A fast algorithm for generating set partitions
The Computer Journal
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Regular Article: Necklaces, MSS Sequences, and DNA Sequences
Advances in Applied Mathematics
A Filtering Algorithm for the Stretch Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
A fast algorithm to generate necklaces with fixed content
Theoretical Computer Science
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Solving necklace constraint problems
Journal of Algorithms
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Some constraint problems have a combinatorial structure where the constraints allow the sequence of variables to be rotated (necklaces), if not also the domain values to be permuted (unlabelled necklaces), without getting an essentially different solution. We bring together the fields of combinatorial enumeration, where efficient algorithms have been designed for (special cases of) some of these combinatorial objects, and constraint programming, where the requisite symmetry breaking has at best been done statically so far. We design the first search procedure and identify the first symmetry-breaking constraints for the general case of unlabelled necklaces. Further, we compare dynamic and static symmetry breaking on real-life scheduling problems featuring (unlabelled) necklaces.