On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Modeling the Regular Constraint with Integer Programming
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Sequencing and Counting with the multicost-regular Constraint
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
SLIDE: A Useful Special Case of the CARDPATH Constraint
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Encodings of the SEQUENCE constraint
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Solving nurse rostering problems using soft global constraints
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Solution neighbourhoods for constraint-directed local search
Proceedings of the 27th Annual ACM Symposium on Applied Computing
The regulargcc matrix constraint
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
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Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables $\mathcal{M}$, with the same constraint defined by a finite-state automaton $\mathcal{A}$ on each row of $\mathcal{M}$ and a global cardinality constraint ${\mathit{gcc}}$ on each column of $\mathcal{M}$. We give two methods for deriving, by double counting, necessary conditions on the cardinality variables of the ${\mathit{gcc}}$ constraints from the automaton $\mathcal{A}$. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances.