Abstract
The AtMostSeqCard constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n − q + 1 constraints AtMost u on each subsequence of size q.
This constraint is useful in car-sequencing and crew-rostering problems. In [18], two algorithms designed for the AmongSeq constraint were adapted to this constraint with a O(2qn) and O(n3) worst case time complexity, respectively. In [10], another algorithm similarly adaptable to filter the AtMostSeqCard constraint with a time complexity of O(n2) was proposed.
In this paper, we introduce an algorithm for achieving Arc Consistency on the AtMostSeqCard constraint with a O(n) (hence optimal) worst case time complexity. We then empirically study the efficiency of our propagator on instances of the car-sequencing and crew-rostering problems.
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Siala, M., Hebrard, E., Huguet, MJ. (2012). An Optimal Arc Consistency Algorithm for a Chain of Atmost Constraints with Cardinality. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_7
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