Exploiting the deep structure of constraint problems
Artificial Intelligence
Artificial Intelligence
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
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Improved Algorithms for Optimal Winner Determination in Combinatorial Auctions and Generalizations
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Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Formal Models of Heavy-Tailed Behavior in Combinatorial Search
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Metaheuristics can solve sudoku puzzles
Journal of Heuristics
Exploiting multivalued knowledge in variable selection heuristics for SAT solvers
Annals of Mathematics and Artificial Intelligence
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
MINION: A Fast, Scalable, Constraint Solver
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Modeling choices in quasigroup completion: SAT vs. CSP
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
The impact of balancing on problem hardness in a highly structured domain
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
Bidding languages and winner determination for mixed multi-unit combinatorial auctions
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Sparse constraint graphs and exceptionally hard problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Problem structure in the presence of perturbations
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Exploiting the deep structure of constraint satisfaction problems with quantum computers
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
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Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in Bailey et al. (Am. Math. Mon. 115:383---404, 2008; J. Agron. Crop Sci. 165:121---130, 1990), Morgan (Latin squares and related experimental designs. Wiley, New York, 2008) and Vaughan (Electron. J. Comb. 16, 2009). On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m驴n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables--variables with the same value in all the solutions of an instance--and hardness of GSP.