Fast Bound-Consistency for the Global Cardinality Constraint
Irit Katriel, Sven Thiel, Francesca Rossi · 2003
We show an algorithm for bound consistency of {\\em global cardinality constraints}, which runs in time $O(n+n')$ plus the time required to sort the assignment variables by range endpoints, where $n$ is the number of assignment variables and $n'$ is the number of values in the union of their ranges. We thus offer a fast alternative to R\\'egin's arc consistency algorithm~\\cite{Regin} which runs in time $O(n^{3/2}n')$ and space $O(n\\cdot n')$. Our algorithm also achieves bound consistency for the number of occurrences of each value, which has not been done before.