A KNOWLEDGE-RICH APPROACH TO THE RAPID ENUMERATION OF QUASI-MAGIC SUDOKU SEARCH SPACES

P. A. Roach, S. K. Jones, S. Perkins, I. J. Grimstead

Abstract

The popular logic puzzle, Sudoku, consists of placing the digits 1, …, 9 into a 9 x 9 grid, such that each digit appears only once in each row, column, and subdivided ‘mini-grid’ of size 3 x 3. Uniqueness of solution of a puzzle is ensured by the positioning of a number of given values. Quasi-Magic Sudoku adds the further constraint that within each mini-grid, every row, column and diagonal must sum to 15±∆, where ∆ is chosen to take a value between 2 and 8. Recently Sudoku has been shown to have potential for the generation of erasure correction codes. The additional quasi-magic constraint results in far fewer given values being required to ensure uniqueness of solution, raising the prospect of improved usefulness in code generation. Recent work has highlighted useful domain knowledge concerning cell interrelationships in Quasi-Magic Sudoku for the case ∆ = 2, providing pruning conditions to reduce the size of search space that need be examined to ensure uniqueness of solution. This paper examines the usefulness of the identified rich knowledge in restricting search space size. The knowledge is implemented as pruning conditions in a backtracking implementation of a Quasi-Magic Sudoku solver, with a further cell ordering heuristic. Analysis of the improvement in processing time, and thereby of the potential usefulness of Quasi-Magic Sudoku for code generation, is provided.

References

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Paper Citation


in Harvard Style

Roach P., Jones S., Perkins S. and Grimstead I. (2009). A KNOWLEDGE-RICH APPROACH TO THE RAPID ENUMERATION OF QUASI-MAGIC SUDOKU SEARCH SPACES . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8111-66-1, pages 246-254. DOI: 10.5220/0001659502460254


in Bibtex Style

@conference{icaart09,
author={P. A. Roach and S. K. Jones and S. Perkins and I. J. Grimstead},
title={A KNOWLEDGE-RICH APPROACH TO THE RAPID ENUMERATION OF QUASI-MAGIC SUDOKU SEARCH SPACES},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2009},
pages={246-254},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001659502460254},
isbn={978-989-8111-66-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - A KNOWLEDGE-RICH APPROACH TO THE RAPID ENUMERATION OF QUASI-MAGIC SUDOKU SEARCH SPACES
SN - 978-989-8111-66-1
AU - Roach P.
AU - Jones S.
AU - Perkins S.
AU - Grimstead I.
PY - 2009
SP - 246
EP - 254
DO - 10.5220/0001659502460254