:10.1038/srep00725.
  6. Jiang, B., Xue, Y., Li, Y., & Yan, G. 2009. Sudoku Puzzles Generating?: from Easy to Evil. Chinese Journal of Mathematics in Practice and Theory, 39, 1-7.
  7. Jilg, J., & Carter, J. 2009. Sudoku Evolution, April 1984, 173-185.
  8. Klingner, J., & Kanakia, A. 2013. Methods for Solving Sudoku Puzzles, 1-10.
  9. Kumar, V. 1992. Algorithms for Constraint Satisfaction Problems: A Survey. AI Magazine, 13(1), 32-44.
  10. Mcguire, G., Tugemann, B., & Civario, G. 2014. There is no 16-Clue Sudoku?: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration. Experimental Mathematics, 23(2), 190- 217.
  11. Moraglio, A., Togelius, J., & Lucas, S. 2006, Product Geometric Crossover for the Sudoku Puzzle. IEEE International Conference on Evolutionary Computation, 470-476. doi:10.1109/CEC.2006. 1688347.
  12. Norvig, P. 2010. Solving Every Sudoku Puzzle, Retrieved July 16, 2014, from http://www.norvig.com/ sudoku.html.
  13. Russell, S., & Norvig, P. 2010. Artificial Intelligence: A Modern Approach (Third Ed., pp. 206-202). Pearson.
Download


Paper Citation


in Harvard Style

Abuluaih S., Mohamed A., Muthukkaruppan A. and Iida H. (2015). Reordering Variables using ‘Contribution Number’ Strategy to Neutralize Sudoku Sets . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-074-1, pages 325-333. DOI: 10.5220/0005188803250333


in Bibtex Style

@conference{icaart15,
author={Saajid Abuluaih and Azlinah Hj. Mohamed and Annamalai Muthukkaruppan and Hiroyuki Iida},
title={Reordering Variables using ‘Contribution Number’ Strategy to Neutralize Sudoku Sets},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2015},
pages={325-333},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005188803250333},
isbn={978-989-758-074-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Reordering Variables using ‘Contribution Number’ Strategy to Neutralize Sudoku Sets
SN - 978-989-758-074-1
AU - Abuluaih S.
AU - Mohamed A.
AU - Muthukkaruppan A.
AU - Iida H.
PY - 2015
SP - 325
EP - 333
DO - 10.5220/0005188803250333