Solving Single-Digit Sudoku Subproblems

We show that single-digit "Nishio" subproblems in n×n Sudoku puzzles may be solved in time o(2n), faster than previous solutions such as the pattern overlay method. We also show that single-digit deduction in Sudoku is NP-hard.

[1]  H. Simonis,et al.  Sudoku as a Constraint Problem , 2005 .

[2]  David Eppstein,et al.  Searching for Spaceships , 2000, ArXiv.

[3]  T. Yato,et al.  Complexity and Completeness of Finding Another Solution and Its Application to Puzzles , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[4]  Richard Ostrowski,et al.  From XSAT to SAT by Exhibiting Equivalencies , 2008, 2008 20th IEEE International Conference on Tools with Artificial Intelligence.

[5]  M. Held,et al.  A dynamic programming approach to sequencing problems , 1962, ACM National Meeting.

[6]  Todd K. Moon,et al.  Sinkhorn Solves Sudoku , 2009, IEEE Transactions on Information Theory.

[7]  Eugene L. Lawler,et al.  A Note on the Complexity of the Chromatic Number Problem , 1976, Inf. Process. Lett..

[8]  G. Dahl Permutation matrices related to Sudoku , 2009 .

[9]  David Eppstein,et al.  Journal of Graph Algorithms and Applications Recognizing Partial Cubes in Quadratic Time 270 Eppstein Recognizing Partial Cubes in Quadratic Time , 2022 .

[10]  Zong Woo Geem,et al.  Harmony Search Algorithm for Solving Sudoku , 2007, KES.

[11]  Laura Taalman,et al.  Gröbner Basis Representations of Sudoku , 2010 .

[12]  Andreas Björklund,et al.  Exact Algorithms for Exact Satisfiability and Number of Perfect Matchings , 2006, ICALP.

[13]  Agnes M. Herzberg,et al.  Sudoku Squares and Chromatic Polynomials , 2007 .

[14]  Thorsten Koch Rapid Mathematical Programming or How to Solve Sudoku Puzzles in a Few Seconds , 2005, OR.

[15]  Julian Togelius,et al.  Geometric particle swarm optimization for the sudoku puzzle , 2007, GECCO '07.

[16]  Rhyd Lewis,et al.  Metaheuristics can solve sudoku puzzles , 2007, J. Heuristics.

[17]  Georgios C. Anagnostopoulos,et al.  Knowledge-Based Intelligent Information and Engineering Systems , 2003, Lecture Notes in Computer Science.

[18]  A. Bj EXACT COVERS VIA DETERMINANTS , 2010 .

[19]  Joël Ouaknine,et al.  Sudoku as a SAT Problem , 2006, ISAIM.

[20]  David Eppstein Nonrepetitive Paths and Cycles in Graphs with Application to Sudoku , 2005, ArXiv.

[21]  T. Moon,et al.  Multiple Constraint Satisfaction by Belief Propagation: An Example Using Sudoku , 2006, 2006 IEEE Mountain Workshop on Adaptive and Learning Systems.

[22]  Richard Bellman,et al.  Dynamic Programming Treatment of the Travelling Salesman Problem , 1962, JACM.

[23]  Jian Li,et al.  Linear Systems, Sparse Solutions, and Sudoku , 2010, IEEE Signal Processing Letters.

[24]  Andries E. Brouwer Sudoku puzzles and how to solve them , 2006 .

[25]  Andreas Björklund,et al.  Exact Covers via Determinants , 2010, STACS.

[26]  Andreas Björklund,et al.  Covering and packing in linear space , 2010, Inf. Process. Lett..

[27]  Timo Mantere,et al.  Solving, rating and generating Sudoku puzzles with GA , 2007, 2007 IEEE Congress on Evolutionary Computation.

[28]  Bolette Ammitzbøll Jurik,et al.  An algorithm for Exact Satisfiability analysed with the number of clauses as parameter , 2006, Inf. Process. Lett..