TY - GEN

T1 - A Knowledge-Rich Approach to the Rapid Enumeration of Quasi-Magic Sudoku Search Spaces

AU - Jones, Sian-Kathryn

AU - Roach, Paul

AU - Perkins, Stephanie

AU - Grimstead, Ian J.

PY - 2009/1/19

Y1 - 2009/1/19

N2 - The popular logic puzzle, Sudoku, consists of placing the digits 1,...,9 into a 9×9 grid, such that each digit appears only once in each row, column, and subdivided ‘mini-grid’ of size 3×3. 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.

AB - The popular logic puzzle, Sudoku, consists of placing the digits 1,...,9 into a 9×9 grid, such that each digit appears only once in each row, column, and subdivided ‘mini-grid’ of size 3×3. 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.

KW - search

KW - constraints

KW - quasi-magic sudoku

KW - coding theory

M3 - Conference contribution

SN - 978-3-642-11818-0

T3 - Communications in Computer and Information Science

BT - ICAART 2009 - Proceedings of the International Conference on Agents and Artificial Intelligence, Porto, Portugal, January 19 - 21, 2009

PB - Springer

T2 - Proceedings of ICAART 2009, the 1st International Conference on Agents and Artificial Intelligence

Y2 - 19 January 2009 through 19 January 2009

ER -