An Optimal Arc Consistency Algorithm for a Chain of Atmost Constraints with Cardinality

The AtMostSeqCard constraint is the conjunction of a cardinality constraint on a sequence of n variables and of n−q+1 constraints AtMostu 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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